Ultrafast Nonlinear Optical Studies of Multilayered Thin Films and Interfaces

Transcription

1 Ultrafast Nonlinear Optical Studies of Multilayered Thin Films and Interfaces Submitted by Leigh Shelford, to the University of Exeter as a thesis for the degree of Doctor of Philosophy in Physics, August This thesis is available for Library use on the understanding that it is copyright material and that no quotation from the thesis may be published without proper acknowledgment. I certify that all material in this thesis which is not my own work has been identified and that no material has previously been submitted and approved for the award of a degree by this or any other University....

2 1 Abstract In this thesis investigations of the static and dynamic properties of magnetic thin films by several optical and magneto-optical techniques are presented. The magentooptical Kerr effect (MOKE) and magnetic second harmonic generation (MSHG) are very effective techniques for detecting magnetisation via the polarisation and intensity of light reflected from a sample, with the latter sensitive to thin film surfaces with atomic scale resolution. Magnetisation dynamics have been investigated by all-optical pump-probe experiments where dynamics were induced by an intense optical pump pulse and detected by a weaker probe pulse with time resolution determined by the laser pulsewidth of up to 50 fs. Element-specific near-interfacial magnetisation has been studied by x-ray magnetic circular dicrhoism (XMCD) at the Advanced Light Source synchrotron in Berkeley, California. These techniques have been applied to the study of uniform precession in the film bulk and interfacial magnetisation in the full-heulser alloy films Co 2 MnX, where X = Al or Si. These materials have been predicted to have 100 % spin polarisation of the conduction electrons, and so could prove to be ideal materials for spintronics applications where strongly polarised spin currents are required. Related to such applications is the damping of dynamics magnetisation which is not well understood. From time-resolved MOKE measurements anisotropy and field strength dependence of the damping of uniform precession have been observed. Studies of the interfacial magnetisation by MSHG are highly relevant in multilayered magnetic strucutures, particularly magnetic tunnel junctions, where interfacial magnetisation is a major factor in device performance. A correlation has been observed between the MSHG response and tunneling magnetoresistance for Co 2 MnSi films with varied fabrication conditions. Interfacial magnetisation has also been studied by XMCD with relavtive magnetic moments investigated as a function of temperature and sample preparation conditions. Static and time-resolved MOKE measurements have also been applied to CoNi/Pt multilayered films which possess perpendicular magnetic anisotropy and therefore are a candidate for high density magnetic data recording media. Ultrafast full demagnetisation of continuous and patterned films has been observed, and strong oscillations in the time-resolved reflectivity from the patterned film are discussed. Finally a study is presented of the multilayer DyFe 2 /YFe 2, which combines the hard and soft magnetic properties of the constituent layers and demonstrates strong exchange-spring behaviour. The magnetisation reversal mechanism has been measured by MOKE and precessional magnetisation dynamics are shown to be induced by

3 2 the torque exerted by the exchange spring in time-resolved MOKE. Some potential future developents and investigations are discussed.

4 Acknowledgments The work presented in this thesis and the completion of several years work would not have been possible without the contributions of many people. Firstly thanks must go to my supervisor Prof. Rob Hicken for giving me the opportunity to study for a PhD and to thoroughly enjoy the past few years. I have been lucky to gain a lot of varied experience and now look forward to a career in research, and this would not have been possible without his support and motivation. Special thanks must also be paid to my colleagues in the magnetic materials group for their priceless experience and advice. Dr Yanwei Liu has been very patient and more than helpful in answering all of my questions and has been an excellent companion during our shared time in the lab. Dr Volodymyr Kruglyak s knowledge and enthusiasm for the subject has been a great inspiration, and thanks to Dr Paul Keatley for his general PhD advice and understanding ear when the going was slow! Also Evgeny Sirotkin, Dr Andreas Neudert and Dr Feodor Ogrin have all directly helped with sample fabrication and group meeting discussions, and all group members for making this such an enjoyable place to work. Russell Edge and all of the workshop staff have provided excellent developments of laboratory and experimental equipment. Dr Tim Harries has, as an undergraduate tutor and postgraduate mentor, offered fantastic support throughout my time at Exeter. I have made many friends in the department who have have provided welcome distraction with tea and beer. In no particular order, Steve, John, Luke, Matt, James, Andreas, Natalie, Paul, Martin, thank you all (apologies for any omissions). And thanks to my family have provided encouragement and indispensable advice. Lastly thanks to Liana, especially for putting up with me over the last few months! She has supported me without fail and always been there when I have needed her.

5 Contents 1 Introduction 17 2 Background Introduction Semi-Classical Descriptions of Magnetism Classical theory of paramagnetism Weiss model of ferromagnetism Quantum Mechanics and Magnetism Magnetic resonance Permanent magnetic moments Quantum theory of paramagnetism Ferromagnetism Spin-orbit coupling Quenching of the orbital moment and the g factor Ferromagnetic Free Energy Contributions Magnetic anisotropy Thin films Ferromagnetism in Metals Spin-polarisation and spin-dependent conductivity Magnetisation Dynamics Ferromagnetic resonance Ultrafast demagnetisation Applications of Magnetic Materials Spin-valves and magnetic tunnel junctions Experimental techniques Introduction

6 CONTENTS Linear Optics Magneto-optical Effects Phenomenological description of the Faraday effect and MOKE Jones matrix and reflectivity calculations Classical microscopic model of magneto-optical effects Quantum-mechanical model Higher-order magneto-optical effects Measuring the magneto-optical Kerr effect Time-resolved magneto-optical Kerr effect measurements Measuring laser spot sizes Magnetic second harmonic generation Second harmonic generation Anharmonic oscillator model of SHG Symmetry arguments and the nonlinear susceptibility tensor Magnetic second harmonic generation Measuring magnetic second harmonic generation X-ray Magnetic Circular Dichroism X-ray absorption spectroscopy Magnetic sensitivity in XAS Analysis of XAS and XMCD spectra Optically induced ferromagnetic resonance Introduction Experimental details Theory Macrospin LLG solution Inhomogeneous broadening model of damping variation Co 2 MnAl Introduction and sample details Experimental results Discussion Co 2 MnSi Introduction and sample details Experimental results

7 CONTENTS Discussion Summary Interfacial studies of Heusler alloys Introduction Magnetic Second Harmonic Generation Experimental details Annealing temperature dependence Temperature dependence of MSHG X-ray magnetic circular dichroism Experimental details Results Discussion Summary CoNi/Pt multilayer films Introduction Experimental Details Experimental Results Static MOKE hysteresis loops Ultrafast demagnetisation Reflectivity oscillations from patterned CoNi/Pt film Discussion Summary Magnetic exchange springs Introduction Sample and Experimental Details Experimental Results Exchange-spring multilayer Reference DyFe 2 and YFe 2 films Discussion Summary and future work Summary Future work

8 CONTENTS Anisotropy of the g factor Heusler alloy films measured by XMCD Time-resolved magnetic second harmonic generation Time-resolved magneto-optical studies of patterned CoNi/Pt films Magnetic exchange springs

9 List of Figures 2.1 Precession of a magnetic moment in a magnetic field Example of magnetisation domains in a ferromagnet Temperature dependence of the K 1 anisotropy constant for ferromagnetic Fe, Ni and Co Spin split 3d energy bands in a ferromagnetic metal Damped precessional magnetisation motion as described by the Landau- Lifshitz-Gilbert equation Schematic diagram of a spin valve or magnetic tunnel junction Two-channel conductivity model for a spin-valve Simple cubic lattice with magnetisation parallel to the [001] axis, with (100) and (010) mirror planes indicated Simple experimental geometry for a MOKE measurement The MOKE geometries, defined by the relative alignment of the detected magnetisation and the plane of incidence Design of an optical bridge detector Example MOKE hysteresis loops from a Co 2 MnAl thin film Typical setup of a TRMOKE experiment, showing orientation of pump and probe beams Example of a time-resolved measurement of ultrafast demagnetisation Polar MOKE and AC-MOKE hysteresis loops measured with and without pump laser excitation, showing demagnetisation Typical TRMOKE data showing ferromagnetic resonance Scanning pinhole beam profiles of a typical 800 nm wavelength pump spot Scanning pinhole beam profiles of a typical 400 nm wavelength probe spot CCD beam profiler images of adjacent focused pump and probe spots

10 LIST OF FIGURES Focused laser spot movement over time, measured by a CCD beam profiler Cubic (001) surface with magnetisation parallel to the [100[ axis, with (100) and (010) mirror planes indicated MSHG experimental setup MSHG experimental setup with optical cryostat Example XAS and XMCD spectra of Co at the L 3 and L 2 absorption edges Decay mechanisms following resonant absorption of an x-ray photon XAS within a spin-split valence band, the origin of XMCD Experimental TRMOKE setup used for measurements of Co 2 MnSi Heusler alloy films Static MOKE loops of Heusler alloy Co 2 MnAl Typical TRMOKE signal from the Co 2 MnAl thin film Variation of magnetisation dynamics with external field orientation for Co 2 MnAl Variation of magnetisation dynamics with external field strength for Co 2 MnAl Mechanism of induced precession by ultrafast modification of magnetocrystalline anisotropy Longitudinal MOKE hysteresis loops of Co 2 MnSi films, made with an intensitystabilised He-Ne laser TRMOKE ultrafast demagnetisation of Co 2 MnSi films annealed at 300, 400 and 450 C TRMOKE of a Co 2 MnSi thin film annealed at 300 C for varied static field orientation TRMOKE of a Co 2 MnSi thin film annealed at 300 C for varied static field strength Pump-pulse energy variation of the TRMOKE signal of a Co 2 MnSi film annealed at 300 C TRMOKE scans of a Co 2 MnSi film annealed at 400 C TRMOKE scans of a Co 2 MnSi film annealed at 450 C Variation of dynamic magnetic response of Co 2 MnSi films with annealing temperature Comparison of MOKE and MSHG hysteresis loops

11 LIST OF FIGURES MSHG intensity, asymmetry and anisotropy as a function of annealing temperature Polar plot of MSHG asymmetry for samples A 300, A 450, B 50, and B Temperature dependence of the MSHG asymmetry Temperature dependence of the MSHG anisotropy Schematic of sample orientation in total electron yield XMCD measurement Variation of Co L 2,3 XAS of Co 2 MnSi films with annealing temperature XAS and XMCD measured at the Mn L 2,3 edges with varied annealing temperature of Co 2 MnSi films XMCD spectra and derivatives for Co 2 MnSi and Co reference film XAS measured at Mn and Co L 2,3 edges with varied Al capping layer thickness Relative total moments of Co and Mn in Co 2 MnSi as a function of temperature Scanning electron microscope images of patterned CoNi/Pt film MOKE and TRMOKE setups with polar magnet Polar MOKE loops of continuous CoNi/Pt films with varied CoNi layer thickness, measured by intensity stabilised CW He-Ne laser Polar MOKE of patterned CoNi/Pt multilayer film measured by intensity stabilised CW He-Ne laser TRMOKE and TR-reflectivity with varied pump fluence from a continuous film CoNi(4.5 Å)/Pt multilayer Peak Kerr rotation and peak reflectivity as a function of pump fluence from time-resolved measurements of continuous film CoNi/Pt TRMOKE and TR-reflectivity from patterned CoNi/Pt multilayer with varied pump fluence Peak Kerr rotation and peak reflectivity as a function of pump fluence from time-resolved measurements of patterned CoNi/Pt M/M S at varied time delay measured by TRMOKE and time-delayed MOKE loops for continuous film CoNi/Pt MOKE hysteresis loops measured with the 400 nm wavelength probe beam for continuous film CoNi/Pt, with varied pump pulse fluence at peak signal time delay

12 LIST OF FIGURES AC-MOKE hysteresis loops from continuous film CoNi/Pt with varied pump pulse fluence AC-MOKE hysteresis loops from patterned CoNi/Pt film with varied pump pulse fluence Strong oscillations in the TR-reflectivity from the patterned CoNi/Pt film with varied pump fluence, shown with Fourier transforms Strong oscillations in the TR-reflectivity from the patterned CoNi/Pt film with varied field strength Average TRMOKE and average TR-reflectivity scans with rotated polarisation axis of the linearly polarised pump at short time delay Average TRMOKE and average TR-reflectivity for scans at opposite field with rotated polarisation axis of the linearly polarised pump for the patterned CoNi/Pt film, with corresponding Fourier transforms TRMOKE and TR-reflectivity scans at zero field with rotated polarisation axis of the linearly polarised pump for the patterned CoNi/Pt film, with corresponding Fourier transforms Crystallographic axes orientations of DyFe 2 /YFe 2 exchange spring multilayer and reference films Schematic of the magnetisation in a giant ferrimagnetic exchange spring MOKE hysteresis loops measured with a He-Ne CW laser for DyFe 2 /YFe 2 multilayer exchange spring MOKE hysteresis loop for field parallel to [110] axis of DyFe 2 layers, with reversal mechanism shown MOKE hysteresis loop from DyFe 2 /YFe 2 multilayer exchange spring measured with a 400 nm wavelength pulsed laser Static and AC-MOKE loops measured with 800 nm wavelength pulsed laser, with and without pump beam, showing demagnetisation TRMOKE of DyFe 2 /YFe 2 with varied field strength Frequency from TRMOKE measurements as a function of field strength TRMOKE of DyFe 2 /YFe 2 with varied pump pulse energy Peak amplitude and frequency from TRMOKE measurements as a function of pump pulse energy

13 LIST OF FIGURES TRMOKE scan of exchange spring, with external field applied parallel to the DyFe 2 [001] hard axis with a pump pulse energy of 0.1 µj nm wavelength MOKE hysteresis loops of 2000 Å thick DyFe 2 reference film nm wavelength MOKE hysteresis loops of 1000 Å thick YFe 2 reference film TRMOKE scans of DyFe 2 and YFe 2 reference films

14 List of Tables 3.1 Nonzero elements of the dipolar MSHG susceptibility tensor for a cubic (001) surface The measured and fitted magnetic parameters from static and time-resolved MOKE Fitted parameter values from the inhomogeneous broadening model and phenomenological curve Coercive field (H C ) and saturation Kerr rotation (θk s ) extracted from polar MOKE hysteresis loops measured with a CW He-Ne laser for varied CoNi layer thickness in CoNi/Pt multilayers (figure 6.3)

15 LIST OF TABLES 14 List of Publications Y Liu, L R Shelford, V V Kruglyak, R J Hicken, Y Sakuraba, M Oogane, Y Ando and T Miyazaki, Ultrafast optical modification of magnetic anisotropy and stimulated precession in an epitaxial Co 2 MnAl thin film, Journal of Applied Physics, 101, 09C106 (2007). L R Shelford, Y Liu, R J Hicken, Y Sakuraba, M Oogane and Y Ando, Magnetic second harmonic generation at the Co 2 MnSi/AlO x Physics, 103, 07D720 (2008). interface, Journal of Applied N D Telling, P S Keatley, L R Shelford, E Arenholz, G van der Laan, R J Hicken, Y Sakuraba, S Tsunegi, M Oogane, Y Ando, K Takanashi and T Miyazaki, Temperature dependence of the interface moments in a Co 2 MnSi thin film, Applied Physics Letters, 92, (2008). Y Liu, L R Shelford, V V Kruglyak, R J Hicken, Y Sakuraba, M Oogane, Y Ando and T Miyazaki, Epitaxial ferromagnetic films and spintronic applications, ed. A. Hirohata and Y. Otani, Research Signpost 37/661 (2), Fort P.O., Trivandrum , Kerala, India Y Liu, L R Shelford, V V Kruglyak, R J Hicken, Y Sakuraba, M Oogane and Y Ando, Optically induced magnetization dynamics and variation of damping parameter in epitaxial Co 2 MnSi Heusler alloy films, Submitted to Physical Review B, under review. S Tsunegi, Y Sakuraba, M Oogane, N D Telling, L R Shelford, E Arenholz, G van der Laan, R J Hicken, K Takanashi and Y Ando, Tunnel magnetoresistance in epitaxially grown magnetic tunnel junctions using Heusler alloy electrode and MgO barrier, Journal of Physics D: Applied Physics, accepted for publication, August 2009.

16 LIST OF TABLES 15 Declaration Chapter 2: Background This chapter covers the background theory relevant to this thesis and has been compiled by myself. The content is not the result of my own work, and the relevant authors and texts are acknowledged throughout the chapter. Chapter 3: Experimental Techniques The optical experiments were built by myself and Dr Yanwei Liu at the University of Exeter, where static and time-resolved magneto-optical Kerr effect measurements have been performed by the research group for several years in other laboratories. The theory of the experimental techniques has not been developed in this thesis, and is referenced to the relevant authors in this chapter. Time-resolved measurements have been developed at Exeter by Prof. R J Hicken, Dr Jing Wu, Dr Ralph Wilks, Dr Anjan Barman, Dr Volodymyr Kruglyak, and Dr Paul Keatley before my arrival in the group. The magnetic second harmonic generation technique is new to the group and was built for the first time by myself with the supervision of Prof. R J Hicken. Software was written in LabVIEW partly by myself based on earlier versions written by previous group members. The x-ray magnetic circular dichroism measurements were performed at the Advanced Light Source Synchrotron in Berkeley, California, in collaboration with principal investigator Dr Neil Telling from the University of Manchester. No development of the techniques was made for this thesis, and the detail included in this chapter serves only as an introduction to the technique. Chapter 4: Optically-induced ferromagnetic resonance The samples studied in this chapter were fabricated at the Department of Engineering at Tohoku University, Japan, by Prof. Yasuo Ando, Dr Yuya Sakuraba and colleagues. All static and time-resolved magneto-optical measurements were performed by myself and Dr Yanwei Liu. The all-optical time-resolved experiment was built by Dr Yanwei Liu and myself, and data analysis was also shared between us. The macrospin theory was developed by Prof. R J Hicken.

17 LIST OF TABLES 16 Chapter 5: Interfacial Studies of Heusler Alloys The Co 2 MnSi Heusler alloy films studied in this chapter are the same as those studied in chapter 4, fabricated at Tohoku University by Prof. Yasuo Ando, Dr Yuya Sakuraba and colleagues. The magnetic second harmonic generation experiment was built and tested at Exeter by myself with the supervision of Prof. R J Hicken. The data presented on the variation with film annealing temperature was recorded by myself. The cryostat-based system was developed by myself and two undergraduate masters project students, Mr James Johnson and Mr Tom Blight. The measurements presented in this thesis were taken by myself and the undergraduate students, who have presented the data in their MPhys dissertations. The x-ray magnetic circular dichroism measurements were made at the Advanced Light Source synchrotron in Berkeley, California, with principal investigator Dr N D Telling. The results presented in this chapter are reproduced from publications of Dr N D Telling that are co-authored by myself and Dr P S Keatley from Exeter. The work of Dr Telling is referenced throughout the chapter. Chapter 6: Ultrafast demagnetisation and elastic oscillations in patterned CoNi/Pt multilayers The time-resolved MOKE measurements presented in this chapter were performed by myself and Dr Yanwei Liu. The samples were fabricated by Dr Gavin Burnell from the University of Leeds. The patterning was performed by Evgeny Sirotkin at the University of Exeter, using the nanosphere lithography technique of Dr Feodor Ogrin, also at Exeter. Chapter 7: Ferromagnetic Exchange Springs The sample studied in this chapter was fabricated at Oxford University. All of the data presented in this chapter was recorded at the University of Exeter by myself.

18 Chapter 1 Introduction The invention of the laser in 1961 and the associated high electric field intensities have opened up the field of study in nonlinear optics. In the following years several nonlinear optical effects were observed which have since become indispensable tools in the study of thin films. Linear and nonlinear magneto-optical effects can be applied to study the magnetisation of magnetic thin films. Commercially available lasers now offer pulse widths of 50 fs allowing dynamic measurements to be made with very high time resolution. With extremely high peak intensities the laser pulses can cause substantial heating in the material under study, changing the magnetic properties on a timescale comparable to the laser pulsewidth. Optical modification of magnetisation is an attractive research area for future technological applications as well as being of interest from a purely scientific viewpoint. Laser heating can be applied to reduce coercivity in magneto-optical recording, and in some cases angular momentum can be transferred from photons to the magnetic system [1, 2]. Magnetic multilayers have been very important in recent developments of magnetic data storage technology, with the magnetic tunnel junction now a key component in hard disk drives that are currently on the market. Two ferromagnetic thin films separated by a thin insulating barrier show a magneto-resistance that depends on the relative magnetisations of the two magnetic films. This and other spintronic phenomena are key to future devices that exploit the spin of the electron as well as its charge. The performance of such devices is highly dependent on the fabrication processes that affect the structural and magnetic properties of the thin films. Techniques capable of measuring magnetisation dynamics and interfacial properties are essential for studies in this exciting area. In this thesis static and time-resolved studies of magnetic thin films are presented. The magneto-optical Kerr effect (MOKE) has been applied to the study of static and

19 CHAPTER 1. INTRODUCTION 18 dynamic magnetisation in a number of thin film materials. Magnetisation dynamics have been induced by 50 fs pulses with several microjoule energy produced by an amplified Ti:sapphire mode-locked laser. Ultrafast sub-picosecond demagnetisation and GHz frequency magnetisation precession have been observed and are discussed. Nonlinear magnetic second harmonic generation (MSHG), which is surface and interface sensitive for materials that possess bulk inversion symmetry, has been used to study interfacial magnetisation of Heusler alloys that have been used as magnetic tunnel junction electrodes. Interface-sensitive measurements of the same sample series have also been made by x-ray magnetic circular dichroism (XMCD) at the Advance Light Source in Berkeley, California. In chapter 2 the theory relevant to magnetic thin films and the studies made in this thesis is presented. The classical and quantum descriptions of magnetism are followed by a more detailed discussion of the contributions to the magnetisation of a ferromagnet. Dynamic magnetisation and applicable macroscopic models are introduced, and spin-valves and magnetic tunnel junctions are described. In chapter 3 the experimental techniques and the theory behind them that are applied in these studies are described. The interaction of light with magnetic materials is briefly covered before more detailed discussions of the magneto-optical Kerr effect and magnetic second harmonic generation. In MOKE the polarisation rotation and/or ellipticity of a linearly polarised laser beam reflected from a magnetic material is linearly proportional to the magnetisation of that material. This effect is used in static and dynamic measurements of the magnetisation, and while it does not yield absolute values of the magnetisation it is very effective at investigating magnetic anisotropy and with a pulsed laser allows time-resolved measurements of the relative magnetisation. MSHG is a second-order optical effect that, for a material with bulk inversion symmetry, is only allowed at surfaces and interfaces. Here it is applied in the study of ferromagnetic interfaces, where the final few monolayers are crucially important in the performance of a magnetic tunnel junction. X-ray magnetic circular dichroism is then introduced which has also been used to study magnetic surfaces. Since XMCD is based on resonant excitation from core electron levels it is element specific and can measure absolute magnet moments. In chapter 4 time-resolved studies of optically-induced ferromagnetic resonance in Heusler alloy ferromagnetic thin films are presented. An intense optical pulse has been used to modify the magnetocrystalline anisotropy and induce magnetisation precession in Co 2 MnAl and Co 2 MnSi Heusler alloy films. The damping of dynamic magnetisation is very low in these materials which is advantageous for spin-transfer torque applications. Time-

20 CHAPTER 1. INTRODUCTION 19 resolved measurements allow investigation of the damping over a continuous frequency range, which offers another perspective for the understanding of damping mechanisms. In these studies the damping was found to vary with field strength and orientation, the origin of which is not well understood. Interfacial studies of magnetisation by MSHG and XMCD in the Co 2 MnSi Heusler alloy are presented in chapter 5. In MSHG the intensity of the reflected second harmonic light is magnetisation dependent and, for a material with bulk inversion symmetry, can only originate from surfaces and interfaces. A correlation with annealing temperature is observed between the MSHG response and the tunnel magnetoresistance. Temperature dependent measurements reveal a temperature variation of the MSHG signal. This may be related to the temperature dependence of the tunnel magnetoresistance that has been observed in magnetic tunnel junctions with Co 2 MnSi electrodes. XMCD is an element specific technique based on the resonant absorption of x-rays that can determine the absolute magnetic moments. When performed in the correct geometry XCMD can be made sensitive to a near-interface region just 2 3 nm from the sample surface. A signature of half-metallicity in the Co 2 MnSi films is shown in the multiplet structure of the XMCD spectra, and the temperature dependence of the near-interface moments is presented. In chapter 6 time-resolved MOKE measurements of multilayer CoNi/Pt films remnant magnetisation perpendicular to the film plane are presented. Complete demagnetisation in less than 1 ps is observed following excitation by an intense laser pulse. The response of continuous and patterned films is compared, with strong oscillations observed in the time-resolved reflectivity of the patterned film. In the final experimental chapter (chapter 7) static and time-resolved MOKE measurements of an exchange spring multilayer are presented. A multilayer of DyFe 2 /YFe 2 combines the properties of the hard DyFe 2 layers and the soft YFe 2 layers. The reversal of the magnetisation in such samples is particularly interesting, and serves as an excellent example of the role of competing energy contributions to the magnetisation. When a field is applied below that required to switch the hard layer the magnetisation of the soft layer will rotate progressively through the depth of that layer to follow the external field. This exchange spring behaviour produces a torque on the hard layers, and this torque can be used to induce magnetic precession. Static MOKE measurements of the magnetisation reversal and time-resolved MOKE scans showing induced magnetisation precession are presented.

21 Chapter 2 Background 2.1 Introduction This chapter will cover some of the theoretical concepts of magnetism encountered in the study of ferromagnetic thin films. I will begin by summarising the semi-classical descriptions of magnetic moments before introducing quantum mechanical descriptions of atomic magnetic moments and their interactions. All magnetic phenomena require a quantum mechanical treatment to explain their origin, in particular the magnetic ordering observed in ferromagnetism. No attempt will be made here to cover rigorous quantum mechanical derivations, rather the key points will be highlighted. I will go into more detail on the interactions that lead to magnetic ordering and ferromagnetism, then discuss various properties and features of ferromagnetic materials. Finally I will introduce some applications of ferromagnetic metals in magnetic tunnel junctions. 2.2 Semi-Classical Descriptions of Magnetism Semi-classical models that view the moments as circulating electric charges can describe some magnetic effects, but long range ordering and permanent magnetisation have no classical analogues. However it is still enlightening to cover the classical model since it offers a useful picture for visualising magnetic phenomena. For an electron moving in a circular orbit the angular momentum, l, is directed perpendicular to the plane of the orbit and is given by [3], l = m e v r, (2.1)

22 CHAPTER 2. BACKGROUND 21 where m e is the electron mass, v is its velocity and r is the radius of the orbit. The current of the orbiting electron is given by, I = ev 2πr, (2.2) where e is the charge of the electron. The magnetic moment of the current loop, µ, which is also directed normal to the plane of the loop, is the current multiplied by the area of the loop, Relating the magnetic moment to the angular momentum gives, µ = Iπr 2. (2.3) µ = e 2m e l. (2.4) By applying the Bohr model to this classical description an estimate of the atomic magnetic moment can be calculated. In the Bohr model the angular momentum is quantised, and the minimum allowed angular momentum in the ground state of hydrogen is. magnetic moment is then, The µ = e 2m e = µ B, (2.5) where µ B is the Bohr magneton, which is often used as a typical fundamental magnetic moment. The spin magnetic moment, µ S, does not obey the same dependence on the angular moment, instead being a twice as large as predicted, µ S = e s, (2.6) m where s has been used to represent the intrinsic angular momentum of the electron. There is no reason for this classically, and the explanation of the origin of the electron spin moment is beyond the scope of this thesis. The total magnetic moment of an atom is due to a combination of orbital and spin moments, and in general the proportionality between magnetic moment and angular momentum can be written, µ = g e 2m e j, (2.7) where j represents the combined angular momentum of the orbital and spin contributions and g accounts for the differing contributions from orbital and spin moments. For a purely

23 CHAPTER 2. BACKGROUND 22 B ω p θ J (-μ) Figure 2.1: A magnetic moment, due to its associated angular momentum, will precess in a magnetic field about an axis parallel to the field. orbital atomic moment g would be 1, while for a purely spin moment g would be 2, and for a combination it would lie somewhere between these values. Since the magnetic moments are proportional to an angular momentum, when a magnetic field is applied they will not simply line up with the field. The situation is analogous to a spinning top with an applied gravitational field, and is shown in figure 2.1. When a field B is applied the moment µ will try to line up with the field to reduce the interaction energy µ B, reducing the angle θ. This generates an angular momentum, θ/ t = Ω, which produces a torque, τ = Ω j, on the moment. This torque causes the moment to precess about an axis parallel to the applied field, B. In a time t the angular momentum will change by an amount j = (j sin θ) (ω p t), where ω p is the frequency of precession. The rate of change of angular momentum must equal the torque, therefore, ω p j sin θ = µb sin θ. (2.8) Substituting for µ/j from equation (2.7), the frequency of precession is, Classical theory of paramagnetism ω p = g eb 2m e. (2.9) A paramagnetic material is one that contains permanent magnetic moments, so that in addition to the diamagnetic response the application of a magnetic field will also tend to align the permanent moments. Classically the atomic moments can have any orientation with respect to the applied field, with θ the angle between the moment and the applied field

24 CHAPTER 2. BACKGROUND 23 and the interaction energy given by µb cos θ. In zero applied magnetic field the moments of a paramagnet are randomly oriented so that there is no net magnetisation. When a field is applied the moments will tend to align with that field with the alignment opposed by thermal atomic motion. The net magnetisation can be calculated using Boltzmann factor e µb cos θ/kbt with µ cos θ the net magnetic moment along B [4]. The average moment along B is then, π 0 µ z = µ cos θeµb cos θ/k BT 1 2 sin θdθ π 0 eµb cos θ/k BT 1 2 sin θdθ. (2.10) From this the fraction of the total moment that is oriented along B can be expressed as a Langevin function, ( ) µ z µb µ = coth 1 k B T µb/k B T L(µB/k BT ). (2.11) When µb/k B T 1 the Langevin function is approximated by µb/3k B T, and the magnetisation, defined as M = n µ z where n is the number of moments per unit volume, is given by, M = nµ2 B 3k B T. (2.12) The magnetic susceptibility is defined by χ = M/H, which for small fields is approximately equal to µ 0 M/B, so that, which is Curie s law, with C the Curie constant. χ = nµ 0µ 2 3k B T = C T, (2.13) Weiss model of ferromagnetism A ferromagnetic material is characterised by a very large magnetic susceptibility, and the persistence of a net magnetisation in the absence of an applied field. These effects are due to a strong interaction between the permanent atomic moments that is absent in a paramagnetic material. Without a proper explanation of this interaction, Weiss proposed that there exists some internal molecular magnetic field acting on the moments. At the Curie temperature thermal agitation of atomic moments is sufficient to overcome the interaction with the internal field, so an estimate of the internal field can be made [4, 5]. For atoms with a moment µ B,

25 CHAPTER 2. BACKGROUND 24 µ B B m k B T C, (2.14) where B m is the molecular field and T C is the Curie temperature. For iron the Curie temperature is approximately 1000 K, therefore B m 10 7 Oe. Weiss was unable to explain the origin of such a strong field (this requires a quantum mechanical treatment, as will be shown in a later section), but he developed a phenomenological theory of ferromagnetism by assuming that the field was proportional to the magnetisation by, B m = λm, (2.15) where λ is the molecular field constant. It is then possible to treat a ferromagnet as a paramagnet in a field B + B m. The discussion can be separated into two regions, the spontaneous magnetisation region with T < T C and the paramagnetic region with T > T C. For T > T C the magnetic susceptibility is the same as that for a paramagnet, with the modified Curie-Weiss law taking into account the Curie temperature, [5], χ = C T T C. (2.16) For T < T C and atoms with an angular momentum J the magnetisation is given by M = Ngµ B JB J (x), (2.17) where N is the number of atoms per unit volume and B J (x) is the Brillouin function with, x = Jgµ BB k B T. (2.18) The field B is replaced by the field B + B m = B + λm, and then to investigate the spontaneous magnetisation B is set to 0. The saturation magnetisation at zero temperature is M(0) = Ngµ B J, so from equation (2.17), and from equation (2.18), M(T ) M(0) = B J(x), (2.19) M(T ) M(0) = k B T Nλg 2 µ 2 x. (2.20) BJ 2

26 CHAPTER 2. BACKGROUND 25 The spontaneous magnetisation M(T )/M(0) can be found by graphically solving equations (2.19) and (2.20) as a function of x. Above a certain temperature the only solution of the two equations is at M(T )/M(0) = 0, so the spontaneous magnetisation vanishes. The temperature at which this happens is the Curie temperature. Experimental measurements of M(T )/M(0) as a function of T/T f can be fitted by the Weiss field theory. Using, M(T ) M(0) = J + 1 ( ) T x, (2.21) 3J T f the variation of the spontaneous magnetisation with temperature for iron and cobalt was best fitted with J = 1/2 [5]. This fitting suggests that the magnetisation does not originate from orbital motion, but instead from electron spin. For J = 1/2 and g = 2, the Brillouin function tends to a tanh() function and equation (2.19) becomes, M(T ) M(0) = tanh x, (2.22) with x = µ B H/k B T. The Weiss field theory does not agree well with the data at low temperatures. At low temperatures T/T f 0 and x is large, and the limit of tanh y as y is 1 2e 2y, and therefore, M(T ) M(0) = 1 2e2(T/T f ). (2.23) Instead the magnetisation falls off much more quickly, following a (1 AT 3/2 ) dependence, where A is a constant. Derivation of the correct low-temperature dependence of the spontaneous magnetisation requires spin wave theory, which will not be covered here. 2.3 Quantum Mechanics and Magnetism In quantum mechanics electrons exist in a finite number of states that are described by the quantum numbers, and the angular momentum is restricted to a finite number of quantised values. The total angular momentum is given by the quantum number j and for any given axis the number of allowed projections of the angular momentum along that axis is (2j + 1). The magnetic moment of an isolated atom can be determined by considering the energy of the various quantum states when interacting with an external field. For any given atom in the absence of an applied magnetic field a measurement of the z-component will yield one of these allowed states with equal probability. For systems of multiple atoms the situation is more complicated and the interaction of atomic moments

27 CHAPTER 2. BACKGROUND 26 with other moments and with the environment must be considered. This will be discussed in more detail in the section on ferromagnetism. The magnetic moment can be defined as the constant of proportionality between the energy of the moment in a field and the field, µ B. Equation (2.7) relates the magnetic moment to the angular momentum, so the z-component of the angular momentum is given by [3], ( ) e µ z = g J z. (2.24) 2m e The interaction energy of a magnetic moment and a magnetic field along the z-axis is, ( ) e U mag = µ z B = g J z B. (2.25) 2m e The values of J z are limited to j, (j 1),..., j so the magnetic energy is quantised. The maximum value is obtained for J z = j, with, ( ) e U mag = g j z B = gµ B jb, (2.26) 2m e where µ B = e /2m e is the Bohr magneton. Therefore the energy of a system with nonzero magnetic moment is changed when a magnetic field is applied, with the energy split into 2j + 1 levels. The number of energy levels is determined by the number of allowed states for any given axis, and the separation of the levels is proportional to the magnetic field. For a single electron j = 1/2 and there are two possible states J z = /2 and J z = /2, which are referred to as spin-up and spin-down for the moment parallel and antiparallel to the applied field. Unlike the classical case the magnetic moment can never fully align with the applied field. The magnitude of the angular momentum in a quantum system is given by J J = j(j + 1), which is always more than j, the maximum projection of J along any given axis Magnetic resonance When an atom is split into two or more energy levels it can make a transition from one to another by absorbing or emitting a photon with energy ω [5]. For energy levels split by a magnetic field these frequencies are typically in the microwave and radio frequency regions. Applying a magnetic field of the appropriate frequency can cause transitions from the lower to higher energy levels. This resonant frequency is given by,

28 CHAPTER 2. BACKGROUND 27 ω p = g e B, (2.27) 2m e where ω p is the precession frequency. This quantum mechanical picture of resonant absorption agrees with the classical description of precessing magnetic moments in equation (2.9). Therefore the absorption of a magnetic field of frequency ω p can be pictured as the excitation of a precession mode of the magnetisation gyroscope. Classically the excitation absorption peak would be broad since µ z can vary continuously. Quantum mechanically µ z can only have certain discrete values, and therefore the resonant peaks will be very sharp with the transition probabilities at other frequencies being very low. By measuring the resonant frequency with swept magnetic field strength the g-factor can be measured very accurately Permanent magnetic moments The net atomic angular momentum and hence the magnetic moment of atomic species varies across the periodic table. The magnetic state of an atom depends on the filling of electronic states and their associated orbital and spin momenta. An approximate distinction can be made between atoms with odd and even number of electrons. An atom with an odd number of electrons will always have a permanent magnetic moment as the spin moments cannot be fully compensated, while an atom with an even number of electrons may have zero net angular momentum. Hund s rules can be used to estimate the ground state and hence the magnetic moment of free atoms or ions [4, 5]. The first rule states that the total spin momentum, S = m s, is the maximum allowed by the Pauli exclusion principle. The second rule states that the total orbital momentum, L = m l, should be the maximum allowed by the first rule. Finally the third rule says that the total angular momentum, J, is given by J = L S for a shell that is less than half occupied, and J = L + S for a shell that is more than half occupied. The ground states are then written using the spectroscopic notation, 2S+1 X J, where X = S, P, D, F, for L = 0, 1, 2, 3. For example the ground state electron configuration of Co is 3d 7 4s 2, so S = 3/2, L = 3 and J = 9/2, and the ground state is 4 F 9/2. The majority of free atoms and ions have an incompletely filled orbital and therefore have a magnetic moment, but these moments are often compensated when the atoms bond to form bulk materials. In general during ionic bonding each ion forms a complete orbital so the net magnetic moment is zero, while in covalent bonding the shared valence electrons also give no net moment. In metallic bonding a magnetic moment can be associated

29 CHAPTER 2. BACKGROUND 28 with the conduction electrons. There are of course exceptions to these rules and many nonmetallic compounds have permanent magnetic moments. The elements responsible for these compounds are the transition elements, where electrons may occupy states of higher principal quantum number n before all lower states are filled. The outer electrons are generally responsible for the interatomic bonding, and the unfilled inner shells contribute a net magnetic moment Quantum theory of paramagnetism In the classical model of a paramagnet the permanent moments can be oriented at any angle with respect to an applied magnetic field. In the quantum mechanical picture the component of the moment along any one axis is limited to J(J + 1) values, where J is the total angular momentum which is limited to integer or half integer values. When J = 1/2 there are only two possible values of the z-component of the moment, m J = ±1/2, which correspond to parallel and antiparallel alignment with the applied field B. These states are split energetically, with energies ±µ 0 B, and from statistical mechanics the number of spin-up and spin down electrons are given by, N = Ae µ 0B/k B T, N = Ae +µ 0B/k B T, (2.28) with A determined from N + N = N. The average magnetic moment is given by, so that the magnetisation is, µ av = µ 0N + µ 0 N, (2.29) N M = Nµ 0 e +µ 0B/k B T e µ 0B/k B T e +µ 0B/k B T + e µ 0B/k B T = Nµ 0 tanh µ 0B k B T. (2.30) This function predicts that the magnetisation will saturate at high field, when the tanh() function tends to 1. At this field all permanent magnetic moments are oriented with the applied field. For low fields and/or high temperatures the magnetisation is approximated by, M = Nµ2 0 B k B T, (2.31)

30 CHAPTER 2. BACKGROUND 29 which is the same as the classical function (equation (2.12)) except for a factor of 1/3. This is accounted for by a correction to the classical equation arising from the difference in the quantum µ 0 and the classical µ. In the classical equation the square of the magnetic moment is µ 2 = µ µ, which is given by, ( ) ge 2 µ µ = J J. (2.32) 2m e J J can be replaced by j(j + 1) 2, which for a spin-1/2 particle is Then, ( ) ge 2 µ 2 3 = µ µ = 2m e 4 2 = 3µ 2 0, (2.33) and the classical result agrees with the quantum mechanical formula. In the general case where J can take any integer or half-integer value the magnetisation is given by the Brillouin function, which reduces to tanh() for J = 1/ Ferromagnetism In ferromagnetic materials the permanent atomic dipoles interact very strongly, and it is this interaction that was represented by Weiss molecular field in the classical theory. It was not until Heisenberg and the development of the exchange interaction that the alignment of atomic moments could be explained. The exchange interaction is the result of Coulombic interaction energy and the Pauli exclusion principle. The concept of direct exchange between two electron spins is often described using the Heitler- London model of the hydrogen molecule [4, 5]. In this model two electrons exist in states described by ψ (r 1, s 1 ) and ψ (r 2, s 2 ), where r i are the spatial coordinates and s i are the spin states. As the two hydrogen atoms are brought closer together the wavefunctions of the electrons overlap and a total wavefunction for both can be written. For electrons the total wavefunction must be antisymmetric to satisfy the Pauli exclusion principle, meaning that upon exchange of the two electrons the sign of the total wavefunction must reverse. The antisymmetry of the total wavefunction can be met by either the spatial or the spin part of the wavefunction, ψ = φ(r)χ where φ are the spatial functions and χ are the spinor functions. The two possible states in the hydrogen molecule are, Ψ S = 1 2 [φ a (r 1 )φ b (r 2 ) + φ a (r 2 )φ b (r 1 )] χ S, Ψ T = 1 2 [φ a (r 1 )φ b (r 2 ) φ a (r 2 )φ b (r 1 )] χ T, (2.34)

31 CHAPTER 2. BACKGROUND 30 where the subscripts S and T refer to the singlet and triplet states respectively. In the antisymmetric state, χ S, the total spin quantum number is s = 0, while in the symmetric triplet state, χ T, the total spin quantum number is s = 1. The degeneracy is given by 2s + 1, hence the singlet and triplet labels. The perturbation to the single atom ground state can be represented by the Hamiltonian, H 12 = e2 r ab + e2 r 12 e2 r 1b e2 r 2a, (2.35) where the terms represent the interaction of the two nuclei a and b with separation r ab, the interaction of the two electrons 1 and 2 with separation r 12 and the interaction of an electron with the nucleus of the other hydrogen atom. The energies of the singlet and triplet states are, E ΨS = 1 2 (K 12 + J 12 ), E ΨT = 1 2 (K 12 J 12 ), (2.36) where K 12 is the average Coulomb interaction energy given by, K 12 = φ a(1)φ b (2)H 12φ a (1)φ a (2)dτ 1 dτ 2, (2.37) and J 12 is the exchange integral, J 12 = φ a(1)φ b (2)H 12φ a (2)φ b (1)dτ 1 dτ 2. (2.38) In order for the spins to be aligned parallel J 12 must be positive. In the hydrogen molecule J 12 is negative, so in the ground state the spins are antiparallel and there is no net spin moment. A qualitative analysis shows that the exchange integral is positive when the interatomic spacing r ab is large compared to the the radii of the orbitals, and therefore is most likely for d and f wavefunctions. The description so far has considered interaction directly between overlapping wavefunctions, which is known as direct exchange. However it is often the case that direct exchange cannot be a significant mechanism in materials that are known to display ferromagnetism [4], for example in the rare earth ferromagnets the 4f electrons are strongly localised and are not involved in bonding. In these cases some form of indirect exchange must exist whereby the interaction is mediated by some other means. In some antiferromagnetic oxides, for example MnO, the antiferromagnetic coupling between Mn ions

32 CHAPTER 2. BACKGROUND 31 is mediated by the oxygen ion in a process known as superexchange [4]. In metals the exchange interaction can be carried by the conduction electrons. A localised magnetic moment can spin-polarise the conduction electrons which will then interact with a neighbouring localised moment. This is known as itinerant exchange, and it has an important effect on the electrical conduction properties of metallic ferromagnets Spin-orbit coupling The spin and orbital moments can interact via the spin-orbit interaction. Classically speaking an electron orbiting a nucleus feels the nucleus in orbit around it. For an electron with velocity v the field is [6], B = r v rc 2 dv (r), (2.39) dr where r v is the classical angular momentum of the electron and V (r) is the potential energy seen by the electron. The interaction energy between the spin moment and this field is, which combined with equations (2.39) and (2.6) gives, E so = 1 2 µ s B, (2.40) E so = e 2 dv (r) 2m e rc 2 l s. (2.41) dr Using the Russell-Saunders spin-orbit coupling the total quantised orbital angular momentum, L = m l, and the total quantised spin angular momentum, S = m s, are coupled by L S. The square of the total angular momentum is J 2 = L 2 + S 2 + 2L S, where J 2 = J(J + 1), L 2 = L(L + 1) and S 2 = S(S + 1), and the interaction energy can be written, E so = λ so [J (J + 1) L (L + 1) S (S + 1)]. (2.42) Quenching of the orbital moment and the g factor In the 3d transition metals Hund s third rule is broken because the crystal field interaction is much stronger than the spin-orbit interaction [4]. The measured magnetic moments for these materials instead suggest that the ground state configuration is chosen

33 CHAPTER 2. BACKGROUND 32 so that L = 0, i.e. the orbital moment is zero. For a ferromagnet the g factor may be written as, ( L z + 2 S z ) / S z, (2.43) where L z and S z are the orbital and spin quantum numbers associated with the quantization direction. If the orbital momentum is quenched, L = 0 and therefore g J = 2. Any difference in the measured g from 2 shows the presence of an orbital moment, with the orbital and spin moments parallel for g > 2 and antiparallel for g < 2. These differences are the result of a weak spin-orbit interaction in the 3d transition metals, which can also result in the g-factor being slightly anisotropic [4]. With a strong crystal field interaction the value of the g-factor could depend slightly on the direction of the applied magnetic field with respect to the crystal axes. 2.4 Ferromagnetic Free Energy Contributions The static magnetisation configuration is determined by competing contributions to the total magnetic free energy. The exchange and spin-orbit interactions have already been covered, and the discussion here will highlight other contributions that, in combination with these, give rise to magnetisation anisotropy and domain structure. The energy contributions can be expressed in terms of macroscopic magnetic parameters of the material without need of a microscopic model. Firstly, there is an energy associated with the interaction between the atomic permanent moments and an applied field called the Zeeman energy. The moments will tend to align with the field in order to reduce this energy, which is expressed as, E Zeeman = H ext MdV. (2.44) V In a sufficiently strong field all magnetic moments in the ferromagnetic material will align with the external field and the magnetisation will reach a maximum. In this state the Zeeman energy is minimised. There is also an energy associated with the magnetostatic interaction between spontaneously magnetised regions of the material. This is expressed as, E ms = 1 2 V H d MdV, (2.45)

34 CHAPTER 2. BACKGROUND 33 where H d is the demagnetising field. The magnetostatic interaction is much weaker than the exchange interaction, but it acts on a far longer range. The competing short range exchange and long range magnetostatic interactions can lead to the formation of magnetisation domains. Figure 2.2 shows some examples of domain structures in a rectangular ferromagnetic element. In (a) the magnetisation exists in a single domain, with uncompensated moments at the edges of the element generating a demagnetising field. In (b) the magnetisation has formed a closure domain structure with no net magnetisation for the element as whole. In (c) a multidomain structure that does not fully compensate the magnetisation of the element is shown, in this case called an s-state. In (a) the exchange energy dominates the magnetostatic interaction, while in (b) the long-range magnetostatic interaction acts to reduce the net magnetisation, while in (c) an intermediate condition is met. A domain structure is energetically stable if the energy gained by reducing the magnetostatic interaction energy is greater than the energy cost associated with the exchange interaction and the misalignment of moments in the domain walls. (a) (b) (c) Figure 2.2: Examples of magnetisation domain in a ferromagnet. In (a) the sample is uniformly magnetised with the stray demagnetising field shown, while in (b) a closure domain state is formed, with no net magnetisation. (c) shows an s-state, which reduces the magnetisation but still gives a nonzero magnetisation Magnetic anisotropy The atomic magnetic moments can interact with the crystalline structure of the material to produce magnetisation energy that is dependent on the orientation of the magnetisation with respect to well defined crystallographic axes. The magnetic anisotropy energy is defined as the energy required to magnetise a material along some axis oriented away from the magnetisation easy axis [5] where the easy axis is the global minimum of the magnetic free energy. The orientations of the easy and hard magnetisation axes are

35 CHAPTER 2. BACKGROUND 34 determined by a number of phenomena, including the shape of the material and interaction of the magnetisation with the crystal field. Magnetic anisotropy does not arise from the exchange interaction, but rather from several sources including the crystal field by means of the spin-orbit interaction. Typically the anisotropies are considered phenomenologically, with the values of various parameters being determined by experiment. Magnetocrystalline anisotropy arising from the spin-orbit is the most common form of anisotropy. The electron orbits are linked to the symmetry of the crystal lattice, and the interaction of the orbits with the spins leads to preferred magnetisation orientations along (or between) crystallographic axes. The magnetocrystalline energy is usually weak compared to the exchange energy, so in phenomenological descriptions the magnetocrystalline anisotropy is not considered to change the magnitude of the magnetisation [7]. However the direction of the magnetisation is determined only by the magnetocrystalline energy. Anisotropy energies are presented as phenomenological expressions by power series expansions in terms of the symmetry of the crystal [7]. For hexagonal crystals, for example Co, a uniaxial anisotropy exists which is a function of the angle between the c-axis and the magnetisation, θ. This uniaxial magnetocrystalline energy density, up to the first two terms, is, w u = K 1 cos 2 θ + K 2 cos 4 θ = K 1 û 2 z + K 2 û 4 z, (2.46) where û = M/M is the unit vector parallel to the magnetisation. The coefficients K 1 and K 2 are the first and second order anisotropy constants, with K 1 K 2. The constants are determined experimentally and are strongly temperature dependent. K 1 and K 2 may be positive or negative, with positive K 1 when the hexagonal c axis is the easy axis and negative K 1 when the easy axis lies in the ab-plane. Typically there is only weak, if any, dependence on the angle within the ab-plane. For cubic crystals there are energy extrema for the x, y and z axes equivalently. The first two terms in the energy density of cubic magnetocrystalline anisotropy are, (û2 w c = K 1 x û 2 y + û 2 yû 2 z + û 2 zû 2 x) + K2 û 2 xû 2 yû 2 z. (2.47) Again the constants K 1 and K 2 may be positive or negative, with positive values corresponding to easy axes parallel to the principle crystal axes and negative values when the crystal axes are the hard axes.

36 CHAPTER 2. BACKGROUND 35 The anisotropy constants depend strongly on temperature, much more so than the magnetisation. It is even possible for the anisotropy constants to change sign with temperature (see K 1 for Co in figure 2.3). It was shown by Akulov [8] and by Zener [9] that the anisotropy constant K 1 can be related to the spontaneous magnetisation by a tenth power law, K 1 (T ) K 1 (0) = [ ] M(T ) 10. (2.48) M(0) While this agrees well with observations for iron, it does not agree with measurements of nickel and cobalt anisotropy, as shown in Figure 2.3. Zener arrived at a tenth power law by assuming that the sole effect of the temperature was to introduce local fluctuations in the direction of the magnetisation vector with the local magnitude of the magnetisation unaffected. Zener noted that it is incorrect to consider that the temperature dependence of the anisotropy is due to the temperature dependence of the spin-orbit interaction, since magnetostriction, which also arises from the spin-orbit interaction, shows a far weaker dependence on temperature than anisotropy. He also states that the g-factor has been found to be temperature independent up to the Curie temperature for nickel, another indication that the spin-orbit coupling is not strongly affected by temperature. Figure 2.3: Temperature dependence of the K 1 anisotropy constant for ferromagnetic Fe, Ni and Co. Reproduced from reference [9]. W J Carr [10] found an agreement for the temperature dependence of the anisotropy of Co by using Zener s theory and the postulate that the intrinsic anisotropy varies with thermal expansion. Carr also said that the additional temperature dependence observed in nickel, for example, could arise from the temperature variation of the anisotropy constants.

37 CHAPTER 2. BACKGROUND 36 He obtained a good agreement with experiment for nickel when K 1 was assumed to have a linear dependence on temperature, with the modified equation, ( K 1 (T ) K 1 (0) = T ) [ ] M(T ) 10. (2.49) T C M(0) However no theoretical reason for this variation of K 1 was given Thin films In very thin films of only a few atomic layers the effects of surfaces and interfaces become more important and can in some cases overcome the influences of shape and bulk crystalline anisotropy [11]. In a thin film the shape anisotropy leads to a strong demagnetising field perpendicular to the plane of the film. Therefore the magnetisation would, in the absence of any surface effect, preferentially lie in the plane of the film. Néel first predicted [12] that magnetic anisotropy could be greatly modified at surfaces and interfaces compared to the bulk due to the different bonding environment. At surfaces and interfaces the bulk symmetry is reduced, and so the exchange energy cannot be the same at surfaces as in the bulk [7]. Therefore the anisotropy of a thin film should be dependent on its thickness. The first observation of such a surface anisotropy was in 1969 by U Gradmann [13] in thin films of NiFe which showed spontaneous magnetisation perpendicular to the film plane. Realising perpendicular magnetic anisotropy in thin films required the fabrication of atomically clean epitaxial films on single crystal substrates. Technologically such films are interesting because they allows for closer packing of bits in a storage medium, therefore enabling increased storage densities. In chapter 6 multilayered films of CoNi/Pt are studied which show strong perpendicular anisotropy. Determining which materials will show perpendicular anisotropy due to surface effects requires calculations with molecular field theory, which is beyond the scope of this thesis. 2.5 Ferromagnetism in Metals Measurements of the magnetic moment per atom in metals usually yield a noninteger value, for example the magnetic moment per atom in iron is 2.2µ B [4]. This cannot be understood in terms of localised moments, and instead requires the band theory of ferromagnetism, also known as itinerant ferromagnetism, where the magnetisation is due to spontaneously spin-split bands.

38 CHAPTER 2. BACKGROUND 37 A spin-split band structure which gives a ferromagnetic state will be energetically stable if the kinetic energy increase is less than the interaction energy between the magnetisation and the molecular field. If spin-down electrons with energies E F δe to E F are moved and spin flipped to the spin-up states in the energy range E F to E F + δe their increase in kinetic energy is given by, E K = 1 2 g(e F )(δe) 2, (2.50) where the number of electrons moved is g(e F )δe/2. There is an energy reduction due to the alignment of the magnetisation with the molecular field. If each electron has a moment µ B the magnetisation is M = µ B (n n ). The molecular field is proportional to the magnetisation, and can be represented by B mf = λm, and the molecular field energy is, M E mf = µ 0 λm dm = µ 0λM 2 = 1 2 µ 0µ 2 Bλ(n n ) 2. (2.51) The magnetisation can be written in terms of the density of states, g(e F ), and the energy difference between spin-up and spin-down electrons. The preceding factors can be written as U = µ 0 µ 2 Bλ with U a measure of the Coulomb energy, E mf = 1 2 U (g(e F )δe) 2. (2.52) The energetically split bands will be stable if the kinetic energy cost is less than the energy gained in the molecular field, i.e. if the total energy E = E KE + E mf < 0, E = 1 2 g(e F )(δe) 2 (1 Ug(E F )) < 0. (2.53) This inequality requires that Ug(E F ) 1, which is known as the Stoner criterion Spin-polarisation and spin-dependent conductivity In a 3d transition metal ferromagnet the 3d and 4s electrons overlap at the Fermi level. The 4s electrons are mainly responsible for electrical conduction since they have a lower effective mass than the 3d electrons. The conductivity of the 4s electrons is partly limited by scattering into empty 3d states which are spin-split as shown in figure 2.4. The scattering rate and therefore the conductivity for spin-up and spin-down electrons will be different, with the difference proportional to the splitting of the band structure. An electrical current in a metallic ferromagnet is then spin-polarised, and can carry with it an

39 CHAPTER 2. BACKGROUND 38 angular momentum associated with the unbalanced spins. The topic of torque associated with spin-polarised currents will not be covered in this thesis, but is a key area of research in the magnetics community. The term spin-polarisation is used to describe the difference in conductivity of spinup and spin-down electrons as well as the difference in the density of spin-up and spin-down states at the Fermi level. A material that has zero density of state in the 3d band for one spin band has a 100 % spin-polarisation, and could in theory give a 100 % spin-polarised current. 2.6 Magnetisation Dynamics Ferromagnetic resonance Due to the strong exchange interactions in a ferromagnet resonance phenomena tend to be coherent among atomic moments. Hence, in a field that is sufficiently strong so as to remove the domain structure, the precession can be viewed macroscopically with the equation of motion attributed to Landau and Liftshitz, dm dt = γm H eff + damping, (2.54) where γ = 2.8 π g MHz/Oe, and H eff is the effective field given by, H eff = 1 M ûe tot. (2.55) (a) E (b) E Spin-up Spin-down Spin-up Spin-down E F E F g(e) g(e) Figure 2.4: (a) Equal density of states for spin-up and spin-down electrons in a non-magnetic metal. (b) Spin split 3d energy bands in a metallic ferromagnet.

40 CHAPTER 2. BACKGROUND 39 M x dm/dt H eff M x H eff M Figure 2.5: Damped precessional magnetisation motion as described by the Landau-Lifshitz- Gilbert equation. The dashed red line shows the relaxation path followed by the magnetisation to reach the equilibrium orientation, parallel to the effective field. The first term in equation (2.54) describes a torque on the magnetisation that causes the magnetisation to precess about the effective field. As mentioned earlier, the common analogy used to describe this motion is the spinning top where the angular momentum of the top spinning on its own axis and precession about the vertical axis is described by the cross product of the angular momenta. Additional terms include the damping of the precession as the magnetisation returns to its equilibrium orientation. A commonly used form of the damping term was added to the Landau-Lifshitz-Gilbert (LLG) equation by Gilbert [14], dm dt = γm H eff + α M [ M dm dt ], (2.56) where α is the damping constant. This term represents a force directed toward the centre of the precession orbit and causes the magnetisation to follow a helical path, as shown in figure 2.5. This phenomenological equation does not allow for variations of the damping that may arise with, for example, anisotropy of the material. Anisotropy and field-dependent damping has been observed, and will be discussed in more detail in chapter 4. In the case of uniform magnetisation precession, the dependence of the frequency on the field and the magnetisation is given by the Kittel equation, ω = γ H (H + 4πM). (2.57)

41 CHAPTER 2. BACKGROUND Ultrafast demagnetisation Consider the effect of an ultrafast ( 50 fs) laser pulse that is incident on and partially absorbed by a ferromagnetic film. The initial response is the generation of a nonthermal, or a non Fermi-Dirac like, electron population. Electron-electron interactions lead to the formation of a new Fermi distribution at a higher temperature, T e, on sub-picosecond timescales. Energy is also distributed to the lattice by electron-phonon interactions, though this has a longer picosecond-range timescale. Demagnetisation of the film can occur on the longer timescale as phonons disturb the alignment of atomic moments, but time-resolved measurements of the magnetisation of thin films made using femtosecond pulsed lasers have shown that the magnetisation can be reduced on subpicosecond timescales [15 18]. The response of a magnetic material to absorption of an ultrafast laser pulse is often discussed in terms of the three temperature model [15] with separate temperatures assigned to the electron, spin and lattice systems. Absorption of the laser pulse increases the electron temperature first by creating a nonthermal electron population which then thermalises by electron-electron interactions and loses energy to the spin and lattice systems. A direct interaction between the electron and spin systems has been suggested that would enable the observed demagnetisation on the timescale of the electron thermalisation. 2.7 Applications of Magnetic Materials Ferromagnetic materials have been used as data storage media for several decades, and the technology continues to advance at an impressive rate. Between 1954 and 2000 hard disk data storage density increased by a factor of 10 million as bit sizes were reduced [19]. The speed of reading and writing data is also a strong driving factor in industry. Also, the spin-dependent conductivity of ferromagnetic metals is promising entirely new spin-based electronics with, for example, non-volatile random access magnetic memory. Major advances in the application of magnetism in both areas are the spin-valve and magnetic tunnel junction Spin-valves and magnetic tunnel junctions The spin-valve and magnetic tunnel junction (MTJ) are similar multilayered magnetic structures that show a change in resistance to an electrical current that depends on the relative magnetisations of two ferromagnetic layers (see Figure 2.6). The principal

42 CHAPTER 2. BACKGROUND 41 Parallel, low-resistance Anti-parallel, high-resistance FM layer 1 NM layer FM layer 2 Figure 2.6: A schematic diagram of a spin valve of magnetic tunnel junction. Two ferromagnetic layers are separated by a nonmagnetic spacer, which is conducting in a spin valve and insulating in a magnetic tunnel junction. The electrical resistance is lowest for parallel magnetisations, and highest for antiparallel magnetisations. difference between the two devices is that the spin-valve uses a conducting metallic spacer layer while an MTJ uses an insulating barrier, usually a metallic oxide. The magnetoresistance effects for the two devices are termed the giant magnetoresistance (GMR) and tunneling magnetoresistance (TMR), and both will be described below. The giant magnetoresistance effect in spin-valves was discovered in 1988 independently by Peter Grünberg [20] and Albert Fert [21], to whom the 2007 Noble Prize in Physics was jointly awarded. A spin-valve is a multilayered structure such as that shown in Figure 2.6 two ferromagnetic metals are separated by a conducting spacer layer. The saturation fields of the two layers are different, so an external field can switch one layer in isolation of the other, giving parallel or antiparallel magnetisation. The parallel magnetisation configuration gives lower electrical resistance than the antiparallel configuration, which can be explained by considering separate conduction channels for spin-up and spindown electrons. Figure 2.7 shows the two conduction channels with 1 and 2 representing the ferromagnetic layers. It was shown earlier that in a ferromagnetic metal the density of states at the Fermi level is spin-split, resulting in different conductivity for spin-up and spin-down electrons. In the parallel magnetisation configuration the conductivity in both ferromagnetic layers is the same, so the conductivity for, say, spin-up electrons is higher than for spin-down electrons. In the antiparallel state the first ferromagnetic layer has higher conductivity for spin-up electrons while the second layer has higher conductivity for spin-down electrons. If R is the resistance for spin-up electrons and R is the resistance the spin-down electrons, the total resistance of the spin-valve, R P/AP for parallel of antiparallel magnetisations, is given by,

43 CHAPTER 2. BACKGROUND 42 For parallel magnetisations the total resistance is, 1 R P/AP = 1 R + 1 R. (2.58) while for antiparallel magnetisations the resistance is, R P = 2R 1R 2 R 1 + R 2, (2.59) R AP = R 1 + R 2. (2.60) 2 The difference in the resistance for parallel and antiparallel configurations is, R AP R P = R2 1 R2 2 2R 1R 2. (2.61) 2 (R 1 + R 2 ) For a spin-valve with a conducting spacer layer this difference in resistance is termed the giant magneto-resistance, with the lower resistance for the parallel magnetisation configuration. A magnetic tunnel junction (MTJ) is essentially a spin-valve with a thin (1 2 nm) insulating spacer layer, however the process of magnetoresistance is rather different. Instead of conduction electrons experiencing a different electrical resistance in each ferromagnetic layer, in a MTJ the magneto-resistance is determined by the probability of electrons tunneling across the barrier layer. Julliere [22] considered that the spin is conserved in tunneling across the barrier and therefore that tunneling of spin-up and spin-down electrons are (a) 1 2 R 1 R 1 R 2 R 2 (b) R 1 R 2 R 2 R 1 Figure 2.7: Two-channel conductivity model for a spin-valve. The conduction of spin-up and spin-down electrons is considered in two separate channels, with conductivity dependent on the relative alignment of the magnetisation in the ferromagnetic layers.

44 CHAPTER 2. BACKGROUND 43 two separate processes. The tunneling probability is determined by the density of initial and final spin-up/down states in the ferromagnetic layers, and so depends on the relative alignment of the magnetisations. The TMR is proportional to the spin-polarisation of the ferromagnetic layers, and in 1975 Julliere [22] expressed this as, R R = 2P 1P 2 (1 + P 1 P 2 ), (2.62) where P 1 and P 2 are the spin polarisations of the conduction electrons of the two ferromagnetic layers. The spin-polarisations are determined by the density of spin-up and spin-down states in the ferromagnetic layers by, P i = n i n i n i +, (2.63) n i with n the density of states at the Fermi level. Tunneling magneto-resistance (TMR) is typically larger than magneto-resistance achievable in spin-valves. From equations (2.62) and (2.63), if the density of states of one spin channel is zero the TMR ratio would be infinitely large, with zero conductance for antiparallel magnetisation. Such materials have been predicted to exist, including some of the full Heusler alloys [23]. Two such materials, Co 2 MnAl and Co 2 MnSi, are studied in this thesis. MTJs are used as the read heads in most hard disk drives that are currently on the market. They can also be applied as data storage bits in magnetic random access memory (MRAM), with the first commercial MRAM chips already on the market. They can be used as a source and detector of spin-polarised currents, which have extensive applications in future electronics devices that are based on the spin rather than the charge of electrons.

45 Chapter 3 Experimental techniques 3.1 Introduction In this chapter I will review the background of and give specific details of experimental techniques used in this thesis. The majority of the measurements have been performed at the ultrafast laser facility at the University of Exeter, where high time-resolution and electric field intensity is provided by femtosecond optical pulses. Magnetisation was studied optically via the magneto-optical Kerr effect (MOKE) and magnetically-induced second harmonic generation (MSHG). Additionally I have assisted Dr N D Telling with x-ray magnetic circular dichroism (XMCD) measurements at the Advanced Light Source synchrotron in Berkeley, California. Time-resolved measurements at Exeter have been applied to investigate ultrafast demagnetisation on sub-picosecond timescales, and to measure optically-induced ferromagnetic resonance with typically GHz frequencies. MSHG and XMCD are applied to study the interfacial magnetisation in Heusler alloys, which may differ significantly from the bulk properties. All of these techniques are built around the understanding of the interaction of electromagnetic radiation with magnetic materials. This chapter begins with a brief revision of the interaction of light and matter according to Maxwell s equations in the linear approximation. Following that the discussion will be expanded to nonlinear optics and magneto-optics. The MOKE will be explained in some detail, with descriptions of the measurement of static magnetisation hysteresis loops and high time-resolution scans of magnetisation dynamics. Secondly, the nonlinear optical effect magnetically induced second harmonic generation is introduced. MSHG is a nonlinear magneto-optical effect that is exciting since it offers very high interface sensitivity in a field where surfaces and interfaces are of extreme importance. The origin of surface and interface sensitivity in MSHG

46 CHAPTER 3. EXPERIMENTAL TECHNIQUES 45 will be explained, followed by a description of the method used detect the weak second harmonic light. Finally I will give a brief summary of x-ray absorption spectroscopy (XAS) and x-ray magnetic circular dichroism (XMCD), so that the reader may better understand the results presented in chapter Linear Optics Maxwell s equations describe light as an electromagnetic wave, and together with the constitutive relations predict the interaction of electromagnetic radiation with matter. It is common in the field of magnetism research to use the cgs system of units, in which the Maxwell equations are, D = 4πρ, B = 0, E = 1 B c t, H = 1 D c t + 4π J, (3.1) c where E is the electric field, H is the magnetic field, D is the electric induction, P is the electric polarisation, B is the magnetic induction and J is the electrical current density. For linear, isotropic media the constitutive relations are, D = E + 4πP, (3.2) B = H + 4πM, (3.3) J = σe, (3.4) The time-varying electric polarisation, P can act as a secondary source of electromagnetic waves, and is found using, P = χe, (3.5) where χ is the dielectric susceptibility. In a linear isotropic medium these proportionality factors are independent of the electric field intensity and are scalar values. They are typically frequency dependent however, leading to a variety of linear optical effects. The

47 CHAPTER 3. EXPERIMENTAL TECHNIQUES 46 constitutive proportionality factors become rank-2 tensors for anisotropic media, with, for example, the electric polarisation given by, P x P y = χ xx χ xy χ xz χ yx χ yy χ yz E x E y, (3.6) P z χ zx χ zy χ zz E z or in Einstein summation notation as, P i = χ (1) ij E j, (3.7) where i and j are each summed over x, y and z, and the superscript indicates that this is a first-order approximation. This anisotropy may exist naturally in the material, or may be induced by applied electric or magnetic fields. Birefringence is an example of a linear optical effect arising from material anisotropy, where orthogonal polarisation components have different propagation velocities and/or absorption coefficients leading to a change of the polarisation axis and/or ellipticity for a transmitted or reflected beam. Birefringence can be induced in a material by, for example, mechanical strain or a static electric field. In the latter case the polarisation of a transmitted light beam can be selectively rotated by any angle depending on the strength of the applied field in the electro-optical Kerr effect and Pockels effect. The Kerr and Pockels effects are distinguished by the formers quadratic dependence on the electric field and latter s linear dependence. 3.3 Magneto-optical Effects In 1845 Michael Faraday found that when linearly polarised light propagated through a material with a magnetic field applied along the propagation axis, its axis of polarisation was rotated. The angle of rotation depended on the distance traveled in the medium and the strength of the applied field. This is the Faraday effect, the first observed magnetooptical effect. In 1877 John Kerr observed a magneto-optical effect in reflection from the polished metallic pole of an electromagnet. 1 Originally these effects were considered to be due to an interaction between the light and the applied field inside the material, 1 This was two years after his discovery of the first electro-optical effect - electrical birefringence. Strictly the magneto-optical Kerr effect should always be referred to as precisely that (or by the abbreviation - MOKE), with the Kerr effect referring to the electro-optical phenomenon. However, in this thesis and in much of the literature on this subject, the magneto-optical Kerr effect is often referred to simply as the Kerr effect.

48 CHAPTER 3. EXPERIMENTAL TECHNIQUES 47 but were later found to be greatly enhanced for ferromagnetic materials and to disappear at temperatures above the Curie temperature. In 1884 Kundt [24] deposited films of Fe, Co and Ni on glass thin enough that light could still be transmitted. He found that the Faraday rotation was 30,000 times larger for light transmitted through these ferromagnetic films than for light transmitted through the same thickness of glass alone. The Faraday and Kerr effects are very similar in their origins and both are linearly proportional to the magnetisation. In both cases the effect is sensitive to the components of the magnetisation that are parallel to the propagation direction of the light. They are both determined by the dielectric tensor which is a complex quantity, and therefore these magneto-optical effects lead to a change in the polarisation rotation and/or ellipticity. In the following sections much of the explanation of these magneto-optical effects is centred around the Faraday effect, but applies similarly to MOKE. In this thesis the films studied are opaque, and so the MOKE in reflection geometry is necessarily used to investigate the magnetisation Phenomenological description of the Faraday effect and MOKE Modification of the polarisation and/or ellipticity requires non-zero off-diagonal elements in the susceptibility tensor in equation (3.6). Examples of calculations of these elements using quantum mechanics follow in a later section, but first the origin of magnetically sensitive elements in the dielectric tensor is considered by symmetry arguments, since only tensor elements that are invariant under any valid symmetry operation are allowed to be nonzero. For a bulk isotropic cubic lattice with principal crystal axes defining the x, y and z orientations the symmetry is very high, with inversion, fourfold rotation and six mirror planes allowed among others. Inversion symmetry leaves all elements unchanged, but reflection in the (100) plane reverses the sign of all x indices. Therefore all tensor elements with an odd number of x indices must be zero. This argument extends to reflections in the (010) and (001) planes, so that only the diagonal tensor elements are nonzero. Then the rotational symmetry gives χ xx = χ yy = χ zz, the result for a linear isotropic medium previously given in equation (3.5). Symmetry arguments can be applied to systems with lower symmetry to show that birefringence can arise from mechanical strain and the presence of a net magnetisation. The presence of a net magnetisation breaks time reversal symmetry, which can be viewed as the breaking of a spatial symmetry operation when the magnetisation is considered to arise from a current loop perpendicular to the magnetisation. If the magnetisation is

49 CHAPTER 3. EXPERIMENTAL TECHNIQUES 48 M [001] (010) (100) z, [001] y, [010] x, [100] Figure 3.1: A cubic lattice with M parallel to the [001] axis, with (100) and (010) mirror planes indicated. An effective current loop describing the origin of the magnetisation is shown. parallel to the z-axis then the current loop lies in the xy-plane, as illustrated in Figure 3.1. The magnetisation breaks the fourfold rotational symmetry, with remaining allowed symmetry operations including reflection in the xy-plane, and reflection in the xz- and yz-planes with M M. The dielectric tensor for a cubic crystal with the magnetisation parallel to the z-axis is then, χ + xx χ xy 0 χ xy χ + xx 0, (3.8) 0 0 χ + xx where the + and - superscripts indicate elements that are even and odd functions of the magnetisation respectively Jones matrix and reflectivity calculations The Faraday and magneto-optical Kerr effects can also be considered to arise from the effect of a net magnetisation on the reflection coefficients in the reflectivity tensor [25, 26], according to, E(r) s E (r) p = r ss r sp r ps r pp E(i) s E (i) p with the Kerr rotation for p-polarised incident light given by, θ K = R ( rsp r pp, (3.9) ), (3.10)

50 CHAPTER 3. EXPERIMENTAL TECHNIQUES 49 and the ellipticity, ε K = I ( rsp r pp ). (3.11) The reflection coefficients were calculated by Metzger et al. [27] at the interface between a vacuum and a magnetic material up to second-order in the magneto-optical constant, Q. To first order in Q the terms are, r ss = n 0 cos θ 0 n 1 cos θ 1 n 0 cos θ 0 + n 1 cos θ 1, (3.12) r pp = n 1 cos θ 0 n 0 cos θ 1 n 1 cos θ 0 + n 0 cos θ 1 + 2iQn 1n 0 cos θ 0 sin θ 1 u y (n 1 cos θ 0 + n 0 cos θ 1 ) 2, (3.13) iqn 0 n 1 cos θ 0 (sin θ 1 u x cos θ 1 u z ) r ps = cos θ 1 (n 0 cos θ 0 + n 1 cos θ 1 ) (n 1 cos θ 0 + n 0 cos θ 1 ), (3.14) r sp = iqn 0 n 1 cos θ 0 (sin θ 1 u x + cos θ 1 u z ) cos θ 1 (n 0 cos θ 0 + n 1 cos θ 1 ) (n 1 cos θ 0 + n 0 cos θ 1 ), (3.15) where θ 0 and θ 1 are the angles of incidence and refraction, n 0 and n 1 are the refractive indices of the vacuum and of the magnetic material, and u i are the Cartesian components of the unit vector parallel to the magnetisation Classical microscopic model of magneto-optical effects The Faraday effect and MOKE are often pictured by considering the linearly polarised incident light as a superposition of left- (LCP) and right-handed (RCP) circularly polarised modes with equal amplitude. Then the Faraday effect and MOKE polarisation rotation and ellipticity arise respectively from a difference of the propagation velocities and absorption coefficients of the LCP and RCP modes. Z. Q. Qiu and S. D. Bader [28] calculated the off-diagonal tensor elements by modeling the electrons as classical harmonic oscillators, where the driving force results from the optical E-field and the pseudo-lorentz force associated with the effective magnetic field arising from the magnetisation. The optical magnetic field is neglected in these calculations since it is a factor c weaker than the optical electric field. The equation of motion for the electrons under a driving electric field and a static magnetic field, B, is, d 2 r m e dt dr τ dt + m eω0r 2 = ee(t) e dr Bẑ, (3.16) c dt

51 CHAPTER 3. EXPERIMENTAL TECHNIQUES 50 where m e is the electron mass, τ is the electron relaxation time and ω 0 is the natural frequency. The direction of the Lorentz force depends on the velocity of the electron, and is therefore opposite for left- and right-handed circularly orbiting electrons induced by left- and right-handed circularly polarised light. For left-handed circularly orbiting electrons the magnetic force points towards the centre of the circle, reducing the radius of the orbit, while for right-handed circular electron orbits the magnetic force acts to increase the radius. It is the difference in the radii of these modes that gives the Faraday or MOKE polarisation rotation for linearly polarised incident light. In this picture it is the Lorentz force on orbiting electrons that gives the magneto-optical effect. Equation (3.16) can be solved, for Cartesian components r i, and from P i = ner i = (ε ij 1)E j /4π where n is the electron density, the dielectric tensor is found to be, ε = 1 + 4πne2 m γ ω 2 γ 2 ωc 2 iω c/ω ω 2 γ 2 ωc 2 iω c/ω ω 2 γ 2 ωc 2 γ ω 2 γ 2 ωc ω 2 γ,, (3.17) where ω is the optical frequency, ω c = eb/mc is the cyclotron frequency, and γ = (ω 2 0 /ω2 ) 1 (i/ωτ). This model can predict roughly experimental observations of the magnitude and the frequency dependence of the Faraday rotation. It does not consider the magnetisation of the medium, and it cannot explain the much stronger effect seen in ferromagnetic materials. For that quantum mechanical arguments are required Quantum-mechanical model Early explanations of the hugely increased Faraday effect in ferromagnetic media suggested that there exists a very strong effective field inside these materials. Voigt found that the field required to give the Faraday effects observed in ferromagnetic fields was Oe, which is the same order of magnitude as the field that was put forward to explain the existence of ferromagnetism by Weiss [29]. The origin of such a strong effective field remained unexplained until quantum theory was developed, specifically the Heisenberg exchange interaction and spin-orbit interaction. The Heisenberg exchange interaction explained the origin of the Weiss field as an effective field acting to align electron spin moments (discussed in more detail in the previous chapter). However this field is not directly coupled to the electron motion, and therefore cannot explain the enhanced magneto-optical effects. Later, Hulme showed that the spin-orbit interaction couples the optical properties of electrons to their spin [30] (also

52 CHAPTER 3. EXPERIMENTAL TECHNIQUES 51 discussed in more detail in chapter 2), and therefore gives optical sensitivity to the net effect of parallel spin alignment and large Faraday effect. While the spin-orbit interaction is present in all materials, there is generally not a strong effect since their are equal numbers of spin-up and spin-down electrons. In a ferromagnet the permanent magnetic moment is the result of a spin imbalance at the Fermi level, and hence spin-orbit interaction can have a net effect on the orbital motion of the electrons. The Faraday and Kerr effects can be expressed in terms of the conductivity tensor. The dielectric tensor is is proportional to the conductivity tensor by, ɛ = 1 + i 4π ω σ, (3.18) where ω is the angular frequency of the electromagnetic field. Argyres calculated the conductivity tensor by calculating the wavefunctions of an electron in an electromagnetic field [31]. The spin-orbit interaction and the interaction of the electron with an electromagnetic wave were included as perturbations to the electron Hamiltonian. In his calculation Argyres makes a number of assumptions. Firstly, the spin-relaxation time is long compared to the optical frequency. Secondly the effect of the external magnetic field is not considered since it is insufficient to explain the larger effects observed in ferromagnetic materials. Third, the interaction between electrons and nuclei within the crystal can be represented by a periodic potential, so that the one-electron approximation can be applied. The Hamiltonian to be considered is then, with, H = H 0 + H + H, (3.19) H 0 = p2 2m + V (r), H = 4m 2 ( V p) σ, c2 H = e A p, (3.20) mc where H 0 represents the energy of the electron in absence of electromagnetic radiation and spin-orbit interaction and p is the momentum operator. H represents the spin-orbit interaction where σ is the spin operator. H describes the interaction of the electromagnetic radiation with the material where A is the vector potential of the electromagnetic field inside the material. Argyres calculated the eigenfunctions of H 0 and then considered

53 CHAPTER 3. EXPERIMENTAL TECHNIQUES 52 H as a perturbation to find the wavefunctions of H 0 + H. Finally H is considered as a time-dependent perturbation. Argyres calculated the current density in order to obtain the conductivity and polarisability tensors from which the polar Kerr and Faraday effects can be calculated. Arygyres also showed that the magneto-optical rotation and ellipticity are proportional to the magnetisation Higher-order magneto-optical effects So far the discussion has covered magneto-optical effects that are linear functions of the magnetisation, and that are sensitive to magnetisation parallel to the propagation axis of the probing light. In measuring the linear magneto-optical Kerr effect in this thesis, magneto-optical effects were observed that are proportional to the magnetisation in the second order. While these contributions were typically removed before analysis of the MOKE signal, they are discussed here for completeness. These effects are not nonlinear in the frequency of the incident radiation, rather they are proportional to higher orders of the magnetisation. MOKE is linearly proportional to the magnetisation, and reversing the magnetisation gives an opposite sign of the polarisation rotation and ellipticity. There are also effects that are proportional to a product of separate components of the magnetisation, and these will give the same sense of polarisation rotation regardless of the orientation of the magnetisation. The components of the magnetisation that are perpendicular to the propagation direction of light give rise to magneto-optical effects that are quadratic in the magnetisation, the Voigt [32] and Cotton-Mouton [33] effects, for example. Example data showing these effects can be found in chapter 4, in the magneto-optical measurements of the Heusler alloy Co 2 MnSi Measuring the magneto-optical Kerr effect Figure 3.2 shows a typical experimental arrangement for measuring the MOKE, with the coordinate axis defined such that xz is the plane of incidence and xy is the sample plane. The sample can be rotated about the z-axis (the surface normal) to investigate in-plane magnetic anisotropy, and when measuring films with perpendicular anisotropy the laser beam is aligned at normal incidence. There are three geometries for measurement of the MOKE, the longitudinal, transverse and polar MOKE geometries shown in Figure 3.3 (a), (b) and (c) respectively. The names refer to the relative alignment of the plane of incidence and the component of the magnetisation vector that is sensed. In longitudinal MOKE the detected component of

54 CHAPTER 3. EXPERIMENTAL TECHNIQUES 53 z y x Sample K E s Ep ε K Figure 3.2: Simple experimental geometry for a MOKE measurement. Θ K is the MOKE polarisation rotation, and ɛ K is the MOKE ellipticity. the magnetisation lies within the plane of the sample and the plane of incidence. In the transverse geometry the detected magnetisation is still within the plane of the film but is perpendicular to the plane of incidence. Finally, in polar MOKE the sensed magnetisation is perpendicular to the film plane and parallel to the plane of incidence. Longitudinal and polar MOKE are manifest as a change of either the polarisation rotation (Θ K ) and/or ellipticity (ε K ) in the reflected light. In transverse MOKE the effect is not in the polarisation of the reflected light but the intensity, ( I), and is only present for p-polarised incident light. In any given measurement one or more of these MOKE signals may be detected. This is particularly true in a time-resolved measurement where a precessing magnetisation is constantly changing orientation. In static and time-resolved measurements the orientation of the applied field and light beam can be adjusted to investigate the components of the magnetisation. For example consider coherent in-plane rotation of the magnetisation of a thin film. The longitudinal Kerr effect is sensitive to the component of magnetisation in the plane of the film and in the plane of incidence, so with the field applied in this orientation the MOKE signal will record a hysteresis loop from positive to negative saturation. If the field orientation is rotated 90 so that it is perpendicular to the plane of incidence, the longitudinal MOKE will sense the in-plane rotation of the magnetisation, with zero Kerr rotation at positive and negative saturation fields. This is particularly useful when looking for the hard and easy axes in a film that has weak anisotropy where hysteresis loops are very similar. When the field is applied parallel to the easy axis the switching will be fast, and only very sharp spikes at ±H C will be observed in the latter geometry. When the field is parallel to the hard axis the magnetisation reversal will typically be more gradual.

55 CHAPTER 3. EXPERIMENTAL TECHNIQUES 54 E s, E p K, ε K E p ΔI M M (a) Longitudinal (b) Transverse E s, E p M K, ε K (c) Polar Figure 3.3: The MOKE geometries, defined by the relative alignment of the detected magnetisation and the plane of incidence. In time-resolved MOKE measurements (discussed in detail later) the same approach can be used to separate the demagnetisation and precession signals. The demagnetisation will normally be along the approximate direction of the applied field, while the precession signal will be largest perpendicular to this direction. By applying the static field perpendicular to the plane of incidence, the demagnetisation is not detected by the longitudinal Kerr effect, while the precession is. In fact both orthogonal components of the precession are observed, by a combination of the longitudinal and polar Kerr effects. As a final example, the magnetisation of samples with perpendicular anisotropy is best investigated by setting the angle of incidence to zero and measuring the polar Kerr effect. Static MOKE measurements were typically performed using a 633 nm He-Ne laser with an active intensity stabilising system giving 0.01 % intensity stability [34]. With the intensity stabilisation system, magnetisation hysteresis loops can be obtained in seconds or minutes depending on the signal amplitude. Two electromagnets were used to supply a variable static field to the sample - an in-plane magnetic capable of supplying ±3 kg, and a perpendicular-to-plane magnet capable of supplying ±10 kg. Polarisation rotation/ellipticity was detected using an optical bridge detector, a schematic of which is

56 CHAPTER 3. EXPERIMENTAL TECHNIQUES 55 Photodiode Input beam Polarising beamsplitter s -pol Rotation axis p -pol Figure 3.4: Schematic diagram of the optical bridge detector. shown in Figure 3.4. Inside the detector a polarising beamsplitter (Glan-Thompson, CVI model CPBS) separates incident laser light into orthogonal linearly polarised components, denoted in the figure as s and p. For the Glan-Thompson polarising beamsplitter the angular separation of the two beams is independent of wavelength. Two photodiode detectors record the intensity of these beams, and amplification circuitry is used to determine the sum and difference signals. The detector is aligned so that light reflected from the sample is normally incident on the front face of the beamsplitter. To increase sensitivity the difference is nulled by rotating about the axis shown in Figure 3.4, so that an equal intensity is divided between the s and p polarisation modes. Typically then the detector is tilted at 45 to the plane of incidence, and s and p polarisation in the detector is not the same as s and p polarisation in the plane of incidence, hence the quotation marks. When the polarisation of the incident light is rotated by the net magnetisation of the sample the difference signal will change, and this signal is linearly proportional to the magnetisation. The sum signal is also monitored in order to check for transverse MOKE, to record the stability of the laser intensity during the measurement and also to measure nonmagnetic intensity changes in time-resolved experiments. To detect changes in ellipticity a quarter-wave plate is placed in the beam path before the detector with its fast axis parallel to major axis of the polarisation ellipse. The waveplate acts to convert the ellipticity to a rotation by adding a 90 phase delay between the orthogonal polarisation modes. Figure 3.5 shows two typical magnetisation hysteresis loops measured by MOKE. The two loops are measured for field applied parallel to the easy and hard axes of a Co 2 MnAl Heusler alloy film.

57 CHAPTER 3. EXPERIMENTAL TECHNIQUES K,S M S E a s y a x is H a rd a x is M O K E ro ta tio n (m d e g ) K,R M R H C -2 0 H S F ie ld (k G ) (a) Field parallel to the plane of incidence e a s y a x is h a rd a x is M O K E ro ta tio n (m d e g ) F ie ld (k G ) (b) Field perpendicular to the plane of incidence Figure 3.5: Example MOKE hysteresis loops from a Co 2 MnAl thin film. In (a) the field was applied parallel to the plane of incidence, and the coercive field (H C ), saturation field (H S ), remnant MOKE rotation (Θ K,R ) and saturation MOKE rotation (Θ K,S ) are indicated. In (b) the field was applied perpendicular to the plane of incidence and shows the component of magnetisation perpendicular to the field during switching. In this geometry the hard axis orientation can be clearly identified.

58 CHAPTER 3. EXPERIMENTAL TECHNIQUES 57 In all MOKE measurements care must be taken to accurately align the field, sample and plane of incidence in order to avoid non-magnetic contributions to the polarisation rotation. In general the reflectivity for s- and p-polarised light are not equal. From equation (3.9) if the incident polarisation is not accurately set as s or p the reflected polarisation will show a rotation that is independent of magnetisation. In static measurements where polarisation rotation is measured as a function of applied field this nonmagnetic artifact is easily removed as a constant offset since the reflectivity elements r pp and r ss are independent of magnetisation, but it is still good practice to optimise the alignment for consistency and repeatability. The reflection coefficients are modified by optical excitation, and so in time-resolved measurements the reflectivity breakthrough can mask the time-dependent magnetic signal. The reflectivity can swamp the magnetic signal, so accurate alignment is important. In all time-resolved measurements scans are recorded for opposite applied field, so that the nonmagnetic signal can be removed by taking their average Time-resolved magneto-optical Kerr effect measurements With a pulsed laser source, MOKE can be used to investigate dynamic magnetic phenomena with a time resolution determined by the width of the laser pulse [35, 36]. The current technology, and that used in this thesis, is Ti:sapphire mode-locked pulsed lasers with pulse widths of around fs. These pulses are capable of resolving ferromagnetic precession with frequency in the GHz range, and ultrafast sub-ps demagnetisation effects. In order to investigate dynamic magnetisation the sample must first be perturbed from magnetic equilibrium. This can be achieved by a magnetic field pulse that knocks the magnetisation away from the equilibrium effective field inside the material. The field is generated by a current pulse that is generated by an electronic pulse generator or a photoconductive switch triggered by a laser pulse, and which travels to the sample along micro-scale strip lines (eg [26, 37, 38]). These field pulses are typically of the order of 1 ns in length with fast sub-100 ps rise time. Magnetisation dynamics can also be induced optically by thermal [36] or nonthermal effects [39]. An intense light pulse can rapidly heat the sample reducing the magnetisation and anisotropy field and therefore reorienting the effective field acting on the magnetisation. Alternatively, circularly polarised light may transfer angular momentum to the magnetic system [2], or optical transitions may change the magnetic state of the sample [40]. In this thesis all time-resolved magneto-optical Kerr effect (TRMOKE) measurements are all optical with an intense pump laser pulse inducing magnetisation dynamics.

59 CHAPTER 3. EXPERIMENTAL TECHNIQUES 58 The specific mechanism of inducing precession is different in each case, and will be discussed in more detail in the experimental chapters, but is typically the result of a reduction in the anisotropy field due to ultrafast heating. All-optical measurements offer very high time resolution determined by the laser pulsewidth, and therefore sub-picosecond demagnetisation can be studied. Unlike field-pumped TRMOKE, the measurements do not require electrical contacts to the sample. The experimental arrangement, shown in Figure 3.6, is very similar to that of a static MOKE measurement with an amplified Ti:sapphire laser replacing the HeNe laser and with a second pump beam overlapped with the probe beam at the sample. The amplified ultrafast Ti:sapphire laser system consisted of a Verdi V-18 pump, Mira seed oscillator and RegA-9050 amplifier, all manufactured by Coherent Inc. The amplifier produced 50 fs pulses at a center wavelength of 800 nm with a maximum energy of 8 µj at a repetition rate of up to 250 khz. The output of the amplifier was separated into two beams by a beamsplitter, and in the majority of cases one of the beams was frequency doubled to 400 nm wavelength in an second harmonic generating crystal. The two-colour arrangement has a number of advantages over a single-colour experiment. For example a Ti:sapphire amplifier pump, 800nm probe, 400nm delay line det A bridge detector det B magnet polariser sample Figure 3.6: Typical TRMOKE experimental arrangement. In this example the 800 nm beam is used as the pump while the frequency doubled 400 nm beam is the probe. Time delay is set by a translation stage in the 800 nm beam path. The pump beam is typically at near normal incidence, while the angle of incidence of the probe can be varied to suit the material under investigation. Intensity and polarisation changes in the reflected probe beam are detected using a bridge detector.

60 CHAPTER 3. EXPERIMENTAL TECHNIQUES 59 band-pass filter can be used to remove pump light scattered from the sample that may enter the detector, and interference of the pump and probe beams when they are incident on the sample at the same time is avoided. In Figure 3.6 the pump wavelength is shown as 800 nm while the probe wavelength is 400 nm, but the reverse configuration was also used. The pump and probe beams were focused to overlap on the sample, with the time delay between the arrival of the pulses at the sample varied by a corner cube retroreflector mounted on a motorised linear translation stage in the 800 nm beam path. The 800 nm wavelength beam was always delayed since the corner cube was coated for high reflection at 800 nm. When the 800 nm wavelength pulse was swapped from the pump to the probe path the direction of the stage motion for increased time delay was reversed. The Newport IMS600CCHA stage has a 600 mm travel range with a resolution of 0.1 µm, which for a double-pass gives a maximum possible time delay of 4 ns and a resolution of 1 fs. The probe beam was typically s-polarised, while the polarisation of the pump beam could be set as s, p or circular using a combination of a polariser and a quarter wave plate. The Glan-Laser calcite polarisers (Thorlabs model GL10) had a high extinction ratio (100,000:1) and were suitable for use with the high pulse intensities experienced. The polarisers were placed as close to the sample as possible to avoid the polarising effects of other optical components. The pump and probe beams were focused to overlap on the sample, with the probe beam focused to a smaller size than the pump, and overlapped with the centre of the pump beam. The Gaussian intensity profile of the laser spot means that there will be a variation in temperature rise over the spot diameter. With a smaller probe diameter the experiment is sensitive to a homogeneously excited region at the centre of the pump spot. Typical pump and probe spot diameters used in the experiments were 150 and 50 µm respectively. Also the intensity of the probe pulse was kept far lower than that of the pump so that the excitation due to the probe pulse was negligible compared to that due to the pump. The size and overlap of the focused pump and probe spots was monitored initially by focusing the beams directly on to a CCD beam profiler (DataRay WinCAM-D UCD12). This camera, with 4.6 µm pixel size, can resolve focused laser spots down to µm in diameter, and is an accurate and reliable means to check for accurate focusing and overlap of the two spots. More details on this and some example beam profile measurements are shown in the following section on measuring laser spot sizes. With a sample in place the overlap of the pump and probe spots on the surface was monitored by a high magnification CCD camera, with fine adjustments to the overlap made by small translations of the

61 CHAPTER 3. EXPERIMENTAL TECHNIQUES 60 focusing lens in the pump beam while monitoring the peak signal. The sample was mounted between the poles of an electromagnet whose geometry depends on the magnetisation of the sample to be studied. Figure 3.6 shows a electromagnet used to apply a field parallel to the plane of the magnetic film. The field can be rotated to any angle about the normal to the sample surface, and the sample can also be rotated through 360 about it s surface normal. An electromagnet used to apply a field perpendicular to the film surface was also used. The angle of incidence of the pump and probe beams can also be varied. In some cases the angle of incidence was limited by the focusing optics and the geometry of the electromagnet. Figure 3.6 shows a setup for measuring a sample with in-plane magnetisation, with the angle of incidence of the probe beam set to 45. Larger angles of incidence typically give a greater sensitivity to the in-plane magnetisation. The angle of incidence of the pump beam is less important when the pumping mechanism is laser heating, but is kept close to normal to maintain a more circular focused spot on the sample surface. In time-resolved MOKE experiments where small angle magnetisation precession is excited is typically of the order of several mdeg only. In addition the the pulsed laser source gives rise to increased intensity noise. Therefore a phase-sensitive detection technique must be used. The pump intensity is modulated at a known frequency by a mechanical chopper, and lock-in amplifiers are used in the Kerr-rotation and reflectivity channels. In this arrangement a Kerr rotation as small as 10 µdeg can be detected. Measuring ultrafast demagnetisation As a result of the heating by the pump laser pulse the magnetisation of the sample can be reduced on a sub-picosecond timescale. This demagnetisation is detected as a sharp peak close to zero time-delay between pump and probe pulses in the TRMOKE signal. The fractional demagnetisation can be determined by comparison of the height of this peak with static hysteresis loops measured by the same probe beam. As always when performing TRMOKE measurements the signal should be recorded for opposite field orientations and averaged, to removed non-magnetic contributions to the polarisation rotation. Figure 3.7(a) shows an example of a TRMOKE scan from a Co 2 MnSi Heusler alloy film (see chapter 4) made with a 5.3 mj/cm 2 at short time delays around the peak signal. At negative time delay the probe pulse is arriving at the sample before the pump pulse. The signal here should be flat and show no offset from zero Kerr rotation if no artifacts are present. Just after the overlap in time of the pump and probe pulses the signal will reach

62 CHAPTER 3. EXPERIMENTAL TECHNIQUES 61 it s peak magnitude, in this case at a time delay of about 650 fs. At these short time delays the magneto-optical response of the sample may be affected by purely electronic effects [35], and so MOKE signal must be interpreted carefully. Measuring the true ultrafast demagnetisation is often not as straight forward as comparing this peak height with the saturation Kerr rotation of a room temperature hysteresis loop. Figure (b) shows the positive time delay data of (a) plotted on a logarithmic time scale, and two separate exponential decays can clearly be seen. It could be assumed that the initial decay is the signature of some thermalisation processes in the film between electron, spin and lattice systems, while the longer decay is the result of cooling of the thermalised system. The sharp peak is unlikely to affect the magnetisation precession at GHz frequencies and in this case the demagnetisation is measured at the time delay where there is a sharp transition between the two exponential decays. The demagnetisation can also be determined by measuring a hysteresis loop at the time delay that corresponds to the peak signal in a TRMOKE scan. Figure 3.8(a) shows three polar MOKE hysteresis loops from a CoNi/Pt thin film, one made in the absence of a pump pulse (black), and two following excitation by a pump laser pulse (red) and more intense pump pulse (green). The height of the red hysteresis loop is reduced compared to that of the black loop due to the demagnetisation of the film. The green loop shows no hysteresis at all, implying that full demagnetisation has been achieved. For K e rr ro ta tio n (m d e g ) (a ) K e rr ro ta tio n (m d e g ) F ie ld (k O e ) K e rr ro ta tio n (m d e g ) 1.2 (b ) T im e d e la y (p s ) T im e d e la y (p s ) Figure 3.7: An example of a TRMOKE measurement of ultrafast demagnetisation, in this case for a Co 2 MnSi thin film, made with a 5.3 mj/cm 2. The inset to (a) shows a room temperature hysteresis loop recorded by the probe beam in the TRMOKE experiment.

63 CHAPTER 3. EXPERIMENTAL TECHNIQUES 62 M O K E ro ta tio n (m d e g ) M O K E ro ta tio n (m d e g ) N o p u m p 1.3 m J /c m m J /c m p u m p p u m p M a g n e tic fie ld (k G ) M a g n e tic fie ld (k G ) (a) Polar MOKE hysteresis loops (b) Polar AC-MOKE hysteresis loops Figure 3.8: Polar MOKE, (a), and AC-MOKE, (b), hysteresis loops measured from a CoNi/Pt multilayer film with and without excitation by a pump laser pulse. The black loops represent the equilibrium magnetisation, while the red and green loops show the reduction of the magnetisation by increasing intensity pump excitation. demagnetisations of just 1 2 % the change in loop height may be too small to resolve from the noise. Hysteresis loops can be measured with the lock-in amplifiers with modulated pump pulses that show the effect of the pump on the hysteresis, which shall be termed AC-MOKE. The increased sensitivity allows for measurement of much smaller changes in the magnetisation, and reduction of the coercive field can also be measured. While modification of the magneto-optical response may occur at high temperature, the approach is very useful when searching for full demagnetisation. Figure 3.8(b) shows an example of demagnetisation measured using AC-MOKE loops, with the same legend scheme as figure 3.8(a). More details of the ultrafast demagnetisation of this sample can be found in chapter 6. Measuring ferromagnetic resonance Figure 3.9 shows a typical TRMOKE scan showing a periodic oscillation of the Kerr rotation. Again at the beginning of the scan a short region of negative time delay, where the probe pulse arrives at the sample before the pump pulse, is recorded to check for offset from zero. Following the overlap in time of the pump and probe pulses the signal reaches a peak before decaying as the delay of the probe pulse relative to the pump pulse is increased. Note that this example does not show a particularly clear demagnetisation background, since the oscillation signal is comparatively large and the time-delay steps

64 CHAPTER 3. EXPERIMENTAL TECHNIQUES Figure 3.9: A typical time-resolved MOKE scan, showing an exponentially damped oscillatory signal characteristic of damped ferromagnetic resonance. are too large. The signal is fitted to an exponentially damped oscillatory function (red curve), with the exponential envelope indicated (dashed blue curve) Measuring laser spot sizes It is vitally important to know the absolute sizes of the pump and probe spots to calculate incident fluence, and to monitor the relative sizes to ensure that the probe spot is significantly smaller than the pump spot. The spot diameter, d, can be estimated by knowing the focal length of the focusing lens, f, and the beam divergence of the incident beam, θ, by, d = fθ. (3.21) Therefore the spot size can be reduced by using a shorter focal length lens and/or by reducing the beam divergence. The beam divergence can be reduced by expanding the beam with a telescope, and this has been applied in some cases when particularly small spots are required. This gives only an estimate of the spot size, so it is necessary to accurately determine the spot sizes and to monitor their overlap. A scanning pinhole beamprofiler was constructed using a 5 µm pinhole and 3 linear translation stages in an xyz configuration. By scanning the pinhole over the focused spot and measuring the transmitted light intensity images of the intensity profile and spot

65 CHAPTER 3. EXPERIMENTAL TECHNIQUES u n its ) ty (a rb. In te n s i x - a x is F W H M m ) y - a x is F W H M = µm ) m (m 0.2 A x is (m A x is X Y In te n s ity ( a r b. u n its ) = 8 0 µm (a) 3D intensity profile W id th ( m m ) 0.5 (b) 2D profile Figure 3.10: (a) Intensity profile and (b) x- and y-axis slices through the peak intensity of an 800 nm wavelength pulsed laser focused by an f = 150 mm lens, measured by a scanning pinhole beamprofiler. The FWHM spot diameter is µm its ) rb. u n s ity ( a In te n A x is (m m ) m ) X Y A x is (m In te n s ity ( a r b. u n tis ) x - a x is, F W H M = 5. 6 µm y - a x is, F W H M = 4. 4 µm (a) 3D intensity profile W id th ( m m ) (b) 2D profile Figure 3.11: (a) Intensity profile and (b) x- and y-axis slices through the peak intensity of an 400 nm wavelength pulsed laser focused by an f = 63 mm doublet lens following expansion by a 10 beam expander, measured by a scanning pinhole beamprofiler. The FWHM spot diameter is µm2.

66 CHAPTER 3. EXPERIMENTAL TECHNIQUES 65 size were obtained. Measurements were also taken of the depth of focus by scanning the pinhole along the propagation direction of the incident beam. Figures 3.10 and 3.11 show profiles of the focused 800 nm wavelength fundamental and 400 nm wavelength frequency-doubled outputs of the RegA pulsed laser amplifier respectively. The x- and y-profiles shown in (b) were fitted by a Gaussian function in a LabVIEW virtual instrument to measure the FWHM and 1/e 2 spot diameters. These profiles show typical spot sizes used in TRMOKE experiments. Here the 800 nm wavelength beam was used as the pump and focused by an f = 150 mm lens to a µm 2 FWHM spot, while the 400 nm wavelength beam was used as the probe and focused by a f = 63 mm doublet lens following expansion by a 10 beam expander to a spot of 5 µm FWHM diameter. With acquisition times of 20 minutes per image the regular use of the scanning pinhole beamprofiler as a tool to aid reliable and repeatable experimental alignment is limited. It has proven very useful in measuring spot sizes and focal depths, but a device that can produce spot images in real time is required to be of real benefit to experiments in the long term. CCD camera-based beam profilers with micron-sized pixels can produce spot images with near video rate refresh rates. The disadvantage is a lower spatial resolution than scanning pinhole systems, but this is far outweighed by the advantage gained by real time acquisition. The CCD beam profiler used in this thesis is a DataRay WinCAM-D UCD12, with a mm 2 CCD with pixel size of 4.6 µm. With an image refresh rate of 5 Hz, the spots could be observed in real time, enabling fast and accurate positioning of the (a) 3D intensity profile (b) 1D profile slice Figure 3.12: Adjacent pump and probe spot profiles measured simultaneously by a CCD camera beam profiler. The larger spot is the 800 nm pump spot, focused by a f = 150 mm lens, and the smaller spot is the 400 nm probe spot focused by a f = 63 mm lens.

67 CHAPTER 3. EXPERIMENTAL TECHNIQUES 66 Figure 3.13: An example of a beam wander measurement of the 400 nm wavelength probe beam measured by a CCD beam profiler. Over a period of a few minutes the focused spot moves an average 0.6 µm from the mean position. focus. The pump and probe spots could be imaged simultaneously to ensure good overlap at the focus position. Figure 3.12 shows adjacent 800 nm wavelength pump and 400 nm wavelength probe spots focused on to the CCD detector. Since short focal length lenses have a small depth of focus the use of a CCD as an alignment tool is essential in order to maintain consistent spot sizes, and therefore laser fluence, from sample to sample. The CCD camera also allowed measurement of beam position stability by plotting the peak intensity position over an extended time period. Figure 3.13 shows the movement of a focused 400 nm wavelength spot, which over a period of a few minutes moves an average of 0.6 µm from the mean position. The CCD beamprofiler quickly established itself as an essential tool in all-optical TRMOKE measurements.

68 CHAPTER 3. EXPERIMENTAL TECHNIQUES Magnetic second harmonic generation All materials show some degree of nonlinearity in their response to applied optical fields, and whilst linearity can be an extremely accurate approximation there are a host of important optical and magneto-optical effects that only exist due to nonlinearities. With the invention of the laser and then pulsed laser sources and the associated high electric field intensities there has been a great deal of interest in all manner of nonlinear effects. Second harmonic generation (SHG) has been used as a surface-sensitive probe for over 20 years [25], with early work showing that surface and bulk contributions to SHG can be of the same order of magnitude [41] while surface SHG can dominate bulk contributions in centrosymmetric media [42]. That SHG could be used as a probe of surface magnetisation was proposed in 1989 by Ru-Pin Pan et al. [43] and by W Hübner and H K Bennemann [44], and first measured in 1991 by J Reif et al. [45]. In the following sections the background of second harmonic generation, specifically from cubic crystals, is presented. The origin of surface symmetry for centrosymmetric media is described, and the origin of magnetisation sensitivity is explained. The explanations are mainly based on symmetry arguments, with microscopic theories covered briefly Second harmonic generation Theories of SHG based on the symmetry of the medium and the associated nonlinear susceptibility tensor have been presented by several authors, with several review articles and books covering the following discussion [46 50]. For weak deviations from linearity and with a single frequency incident optical electrical field the induced electrical polarisation can be expanded as a power series in higher order harmonics as, P = P (1) (ω) + P (2) (2ω) + P (3) (3ω) +... = χ (1) E(ω) + χ (2) E(ω) 2 + χ (3) E(ω) (3.22) The first term gives the linear optical electrical polarisation (it is within this term that the MOKE can be found), while the second and third terms give second and third harmonic generation respectively. It should be noted at this point that, in this discussion, nonlinear magneto-optical effect refers to nonlinearity of the optical response, not to the order of the magnetisation response. We shall look now in more detail at the induced second harmonic polarisation, which can be expressed as,

69 CHAPTER 3. EXPERIMENTAL TECHNIQUES 68 P i (2ω) = χ (2),d ijk E j (ω) E k (ω) + χ (2),q ijkl E j (ω) k E l (ω) +... (3.23) with the superscript d referring to the dipolar contribution and q to the quadrupolar contribution. It is a property of any material tensor that it remain invariant under any valid symmetry operation. The inversion symmetry operations reverses the sign of all polar vectors including the polarisation and electric field vectors, and when this is applied to the equation above this gives, P i (2ω) = χ (2),d ijk E j (ω) E k (ω) χ (2,q) ijkl E j (ω) k E l (ω) +... (3.24) which can only be satisfied if χ (2),d ijk is zero. Therefore electric dipole second harmonic generation (SHG) is forbidden when inversion symmetry applies, while quadrupolar SHG is allowed. In cubic crystals inversion symmetry is allowed in the bulk but broken at surfaces and interfaces, and therefore dipolar SHG can be used as a surface-sensitive probe in cubic crystals. While the quadrupolar contributions are weaker than the dipolar term, the large volume difference between the bulk and interface regions means that the quadrupole contribution to the total SHG is not necessarily negligible. P Guyot-Sionnest et al. present a theory of the contributions to SHG from surfaces and interfaces [42]. They show that in the case of centrosymmetric media with a high dielectric constant such as metals the surface contribution to SHG should dominate. Surface sensitivity is demonstrated in several experiments by the large effect of surface adsorbates [51, 52] Anharmonic oscillator model of SHG Just as the classical harmonic oscillator was used as a simple model of linear magnetooptical effects, a classical anharmonic oscillator can describe the nonlinear response [46, 47, 53]. For intense optical electric fields, and therefore for large amplitude oscillations, the anharmonicity of the electron oscillators must be taken into account. The equation of motion for an electron driven by an optical electric field is then, d 2 r m e dt dr τ dt + m eω0r 2 + ar 2 = ee (t), (3.25) where m e is the electron mass, τ is the electron relaxation time, ω 0 is the natural frequency, and a represents the degree of nonlinearity. When the anharmonicity is small the ar 2 term can be considered as a perturbation, with the solution,

70 CHAPTER 3. EXPERIMENTAL TECHNIQUES 69 r(t) = r (1) (t) + r (2) (t) +... (3.26) The first-order solution is the same as that given in the discussion of the linear Kerr effect. The second-order solution is then obtained by approximating the anharmonicity ar 2 by ar (1)2, where r (1) is the first order solution. For a single frequency driving force the second order solution is, r (2) (2ω) = a (e/m e ) 2 E 2 ( ω 2 0 ω 2 iω/τ ) 2 ( ω 2 0 4ω 2 i2ω/τ ) e i2ωt, (3.27) with oscillation at twice the incident optical frequency. This oscillation gives a polarisation at 2ω, that leads to reflection at the second harmonic frequency Symmetry arguments and the nonlinear susceptibility tensor Simple symmetry arguments can be applied to determine the nonzero elements of the susceptibility tensor, allowing a qualitative prediction of the outcome of SHG measurements in various experimental geometries. The surface under consideration will have a number of allowed symmetry operations and only those tensor elements which are invariant under all operations can be nonzero. In some cases these operations can simplify the tensor representation dramatically. The symmetry operations are applied according to, χ i j k = T i it j jt k kχ ijk, (3.28) where the T represent the one dimensional symmetry operations. For inversion symmetry T i i = T j j = T k k = 1, and therefore χ i j k = χ ijk, which is only satisfied if χ ijk = 0. The second order dipolar susceptibility tensor is a rank-3 tensor, and so is represented as a matrix. When a single frequency incident optical E field is used, χ ijk χ ikj, and the tensor representation can be reduced to a 3 6 matrix, with the second harmonic polarisation given by,

71 CHAPTER 3. EXPERIMENTAL TECHNIQUES 70 P x (2ω) P y (2ω) P z (2ω) = χ xxx χ xyy χ xzz χ xyz χ xzx χ xxy χ yxx χ yyy χ yzz χ yyz χ yzx χ yxy χ zxx χ zyy χ zzz χ zyz χ zzx χ zxy Ex 2 Ey 2 Ez 2 2E y E z 2E x E z. (3.29) 2E x E y Pan et al. give the nonzero elements of the susceptibility tensor of isotropic and cubic surfaces [43]. An isotropic surface has very high symmetry with any angular rotation about the surface normal allowed and an infinite number reflection planes. Let the surface define the xy plane, with the z-axis normal to the plane. Then reflections in the yz and xz planes are represented respectively by, , (3.30) For example, reflection in the yz-plane changes the sign of the x-index, and therefore χ xxx = χ xxx, and therefore χ xxx must be zero. On the other hand, χ zxx = χ zxx, and therefore χ zxx is nonzero. In fact all elements with an odd number of x and/or y indices must be zero, leaving only 5 nonzero elements in the 3 6 representation of χ (2), χ xzx χ yyz 0 0 χ zxx χ zyy χ zzz (3.31) In addition some of these elements are equivalent, with the equivalent terms found by applying the rotational symmetry operation. A rotation of any angle leaves an isotropic surface unchanged, meaning that the x and y indices are equivalent, and so χ zxx = χ zyy, and χ xzx = χ yzy. Therefore for the case of an isotropic surface the second order susceptibility tensor is reduced to just 5 nonzero elements (or 7 if the permutations χ xzx χ xxz and χ yzy χ yyz are considered), with three independent values. Consider now a cubic (001) surface which has four reflection planes and fourfold rotational symmetry. The operations below represent a fourfold rotation about the z-axis, reflection in the [100] plane and reflection in the [110] plane respectively,

72 CHAPTER 3. EXPERIMENTAL TECHNIQUES , , (3.32) Application of these symmetry operations leaves the nonzero elements as, χ xzx χ yyz 0 0 χ zxx χ zyy χ zzz 0 0 0, (3.33) which is the same as the result for the isotropic surface. Therefore an isotropic second harmonic optical response is expected from the cubic (001) surface. When a net magnetisation is introduced the symmetry of the surface is reduced, leading to extra nonzero elements in the nonlinear susceptibility tensor and therefore further contributions to the SHG Magnetic second harmonic generation In 1989 it was proposed [43, 44] that MSHG could be employed as a surface sensitive probe of magnetism, which was later confirmed by experiment in 1991 [45]. Kirilyuk and Rasing present a good summary of magnetically-induced SHG [50], and several authors have contributed to the text Nonlinear Optics in Metals, edited by H K Bennemann [54]. A new term in the expansion of the induced electrical polarisation can be added that contains the static magnetisation in the dipole approximation, P i (2ω) = χ (3),d ijkl E j (ω) E k (ω) M L, (3.34) where M L is the magnetisation component. The magnetisation is an axial vector that does not change sign under the inversion symmetry operation, and therefore this term also does not allow SHG from the bulk of a cubic lattice. The magnetic and nonmagnetic contributions to the total dipolar SHG can be combined to a single dipolar MSHG susceptibility tensor, χ (2),d ijk = χ (2),d ijk + χ (3),d ijkl M L. (3.35) The first term is a crystallographic contribution to the SHG, while the second term is magnetically-induced second harmonic generation. The magnetisation sensitivity arises from the breaking of time reversal symmetry in some of the symmetry operations. The

73 CHAPTER 3. EXPERIMENTAL TECHNIQUES 72 (010) (100) M [100] z, [001] y, [010] x, [100] Figure 3.14: The cubic (001) surface with magnetisation parallel to the [100] axis and with (100) and (010) mirror planes indicated. An effective current loop responsible for the magnetisation is shown. magnetisation can be pictured to be the result of a current loop perpendicular to the magnetisation vector, and it is the symmetry of this current loop that must be considered. Pan et al. [43] also give the nonzero elements for a cubic (001) surface with magnetisation parallel to a number of principle axes. A net magnetisation reduces the symmetry of the surface and allows further nonzero elements in the second order susceptibility tensor. Consider first the case of the net magnetisation parallel to the [100] axis of the (001) cubic surface, shown in Figure The fourfold rotational symmetry is no longer allowed, leaving only reflection in the (100) and (010) planes (or equivalently a two-fold rotation). Reflection in the (100) plane does not affect the magnetisation direction, while reflection in the (010) plane requires reversal of the magnetisation as the helicity of the current loop is reversed. The valid symmetry operations are, - reflection in (100) plane: , (3.36) - reflection in (010) plane with M M: (3.37) The nonzero elements of χ (2),d ijk are the same as those for the nonmagnetic surface, though with the lowered rotational symmetry the equivalence of some elements is removed. The

74 CHAPTER 3. EXPERIMENTAL TECHNIQUES 73 nonzero elements for χ (3),d ijkl can be derived in much the same way as for a nonmagnetic surface, so long as care is taken to correctly analyse the symmetry of the magnetisation. χ (3),d ijkl is a rank-4 tensor, represented by a ( ) matrix. This can be reduced to a rank-3 form by noting that M L = M x for M parallel to the [100] axis, and can reduced further to a (3 6) form since χ ijkl χ ikjl. The symmetry operations can then be applied to this matrix whose elements have 4 indices. Reflection symmetry in the (001) plane gives x x, y y, z z, and X X where X is the component of the magnetisation. This forbids all elements with an odd number of x indices. Reflection symmetry in the (100) plane gives x x, y y, z z, and X X since the magnetisation is reversed. This operation forbids all elements with zero or an even number of y indices. The remaining elements of χ (3),d ijkl are then, χ xxyx χ yxxx χ yyyx χ yzzx (3.38) χ zyzx 0 0 When combined with the non-magnetic elements using equation (3.35) the dipolar MSHG susceptibility tensor for M parallel to [100] is, χ + xzx χ xxy χ yxx χ yyy χ yzz χ + yyz 0 0 χ + zxx χ + zyy χ + zzz χ zyz 0 0, (3.39) where the + and - superscripts denote tensor elements that are even and odd functions of the magnetisation. Consider next the case of M parallel to the [110] axis. The symmetry operations in this case are a reflection about in the (110) and (110) planes, with M M for the latter reflection. Applying these operations gives for the susceptibility tensor, χ xxx χ xyy χ xzz χ + xyz χ + xzx χ xxy χ yxx χ yyy χ yzz χ + yyz χ + yzx χ yxy χ + zxx χ + zyy χ + zzz χ zyz χ zzx χ + zxy. (3.40) Table 3.1 gives the nonzero elements for the magnetised cubic (001) surface, reproduced from Pan et al. [43]. This qualitative knowledge of the nonlinear susceptibility tensor allows one to design an experiment to measure the contributions to the MSHG, and to predict the basic polarisation dependence. The second harmonic intensity will be a function of the magnetisation,

75 CHAPTER 3. EXPERIMENTAL TECHNIQUES 74 Table 3.1: Nonzero elements of the dipolar MSHG susceptibility tensor for a cubic (001) surface Nonzero tensor elements, χ ijk Orientation of M Even Odd [100] [110] [001] xzx = xyz, yzy = yyz, zxx, zyy, zzz xyz = xzy = yzx = yxz, xzx = xxz = yzy = yyz, zxx = zyy, zzz, zxy = zyx xzx = xxz = yzy = yyz, zxx = zyy, zzz xyx = xxy, yxx, yyy, yzz, zyz = zzy xxx = yyy, xyy = yxx, xzz = yzz, xxy = xyx = yxy = yyx, zxz = zzx = zyz = zyy xyz = xzy = yzx = yxz, zxy = zyx and by limiting the incident fundamental and detected second harmonic polarisations the different elements of the susceptibility tensor can be detected Measuring magnetic second harmonic generation There are different measurement geometries in MSHG analogous to the MOKE geometries in Figure 3.3, in which the MSHG may be manifest in different ways. In the longitudinal and polar geometries the polarisation of the second harmonic light is rotated as a function of the magnetisation of the sample, with very large polarisation rotations reported [55]. In the transverse geometry the intensity of the second harmonic light changes as a function of the magnetisation. In this thesis all MSHG measurements were performed in the transverse geometry, where the detected second harmonic intensity, I 2ω, is proportional to the susceptibility tensor by [50], I 2ω (±M) Ein 4 [ χ χ 2 ] ± 2χ + χ. (3.41) where E in is the incident optical electric field. The MSHG signal is the result of interference of odd and even elements of the second harmonic susceptibility tensor, and the intensity is magnetisation dependent. By measuring the SH intensity as a function of applied field strength, interface sensitive hysteresis loops are recorded. A reliable and repeatable quantity in these measurements is the MSHG asymmetry, A, defined as the ratio of MSHG loop height to the average MSHG intensity,

76 CHAPTER 3. EXPERIMENTAL TECHNIQUES 75 A = I(+M) I( M) I(+M) + I( M), (3.42) where I is the second harmonic intensity. We have defined the difference in MSHG asymmetry for magnetisation parallel to two principal axes, for example the [100] and [110] axes, as the MSHG anisotropy, MSHG anisotropy = A ([110]) A ([100]). (3.43) MSHG measurements were performed using the same amplified Ti:sapphire pulsed laser source as in TRMOKE measurements, with the set up shown in Figure The 800 nm wavelength output from the RegA amplifier was focused on to the sample to increase intensity and therefore the efficiency of second harmonic generation. The second harmonic light in the reflected beam was separated from the fundamental beam and the intensity detected by a sensitive photon counting system. The fundamental (λ = 800 nm) and second harmonic (λ = 400 nm) beams were separated by one of two methods. The first method used dispersive prims to spatially separate the beams by the difference in their refractive indices, as shown in Figure This was a very effective method of separating the beams and was used with great success. However the prisms have a disadvantage in that their transmission is polarisation dependent, with transmission of s-polarised light far lower than that for p-polarised light. To avoid this potential complication a second method of separating the beams used dichroic mirrors that had a very high reflectivity at 400 nm wavelength and high transmissivity at 800 nm wavelength. By using a number of these mirrors in series the intensity of the reflected fundamental light in the second harmonic beam path could be greatly reduced, and the mirrors could be used in place of the prisms without an increase in the background count level. A setup with the dichroic mirrors is shown in Figure The weak second harmonic light was detected by a photomultiplier tube (PMT) and digital counting system. The detection of background light was reduced by a spatial filter in front of the PMT and shrouding of the beam path. A fundamental (800 nm) bandpass filter was placed before the sample to reduce the intensity reaching the detector of second harmonic light that was generated in components before the sample (for example in the waveplate, polariser and the laser cavity). Signal to noise was increased by taking the average of several readings and by tuning the measurement time and interval settings of the digital counting system. The background count rate was measured by removing the focusing lenses so that no (or at least extremely reduced) SH light arrived at the PMT from

77 CHAPTER 3. EXPERIMENTAL TECHNIQUES 76 the sample. Typical background count rates of counts/s were obtained, compared with experimental signals in the range of several hundreds to thousands cps. Four main combinations of incident fundamental and reflected second harmonic polarisation were typically measured: p-incident to p-second harmonic (p-p), p-incident to s-second harmonic (p-s), s-incident to p-second harmonic (s-p), and s-incident to s- second harmonic (s-s). Note the abbreviations used for the incident fundamental (lower case) and reflected second harmonic (upper case) polarisations. To investigate anisotropy of the MSHG response the sample was rotated about the normal to its surface with the applied field fixed perpendicular to the plane of incidence. Two Cartesian coordinate systems must be considered. The first is the system discussed so far, that of the sample lattice. The second is a laboratory reference frame, (x,y,z ). Then the optical E-field in the sample frame is related to the E-field in the laboratory frame by, E x E y E z = cos φ sin φ 0 sin φ cos φ E x E y E z, (3.44) Ti:sapphire amplifier H L s x p x H T λ/4 plate f 800 nmpass filter y S y P polariser analyser magnetic field PMT 400 nmpass filter Figure 3.15: Experimental arrangement for recording magnetic second harmonic generation. The inset shows the orientation of the coordinate systems of the crystal lattice, (x,y,z), and the laboratory frame, (x,y,z ), for a sample rotated about its surface normal by an angle φ. The longitudinal (H L ) and transverse (H T ) field orientations are also shown.

78 Microstat He CHAPTER 3. EXPERIMENTAL TECHNIQUES 77 optical cryostat dichroic mirrors to PMT analyser 400nm-pass filter magnetic field polariser 800nmpass filter λ/4 plate Ti:sapphire amplifier Figure 3.16: Experimental arrangement for recording the temperature dependence of magnetic second harmonic generation. The sample is mounted in an optical cryostat, and the plane of incidence is rotated to the vertical to accommodate the cryostat and electromagnet. where φ is the rotation angle (see Figure 3.15, inset). It is now possible to determine a measurement geometry that will probe the lowest number of tensor elements. Firstly the magnetisation should be parallel to the [100] axis, and secondly the rotation angle of the sample should be 0. The incident E-field should be s-polarised, so E(ω) = E x (ω) = E x (ω), and only s-polarised second harmonic light should be detected, P(2ω) = P x (2ω) = P x (2ω). Then with field H T (see figure 3.15 inset) equation (3.29) becomes, P x (2ω) = E 2 x , (3.45) where - indicates a tensor element that is not necessarily zero but is not sensed in this measurement geometry. In this geometry no SHG is predicted by symmetry analysis. In fact s-polarised SHG was not seen in any measurements performed in this thesis. It may be the case that s-polarised SHG is much weaker than p-polarised SHG and that it fell below the measurable threshold of this experiment. By limiting the polarisation of the incident fundamental light and measured second harmonic, the sensed elements of the

79 CHAPTER 3. EXPERIMENTAL TECHNIQUES 78 nonlinear susceptibility tensor can be reduced. The example above is the extreme case, since in general more elements contribute to the measured MSHG signal as φ is increased or if p-polarised light is used. For temperature dependent measurements the sample was mounted inside an optical cryostat (Oxford Instruments Microstat HE). The outer vacuum chamber has optical access through windows that have a low Verdet constant in order to prevent a Faraday rotation of the polarisation of the transmitted light. The cryostat-based MSHG experimental arrangement is shown in Figure There are some practical issues that determine this arrangement since the cryostat must be installed vertically due to the geometry of the rigid liquid-he transfer line. With the vertical cryostat the static field must be applied in the horizontal direction, and therefore the plane of incidence must be vertical for the transverse measurement geometry.

80 CHAPTER 3. EXPERIMENTAL TECHNIQUES X-ray Magnetic Circular Dichroism While x-ray measurements have not formed a major part of my work in this thesis, they have been used in tandem with our studies of the Co-based Heusler alloys fabricated by the group at Tohoku University in Sendai, Japan. I worked with Dr N D Telling at the Advanced Light Source in Berkeley, California, where x-ray magnetic circular dichroism (XMCD) was used to measure the near-interfacial magnetisation in these materials. The results of these studies are of interest to the core material of this thesis, and provide a useful comparison to my own magnetic second harmonic generation measurements in chapter 5. For this reason the basic principles of the technique are described here. The term dichroism here refers to the difference in the resonant absorption of circularly polarised x-ray photons by a magnetic sample with reversed magnetisation. The circularly polarised x-ray photons act as a probe of the magnetic state of the material, specifically of the valence electrons. The technique is element specific since the absorption energies are specific to different chemical species. The requirement for intense, polarised and x-rays of tunable energy means that x-ray absorption spectra (XAS) and XMCD experiments are typically performed at a synchrotron light source, such as the Advanced Light Source in Berkeley, California. In this section XAS will be briefly described, followed by more detail on the origin of magnetic sensitivity and how the technique can be used to probe a near interfacial region. The information in these sections was obtained from several texts [11, 56] and through several enlightening discussions with Dr Telling X-ray absorption spectroscopy An x-ray photon is absorbed when its energy is equal to or greater than the binding energy of a core electron, generating a photo-excited electron. When the x-ray photon energy is equal to the core level binding energy there is a sharp peak in the absorption called an absorption edge. Since the binding energies are different for different atomic elements, tuning the x-ray energy allows for element specific measurements of absorption. The intensity of the absorption peaks is proportional to the density of available states in the valence band, as well as the intensity of the incidence x-rays. An example of an XAS spectra obtained for Co is shown in Figure This figure shows XAS spectra taken for opposite magnetisation orientations, which will be covered in the next section. The x-ray absorption coefficient can be measured directly as the loss of x-ray intensity transmitted through the sample, however this is not always practical and does not

81 CHAPTER 3. EXPERIMENTAL TECHNIQUES 80 X M C D (a rb.) D ra in c u rre n t (a rb.) X A S X M C D L 3 L 2 + M -M A v e ra g e X -ra y p h o to n e n e rg y (e V ) Figure 3.17: An example of XAS and XMCD spectra measured at the Co L 3 and L 2 absorption edges. XAS are measured for positive and negative saturated magnetisation, with the XMCD given by their difference. Also shown is the average XAS (green). Continuum states Continuum states M L K Figure 3.18: Decay mechanisms following resonant absorption of an incident x-ray photon. In both cases an electron from a higher energy levels loses energy and falls into an empty core level. In x-ray fluorescence, on the left, the energy is emitted as a photon. In Auger-electron emission, on the right, the energy causes the emission of a secondary electron.

82 CHAPTER 3. EXPERIMENTAL TECHNIQUES 81 allow for interface-sensitive measurements. The absorption can be detected indirectly by probing the relaxation mechanism of the material, of which there are two main processes, illustrated in Figure In the first process a higher energy electron loses energy to fill the available core state, emitting a photon. The energies of the emitted photons can be measured, and are specific to the atom under study. The second relaxation process is the Auger effect, in which the transition of an electron to fill the core level causes the emission of a shower of lower energy secondary electrons. In some cases the secondary electrons may be ejected from the sample completely, in which case a drain current can be detected through the sample. Since the escape length of the secondary electron is 2 3 nm only, measurements of the drain current are sensitive to the near-interfacial region of the sample. Auger electron spectroscopy is often used as a surface sensitive probe, and in this application it allows for a element-specific investigation of interfacial magnetisation Magnetic sensitivity in XAS The peak intensities in an x-ray absorption spectrum are related to the transition probilities between core and valence states in the atom under study. Each state is defined by the quantum numbers n, l, m l and m s, with the allowed values given by l = 0, 1, 2,..., n 1, m l = 0, ±1, ±2,..., ±l, and m s = ±1/2. In the electric dipole approximation, transitions between states are governed by the quantum mechanical selection rules, l = ±1, m l = 0, ±1, m s = 0, j = 0, ±1, (3.46) where j = l+m s. Consider for example Co, which is a ferromagnetic material with the net spin moment given by an imbalance of spin-up and spin-down electrons in the 3d band. To investigate the magnetisation of this element the energy of the x-ray photons must be tuned to give transitions in to the 3d valence states. From the transition rules of equation (3.46), this is achieved with transitions from the 2p core states. In the presence of an external magnetic field the l = 0 and l = 1 2p states are split energetically to the 2P 1/2 and 2P 3/2 levels where the subscript is the value of j. Transitions from the p to d states are called the L-edges, with 2 L edges, L 3 and L 2, corresponding to transitions from 2P 3/2 and 2P 1/2 states respectively.

83 CHAPTER 3. EXPERIMENTAL TECHNIQUES 82 Spin-up E Spin-down E F RCP LCP 2P 3/2 2P 1/2 Figure 3.19: A schematic of x-ray absorption within a spin-split valence band. Circularly polarised x-ray photons of opposite helicity preferentially excite spin-up and spin-down photoelectrons, and the absorption intensity for each is different by an amount proportional to the difference of the spin-up and spin-down density of states at the Fermi level, E F. In Co the density of states of the 3d band at the Fermi level is spin-split with, for example, a higher density of available spin-down states than spin-up states. The dipolar transition rules state that the spin of an electron cannot change during an optical transition ( m s = 0), and therefore spin-down electrons can only be excited to spin-down states, and vice versa. Since they have a different density of states there will be different transition probabilities for spin-down and spin-up electrons. Figure 3.19 is a schematic of a spin-split band structure, and illustrates the origin of magnetic sensitivity in XAS measurements. Circularly polarised x-rays carry an angular momentum that is transferred to the excited photoelectron on absorption, with spin momentum transfered by the spin-orbit interaction. Since left-handed and right-handed circularly polarised photons have opposite angular momentum, they will preferentially excite photoelectrons with opposite spin. Since the spin of the photoelectrons cannot change during the transition, the spin-split 3d valence band then acts a detector of the spin of the excited photo electrons, with greater absorption of one spin orientation than the other. By reversing the helicity of the polarised x-ray photons, or equivalently reversing the magnetisation of the material, the opposite spinstates can be probed. XMCD spectra are then obtained as the difference in the XAS spectra for measurements of opposite photon helicity, or positive and negative saturating

84 CHAPTER 3. EXPERIMENTAL TECHNIQUES 83 magnetic fields. The maximum XMCD effect is obtained when the momenta of the photons and spins are parallel, i.e. when the magnetisation and x-ray propagation directions are parallel Analysis of XAS and XMCD spectra XAS and XMCD allow element specific studies of the orbital and spin magnetic moments. Quantitative analysis is performed by relating the integrated area of the XAS and XMCD spectra to the transition probabilities, and hence to the number of available states in the valence band. The total number of 3d holes is proportional to the integrated intensity of the XAS for linearly polarised x-rays (or equivalently the average XAS from LCP and RCP x-rays) from the L 3 and L 2 edges. In figure 3.17 the sign of the XMCD peaks at the L 3 and L 2 edges are opposite, due to the opposite sign of the spin-orbit coupling in the 2P 3/2 and 2P 1/2 states. The peaks have different amplitude partly because they are the sum of contributions from spin and orbital moments, with the orbital moments giving the same sign in the XMCD peak at both edges. There are therefore sum rules that allow the separation of the spin and orbital moments, with values determined by the integrated area of the peaks. The difference in the x-ray absorption intensities for LCP and RCP x-rays can be denoted A for the L 3 edge and B for the L 2 edge. The L 2 orbital XMCD signal will be half the intensity of the L 3 orbital XMCD signal, since the density of states of 2P 1/2 is half that of 2P 3/2. No such simple analysis can be made of the spin XMCD signal unless the density of available states in the 3d shell is known. The L 3 edge represents total angular momentum l + m s, while the L 2 edge represents l m s. Therefore summing over the L 3 and L 2 edges removes the influence of the spin moment, leaving the orbital moment in isolation. The orbital, µ L, and spin, µ S, moments are then given by, µ L (A + B), (3.47) µ S (A 2B). (3.48)

85 Chapter 4 Optically induced magnetisation dynamics in Heusler alloy thin films 4.1 Introduction Heusler alloys have recently attracted great interest for use in spintronic devices since high spin polarisation, and even half-metallic behaviour, can be realised in some phases [23]. High spin polarisation increases the tunneling magnetoresistance (TMR) ratio, which is a key factor determining the performance of a magnetic tunnel junction (MTJ). To realise the potential of these materials and structures very high quality thin films must be fabricated. Recently it has been shown that epitaxial films may be obtained by sputter deposition and post-deposition annealing [57], and large room temperature tunneling magneto-resistance values have been observed in magnetic tunnel junctions, in which Co 2 MnAl [58] and Co 2 MnSi [59, 60] Heusler alloys were used as electrodes. Furthermore it is expected that the half-metallic band structure may suppress spin-flip processes [61], leading to reduced magnetic damping and hence lower critical currents in spin transfer torque devices. The full exploitation of Heusler alloys requires an improved understanding of the intricate relationship between structural and magnetic properties, and particularly dynamic magnetic properties such as damping. Measuring precessional magnetisation dynamics is an effective method to determine macroscopic magnetic properties. By making measurements in the time domain the relaxation rate of the precessing magnetisation can be measured directly. In this chapter

86 CHAPTER 4. OPTICALLY INDUCED FERROMAGNETIC RESONANCE 85 intense femtosecond laser pulses are used to excite and measure precessional magnetisation in Heusler alloy ferromagnetic thin films in a pump probe experiment. Damping of precessional magnetisation is not a well understood process. By investigating the dependence of the frequency and amplitude of precession on the strength and orientation of the applied field the method of exciting precession is revealed. The variation of the derived damping parameter is discussed as it highlights several possible contributions to the total damping. Frequency domain ferromagnetic resonance (FMR) has previously been used to study the intrinsic Gilbert damping parameter of thin Co 2 MnAl [62, 63] and Co 2 MnSi [64, 65] films. Frequency domain FMR has become a widely used tool in the investigation of magnetic thin films (for a typical review see [66]), however is is typically limited to measurements at a limited number of frequencies as defined by the resonant condition of the microwave cavity. Time domain measurements of the damping parameter over a continuous range of frequencies are needed to achieve a comprehensive understanding of the dynamic properties, while measurements within the low field regime are of particular technological relevance. All-optical pump-probe techniques have been demonstrated in the last decade that enable ultrafast demagnetisation, coherent magnetisation rotation and hot electron relaxation in magnetic thin films to be studied over an extended range of frequencies [15, 36, 67 70]. It is a challenge for all dynamic magnetisation measurements to investigate the intrinsic damping mechanism in the presence of extrinsic processes. Recent studies have shown that the damping of precessional dynamics in ferromagnetic metals can be complicated by the action of many extrinsic damping processes such as inhomogeneous broadening [71], two-magnon scattering [72 74], and spin diffusion into adjacent metallic layers [71, 75, 76], with Cr in particular shown to be a strong spin scatterer [77]. Differences in damping have been found when direct comparison has been made between different frequency, field and time domain techniques [78]. Time resolved optical measurements have the advantage that they can probe a much smaller volume than microwave resonance experiments, but may be susceptible to additional contributions to the damping. For example, the spatial profile of a pulsed magnetic field or a focused pump laser spot may lead to the generation of magnons that propagate away from the region that is being probed. Eilers et al. [79] performed simulations of nonlocal damping by spin wave emission and found that spin wave emission becomes a significant damping mechanism when the excitation area is less than 1 µm, while Wu et al. [80] showed that propagation of magnetostatic spin waves could be significant even for probed regions of tens of microns in size.

87 CHAPTER 4. OPTICALLY INDUCED FERROMAGNETIC RESONANCE 86 The TRMOKE technique allows the magnetisation dynamics to be studied over a continuous range of frequencies. From the amplitude of the measured signals it will be shown that precession is induced by ultrafast modification of the magnetocrystalline anisotropy. A macrospin solution of the Landau-Lifshitz-Gilbert equation will be presented which is fitted to the field strength and orientation dependent precession frequency in order to obtain values for the macroscopic magnetic parameter. Specific sample details and results for Co 2 MnAl and Co 2 MnSi films will be presented and discussed separately with comparisons drawn in the summary. For Co 2 MnAl and Co 2 MnSi films the effective damping parameter was found to vary as a function of field strength and orientation. Furthermore a series of Co 2 MnSi films were studied that showed a variation in the damping parameter with annealing temperature. In the case of the Co 2 MnSi films the presence of different putative extrinsic damping mechanisms will be considered, and the data will be fitted to a generalised model of inhomogeneous broadening that can account for most but not all of the observed variations of the damping parameter. 4.2 Experimental details The static magnetic properties of the Heusler films were investigated by vibrating sample magnetometry (VSM), and longitudinal magneto-optical Kerr effect (MOKE) magnetometry measurements performed with a 633 nm He-Ne laser with intensity stability of better than 0.1 % [34]. In MOKE measurements the sample and electromagnet were mounted on separate rotating mounts so that the magnetic field could be applied at any orientation within the plane of the film, and the longitudinal MOKE could be used to sense the in-plane component of magnetisation either parallel or perpendicular to the field [81]. In this way the hard and easy axes of the samples could be quickly identified at room temperature and the saturation fields determined. Time-resolved optical pump-probe measurements were made using pulses of 100 fs duration from a 100 khz Ti:sapphire regenerative amplifier. The sample was pumped with the p-polarised 800 nm wavelength output of the amplifier at near normal incidence with pulse energy up to 0.9 µj. The dynamic magnetisation was determined from the Kerr rotation of a time-delayed frequency-doubled 400 nm wavelength s-polarised probe beam. The probe, incident at 40 to the sample normal, had a much weaker pulse energy of 4 nj, and was focused to overlap with the pump spot on the sample surface. The sizes of the pump and probe spots were typically 140 µm and 80 µm, respectively. The focusing

88 CHAPTER 4. OPTICALLY INDUCED FERROMAGNETIC RESONANCE 87 lenses were mounted on 3-axis translation stages so that the overlap of the spots could be adjusted as they were viewed with a high-magnification CCD camera. The pump beam was modulated by a mechanical chopper and phase-sensitive detection was used to detect the dynamic Kerr rotation. Static hysteresis loops were acquired with the probe beam in the absence of the pump in order to calibrate the size of the magneto-optical response. (a) H T Sample y z x (b) [110] H L M Probe beam Pump beam φ 4 φ H [100] Figure 4.1: (a) Orientation of sample, applied field and probe beam. Two orientations of the static field were used. H L and H T are parallel and perpendicular to the plane of incidence respectively. (b) Definition of the angles φ and φ 4. Assuming that the magnetisation lies close to the direction of the applied field prior to the arrival of the pump pulse, the total MOKE signal will generally contain an oscillatory component due to magnetisation precession and a component that rises sharply due to ultrafast demagnetisation before decaying much more slowly. When the oscillatory signal is small it may be beneficial to measure the oscillatory signal in the absence of the ultrafast demagnetisation signal. Figure 4.1(a) shows the relative orientation of the sample (xy-plane), applied static field and plane of incidence of the probe (xz-plane). In this orientation an s-polarised probe is sensitive to changes of the x and z components of the magnetisation due to the longitudinal and polar magneto-optical Kerr effects respectively. Two orientations of the static applied field are used - parallel to (H L ) and perpendicular to (H T ) the plane of incidence. The former geometry gives a time-resolved signal that includes a demagnetisation background from the longitudinal MOKE signal and an oscillatory signal from the polar MOKE, while in the latter geometry both the longitudinal and polar MOKE yield oscillatory signals. Within Figure 4.1(b) φ 4 is the angle that the applied field subtends with the [100] axis while φ is the angle between the applied field and the magnetisation.

89 CHAPTER 4. OPTICALLY INDUCED FERROMAGNETIC RESONANCE Theory Macrospin LLG solution The intense optical pump pulse is expected to induce a partial demagnetisation of a metallic ferromagnetic sample on sub-picosecond timescales [15]. The temperature dependence of the cubic magnetocrystalline anisotropy constant K 1 can be deduced from its dependence upon the magnetisation M S which is predicted to have the form K 1 (T ) M S (T ) n where n is equal to 10 [5]. It is therefore reasonable to assume that the demagnetizing and magnetocrystalline anisotropy fields of the sample will be modified on timescales short compared to the period of precession. After pumping, the effective magnetic field will no longer be parallel to the magnetisation (unless H is parallel to the easy or hard axis), and precession will be induced by a torque acting on the magnetisation. Since the measured Kerr rotation is, to first-order, linearly dependent upon the time dependent linear components of the precessing magnetisation [26], the oscillatory part of the measured Kerr rotation, θ K, may be written in the general form, θ K φ cos [2π (f 0 + bt) t + ϕ] exp ( t/τ), (4.1) where φ, f 0, 1/τ, and ϕ are respectively the initial amplitude of precession, which is the initial angle of misalignment of the magnetisation from equilibrium, the frequency, the relaxation rate, and the initial phase of the precessional signal. The parameter b is included to allow for a chirp that occurs as the values of magnetic parameters such as M S and K 1 change gradually as the probed volume cools. However, if the chirp is neglected and the values of the magnetic parameters are assumed to be constant after initial modification by the pump, then algebraic expressions may be obtained that relate the frequency, amplitude and relaxation time to the magnetic parameters as will now be discussed. equation, The precessing magnetisation may be described by the Landau-Lifshitz-Gilbert (LLG) M t = γ M H eff + α M ( M M t ), (4.2) where α is the phenomenological damping parameter, γ = 2.8 π g MHz/Oe is the gyromagnetic ratio of the electron, and g is the spectroscopic splitting factor. H eff is the total effective magnetic field acting upon the magnetisation, and may be evaluated from,

90 CHAPTER 4. OPTICALLY INDUCED FERROMAGNETIC RESONANCE 89 H eff = 1 M ûe tot, (4.3) where E tot is the total magnetic free energy which can be written as, E tot = M H + 2πM 2 û 2 z K u û 2 z K 1 2 [ (û ˆx 4 ) 4 + (û ŷ 4 ) 4] K 1 2 (û ẑ 4) 4, (4.4) where the terms on the right hand side represent the Zeeman energy, the demagnetizing energy, a uniaxial anisotropy with axis parallel to the film normal, and then two contributions to the magnetocrystalline anisotropy. Here û is a unit vector parallel to the magnetisation, while ˆx 4, ŷ 4 and ẑ 4 are unit vectors parallel to the 100 crystal axes. Two magnetocrystalline anisotropy constants, K 1 and K 1, are included to allow for a tetragonal distortion of the cubic lattice perpendicular to the film plane, while K 1 = K 1 = K 1 in the undistorted case. In this study no evidence of such a distortion was observed, so K 1 will be used to represent the anisotropy from here on. It will be assumed that the magnetisation undergoes a spatially uniform small amplitude precession, in which case the LLG equation may be linearized. Since the magnetisation lies within the plane of the film initially, the change in the in-plane magnetocrystalline anisotropy field is most significant in stimulating precession. In the limit α 1, it may be shown that, φ = (1/2) sin [4 (φ φ 4)] (K 1 /M S ) ( ), (4.5) H cos φ + 2K (0) 1 /M S cos [4 (φ φ 4 )] f 0 = 1 2π γ (H αh β ) 1/2, (4.6) τ = 2 γ (H α + H β ) α, (4.7) where φ is the amplitude of precession, φ 4 is the angle between the applied magnetic field and the Co 2 MnSi [100] axis and K (0) 1 is the room temperature value of the cubic magnetocrystalline anisotropy constant. (K 1 /M S ) is the pump-induced reduction of the anisotropy field at the increased temperature. The effective fields H α and H β are given by, H α = H cos φ + K 1 2M S {3 + cos [4 (φ φ 4 )]} + 4πM S 2K u M S, (4.8)

91 CHAPTER 4. OPTICALLY INDUCED FERROMAGNETIC RESONANCE 90 H β = H cos φ + 2K 1 M S cos [4 (φ φ 4 )]. (4.9) The value of φ can be determined from the static equilibrium condition, M S H sin φ + K 1 2 sin [4 (φ φ 4)] = 0. (4.10) If H is sufficiently large that φ is small, then equation (4.10) may be expanded to give an algebraic expression in φ 4 of the form, φ = K 1 sin (4φ 4 ) 2M S H + 4K 1 cos (4φ 4 ). (4.11) At low field the small angle approximation for the canting angle φ becomes invalid, but by retaining quadratic terms in φ, the expansions of sin φ and cos φ are accurate to 2.5 % and 1 % respectively. In this case the value of φ is obtained to a reasonable approximation from the expression, φ = [M SH + 2K 1 cos (4φ 4 )] + [M S H + 2K 1 cos (4φ 4 )] 2 + 8K1 2 sin2 (4φ 4 ). (4.12) 8K 1 sin (4φ 4 ) It should be noted that the parameter K 1 does not enter the above expressions for which the sample is initially magnetized within the film plane Inhomogeneous broadening model of damping variation From the TRMOKE measurements the value of an effective damping parameter can be deduced that contains contributions from all the damping processes that are present. Inhomogeneous broadening may occur due to the dephasing of an ensemble of magnetic moments precessing independently with slightly different frequency. Assuming a Lorentzian frequency distribution of the precession amplitude A of the form, A (ω) = A 0 (ω ω 0 ) 2 + ( ω FWHM /2) 2, (4.13) where ω 0 is the peak frequency and ω FWHM is the A(ω) full width at half maximum, it may be shown using elementary Fourier analysis that the time dependent Kerr rotation has the form of equation (4.1) but with a modified relaxation rate 1/τ where 1/τ = 1/τ + 1/τ inhom. The relaxation rate due to inhomogeneous broadening is given by 1/τ inhom = ω FWHM /2, while contributions of other mechanisms to the observed relaxation rate can be included by adding further relevant relaxation rates. In this case 1/τ

92 CHAPTER 4. OPTICALLY INDUCED FERROMAGNETIC RESONANCE 91 accounts for all other damping mechanisms, including intrinsic damping. The measured damping parameter is derived from equation (4.7) using the modified relaxation rate 1/τ as follows, α = = 2 γ (H α + H β ) τ 2 γ (H α + H β ) ( 1 τ + ω FWHM 2 ). (4.14) The contribution to the damping from inhomogeneous broadening is given by, 1 α inhom = γ (H α + H β ) ω FWHM = 1 γ (H α + H β ) ( ω M S M S + ω ) K 1 K 1 + ω φ 4 φ 4 + ω K u K u, (4.15) with M S, K 1, φ 4 and K u describing the inhomogeneity of the magnetic parameters. The partial derivatives are calculated from equations (4.6), (4.8), (4.9), and (4.12). A combined contribution of M S and K 1 is assumed since K 1 (T ) is known to depend strongly on M S (T ). The significance of damping mechanisms other than intrinsic damping in the value of 1/τ will be tested for by experiment. 4.4 Co 2 MnAl Introduction and sample details The MgO(001)/Cr(40 nm)/co 2 MnAl(30 nm)/mgo(10 nm) structure was grown by magnetron sputtering at room temperature on a MgO (001) substrate [57]. Co 2 MnAl films deposited at ambient temperature adopt the A2 structure in which the Co, Mn and Al ions are randomly located upon a body centred cubic lattice. The sample studied in this chapter was annealed post-deposition at 300 C, leading to the formation of the more highly ordered B2 phase. In this phase the Co ions occupy the simple cubic sites while the Mn and Al ions are randomly distributed among the body centre cites. Achieving a low site-disorder is necessary for the very high spin-polarisation expected of the Heusler alloys. Half-metallicity is predicted for the L2 1 phase [23], which is difficult to obtain in this system. Other full-heusler compounds can form the highly ordered L2 1 state (see Co 2 MnSi later), but to do so requires annealing at high temperatures of C, and

93 CHAPTER 4. OPTICALLY INDUCED FERROMAGNETIC RESONANCE 92 such high temperature treatment can cause the performance of an MTJ to deteriorate. Co 2 MnAl is expected to have a large spin polarisation of 0.76 in the B2 phase and requires annealing at only C to achieve this [82], and is therefore an attractive material as an MTJ electrode. Unless otherwise stated the static field is applied perpendicular to the plane of incidence (H T in Figure 4.1) Experimental results Characterisation of static magnetic properties Figure 4.2 shows static magnetisation hysteresis loops as measured by MOKE with the intensity-stabilised He-Ne system, for field parallel to the [100], [110] and intermediate (φ 4 =22.5 ) axes of the Co 2 MnAl film. The MOKE loops reveal a clear fourfold anisotropy, with the easy and hard magnetisation axes parallel to the [100] and [110] crystal axes respectively. The coercive field is 11 Oe for all field orientations, and the hard axis saturation field is 60 Oe. Dependence of dynamic magnetic response on applied field orientation A typical time-resolved rotation Kerr signal is shown in 4.3, for which the magnetic field of 850 Oe was applied with φ 4 = 25. By comparing fine scans of the initial rise of the signal with the longitudinal hysteresis loop (not shown), the peak demagnetisation was found to be 10 %. The inset to Figure 4.3 shows that the precession amplitude is linearly proportional the pump pulse energy. The fast rise and slower exponential decay associated with the ultrafast demagnetisation could swamp the oscillatory signal. In order to eliminate the contribution from the demagnetisation signal the experiments were mainly conducted with the static field applied perpendicular to the plane of incidence, H T, as shown in Figure 4.1(a). Figure 4.4(a) shows the transient Kerr rotation signals obtained in this transverse field geometry as a static field of 210 Oe, sufficient to saturate the sample, was applied in different in-plane directions relative to the [100] axis of the Co 2 MnAl, φ 4. The transient Kerr rotation signals show very clearly that the precession amplitude depends strongly upon the orientation of the static magnetic field. The raw time-resolved signals were fitted to the sum of a damped sinusoid, equation (4.1), and a small exponentially decaying background that accounts for the slow recovery of the magnetic anisotropy. Equations (4.5), (4.6), (4.8), (4.9) and (4.11) were used to fit the amplitude and frequency of the precession of the magnetisation shown

94 CHAPTER 4. OPTICALLY INDUCED FERROMAGNETIC RESONANCE Kerr Rotation (mdeg) Amplitude (mdeg) 2 0 F ie ld p a ra lle l to : [1 0 0 ] [1 1 0 ] in te rm e d ia te a x is ( 4 = o ) K e rr R o ta tio n (m d e g ) M a g n e tic F ie ld (k O e ) Figure 4.2: Static magnetisation loops measured by MOKE for Co 2 MnAl, with field parallel to the [100] (black), [110] (red) and intermediate φ 4 = 22.5 (green) crystal axes Pulse Energy ( J) Time Delay (ns) Figure 4.3: A typical TRMOKE signal from the Co 2 MnAl film. The inset shows that the precession amplitude increases linearly with pump pulse energy.

95 CHAPTER 4. OPTICALLY INDUCED FERROMAGNETIC RESONANCE (a ) 4 7 o 5 2 o 5 7 o A m p litu d e (m d e g ) (b ) K e rr ro ta tio n (m d e g ) o 7 7 o 8 7 o 9 2 o o o o T im e d e la y (n s ) F re q u e n c y (G H z ) D a m p in g p a ra m e te r (c ) (d ) [1 1 0 ] [1 0 0 ] A n g le 4 (d e g ) Figure 4.4: (a) Transient Kerr rotation signals obtained with a 210 Oe field applied perpendicular to the plane of incidence with varied φ 4. The dependence of the precession amplitude (b), the precession frequency (c), and the damping parameter (d) on the orientation of the magnetic field are shown. Error bars in (b) and (c) are obtained from fitting to the TRMOKE scans. The errors in the damping parameter are derived from the combined contributions of the errors in M, K 1, g-factor and the relaxation time. in figures 4.4(b) and 4.4(c) respectively, with the saturation magnetisation set to the bulk value of 730 emu/cm 3 with an uncertainty of 10 % [62][57]. The program used to perform the fitting (Origin) arrives at the fitted values by minimising the sum of the squares of the deviations of the experimental points from the theoretical function. The errors in the fitted parameters are then calculated from the least squares value and the diagonal elements of the variance-covariance matrix. These errors are included in the figures as error bars. Figure 4.4(b) shows that the precession amplitude has a clear fourfold variation with the orientation of the static field. No precession was observed with the field applied parallel to or 45 from the [100] axis, while the maximum amplfitude was found for the field ap-

96 CHAPTER 4. OPTICALLY INDUCED FERROMAGNETIC RESONANCE 95 plied midway between these orientations. The precession signal is also seen to undergo a 180 phase change as the static field crosses either of these orientations. The precession frequency also shows a fourfold variation, with minimum when the applied field is parallel to the [100] and maximum for the external field is parallel to the [110] axis. The frequency will be greatest when the applied field is parallel to the easy axis, and therefore the effective field is strongest. Therefore the TRMOKE measurements show that [110] is the easy axis and [100] is the hard axis. This disagrees with the static MOKE measurements, which showed that [100] was the easy axis and [110] the hard axis. This initially surprising result is most likely due to the temperature dependence of the magnetocrystalline anisotropy, which can change sign with temperature [5]. The field orientation and magnitude (see next section) variation of the precession frequency were simultaneously fitted by equation (4.6) to obtain values of g = 2.1±0.1 and K 1 = 0.046± erg/cm 3. The uncertainties in these quantities were derived by fitting the field orientation and strength dependence of the frequency taking in to account the 10 % uncertainty in the magnetisation. With these values the effective damping parameter, α, was calculated using equation (4.7), and is presented in figure 4.4(d). The uncertainty in the damping parameter was calculated from the combined uncertainties of the magnetisation, magnetocrystalline anisotropy constant, g-factor and relaxation time. The damping parameter varies from with an uncertainty of ±0.01 for field parallel to the [100] and [110] axes respectively, with the red curve a sine function acting as a guide to the eye only. Note that approximately 50 % of the uncertainty in the calculated damping parameter is derived from the systematic 10 % uncertainty of the magnetisation. Dependence of dynamic magnetic response on applied field strength Figure 4.5(a) shows the dependence of the transient Kerr rotation signal upon the strength of the magnetic field where φ 4 was fixed at 25. The transient precession signals were again fitted using equation (4.1), and the extracted and calculated parameters are shown in Figure 4.5(b-d), with error bars calculated in the same manner as for the field orientation data. As the magnetic field is increased the precession frequency increases while the precession amplitude and the damping parameter decrease. The solid lines in Figure 4.5(b) and Figure 4.5(c) are fits to equations (4.5) and (4.6) respectively.

97 CHAPTER 4. OPTICALLY INDUCED FERROMAGNETIC RESONANCE 96 T ra n s ie n t K e rr R o ta tio n (m d e g ) (a ) O e O e O e O e O e T im e D e la y (n s ) D a m p in g P a ra m e te r F re q u e n c y (G H z ) A m p litu d e (m d e g ) (b ) (c ) (d ) M a g n e tic F ie ld (k O e ) Figure 4.5: (a) Transient Kerr rotation signals with H perpendicular to the plane of incidence and φ 4 = 25. The dependence of the precession amplitude (b), the precession frequency (c), and the damping parameter (d) on the strength of the magnetic field (the solid line is a guide to the eye, while (b) and (c) show fits to the macrospin model) Discussion The fourfold variation of the precession amplitude with the orientation of the magnetic field confirms that magnetisation precession is induced by an ultrafast optical modification of the magnetocrystalline anisotropy [68][83] leading to a reorientation of the effective field acting upon the magnetisation. Figure 4.6 illustrates the mechanism of inducing precession. In (a) the magnetisation is in equilibrium prior to the arrival of the laser pump pulse. The magnetisation is parallel with the effective field, and there is an angle between the effective field and the external applied field due to the magnetocrystalline anisotropy. In (b) the pump pulse has heated the sample, reducing the magnitude of the magnetisation and the anisotropy constant. With the weaker anisotropy the effective field is reoriented to lie closer to the external field, and the magnetisation is no longer in equilibrium. In (c) the magnetisation experiences a torque, M H eff, which causes it

98 CHAPTER 4. OPTICALLY INDUCED FERROMAGNETIC RESONANCE 97 [110] EA [110] EA M H eff H ext M H eff H ext [100] HA [100] HA (a) At equilibrium (b) Heating by laser pump pulse reduces the anisotropy, H eff rotates towards H ext [110] EA M(t) H eff H ext [100] HA (c) Magnetisation experiences torque and precesses Figure 4.6: Mechanism of induced precession by ultrafast modification of magnetocrystalline anisotropy. to precess about H eff. As H eff returns to its equilibrium value M will relax by a damped precessional path. When the static field is applied along either the easy or hard axes no precession is induced. In these orientations there is no canting angle between H eff and H ext, so there is no reorientation of H eff after laser heating and therefore no torque on M. The field strength variation of the amplitude and frequency are well fitted by the macrospin LLG solution. The increase in amplitude at low fields occurs due to the in-

99 CHAPTER 4. OPTICALLY INDUCED FERROMAGNETIC RESONANCE 98 creased canting angle between the equilibrium magnetisation and the external field. The damping parameter, α, calculated using equation (4.7) shows a weak fourfold variation, to which a sine curve has been added as a guide to the eye. The damping parameter is also found to decrease with increasing external field strength, reducing by a factor of 5 between 0 and 2 koe. However, we note that the extracted values of α are slightly modified if the frequency of the fitted function is allowed to vary with time so as to account for the slow recovery of the magnetocrystalline anisotropy, and so further measurements are required to determine whether the observed four-fold variation is an intrinsic property of the sample or an artifact of the fitting procedure. The value of the damping parameter that we obtain by TRMOKE at 10 GHz (α = ± 0.003) is twice the value obtained in FMR measurements at the same frequency [62], but this is not surprising as FMR and time-domain techniques have already been shown to yield different values for the damping parameter [78]. A number of authors have reported a field dependent damping parameter and suggested a variety of underlying mechanisms [76, 80, 84 86]. The damping parameter extracted from the fits reported here should be regarded as a phenomenological parameter that accounts for the combined effect of intrinsic damping, inhomogeneous broadening, two magnon scattering, any higher order spin waves processes, and propagation effects resulting from the non-uniform spatial profile of the precession. Further work is now required to understand which of these mechanisms make significant contribution to the damping observed in the present study. Such further measurements have been performed on the Co 2 MnSi films, reported in the following section. The anisotropy has been determined from static and time-resolved MOKE measurements, and the two disagree on the assignment of the magnetic easy and hard axes. This is likely the result of TRMOKE measurements effectively being performed at higher temperature, since the magnetocrystalline anisotropy has been shown to be strongly dependent on temperature. In this case the magnetocrystalline anisotropy constant K 1 may have changed sign between room temperature and the elevated temperature of the TRMOKE measurements. 4.5 Co 2 MnSi Introduction and sample details To further investigate the variation of damping with field strength and orientation and how it may depend on film preparation conditions, TRMOKE measurements were

100 CHAPTER 4. OPTICALLY INDUCED FERROMAGNETIC RESONANCE 99 made on a series of Co 2 MnSi films annealed at 300, 400 and 450 C. In this study the variation of the damping parameter with field strength and orientation was fitted by an inhomogeneous broadening model, to check whether this effect is solely responsible for the variation. Co 2 MnSi thin films of 30 nm thickness were deposited by magnetron sputtering upon MgO(001) substrates coated with a 40 nm buffer layer of Cr [57] OR [87]. The films were then annealed at a temperature of up to 450 C to improve the lattice structure and the atomic ordering among Co, Mn, and Si sites. The films were finally capped with 1.3 nm of Al. The fraction of the L2 1 phase within the film can be deduced from a careful analysis of different peak intensities in x-ray diffraction experiments, and was confirmed to increase continuously with annealing temperature T an [88]. We focus the investigation on three samples: sample A 300, annealed at 300 C has B2 phase; A 400, annealed at 400 C has L2 1 phase; and A 450, annealed at 450 C also has L2 1 phase. The nomenclature is the same as that used for XMCD [89] and MSHG [90] measurements performed on the same samples. X-ray diffraction analysis confirmed that the films possessed the (001) orientation with the [100] and [110] axes of the film being aligned with the [110] and [110] axes of the MgO substrate. Magnetometry measurements of bulk L2 1 Co 2 MnSi yield a low temperature magnetisation of 138 emu/g [91] corresponding to a value of 1030 emu/cm 3 for a lattice parameter of nm. Since Co 2 MnSi has a Curie temperature of 985 K [91], the room temperature magnetisation is expected to be close to 1000 emu/cm 3. However recent measurements made upon epitaxial films yielded a reduced magnetisation [87], its value falling from 850 to 800 emu/cm 3 as T an was increased from 350 to 500 C [88]. In that case the magnetisation was found to be independent of temperature in the range of K [92] suggesting that the Curie temperature remained high. A four-fold anisotropy with the easy axes corresponding to the 110 axes of the Co 2 MnSi was observed [88]. The cubic anisotropy constant K 1 had a value of erg/cm 3 for T an = 375 C, decreasing in magnitude to K 1 = erg/cm 3 for T an = 450 C. While the dependence of the magnetic properties upon T an might be related to the changing fraction of the L2 1 phase present in the films, the authors could not exclude the possibility that annealing promoted diffusion of Cr from the buffer layer into the Co 2 MnSi film. Since the TMR observed in MTJ structures is largely determined by the properties of the electrode-tunnel barrier interface, measurements sensitive to the near interfacial region have recently been performed upon Co 2 MnSi films capped with thin layers of plasma

101 CHAPTER 4. OPTICALLY INDUCED FERROMAGNETIC RESONANCE 100 oxidized aluminium oxide. X-ray magnetic circular dichroism (XMCD) measurements, performed in total electron yield mode, probe a near interface region of 1 2 nm thickness that is determined by the escape length of the secondary electrons. Such measurements were performed upon the series of samples for which dynamic measurements will be presented in the present paper and which have been labeled A x where x is the annealing temperature in the range of C [89]. The Co and Mn x-ray absorption spectra revealed both x-ray absorption near edge structure (XANES) and extended x-ray absorption fine structure (EXAFS) oscillations that confirmed that L2 1 ordering improved with increasing annealing temperature. Magnetic moments were observed on both the Co and Mn sites, but for these samples the moment per 3d hole was found to be independent of annealing temperature in the range of C. The emergence of a multiplet structure in the XMCD spectra was attributed to the localization of minority spins in the halfmetallic state. A further study confirmed that the magnetisation of the near interface region remained constant between liquid Helium and room temperatures [93]. Magnetic second harmonic generation (MSHG) measurements were performed upon this same set of samples in order to probe the magnetic response of the Co 2 MnSi/AlO x interface [90]. The MSHG was found to depend upon whether the magnetic field was applied parallel to an easy or hard axis, and this anisotropy in the MSHG was shown to be well correlated with the TMR achieved in MTJs fabricated with similar electrodes. The MSHG and XMCD studies are presented in this thesis in chapter 5. Yilgin et al. have used X-band ferromagnetic resonance (FMR) to study the dynamic properties of epitaxial Co 2 MnSi thin films [64]. The samples were rotated so that the orientation of the magnetic field varied either within the plane of the film, or from an in-plane to an out of plane configuration. The magnetisation and the magnitude of K 1 were observed to decrease dramatically as T an increased from C. The variation of the FMR linewidth was fitted to a model [84] that allowed the inhomogeneous broadening contribution to the total linewidth to be removed [75]. However, for the film annealed at 300 C the damping parameter extracted after removal of the inhomogeneous broadening contribution was found to be anisotropic, with a value of when the field was parallel to the easy axis, and when the field was parallel to the hard axis. This damping parameter was found to increase with annealing temperature, while the anisotropy of the damping parameter was reduced at higher annealing temperatures. The intrinsic damping is normally attributed to spin-orbit coupling [94], and is expected to be isotropic for cubic transition metal ferromagnets. It was suggested that the anisotropy of the Gilbert

102 CHAPTER 4. OPTICALLY INDUCED FERROMAGNETIC RESONANCE 101 damping parameter may be associated with an anisotropy of the g factor, that has been discussed previously for semiconductor materials [95]. For a ferromagnet the g factor may be written as ( L z + 2 S z ) / S z, where L z and S z are the orbital and spin quantum numbers associated with the quantization direction. While the spin S tends to align with the magnetic field, the orbital angular momentum L prefers to align with the easy axes of magnetocrystalline anisotropy, but is canted towards S by the weaker spin-orbit interaction. Anisotropy of the g factor occurs because the canting of L relative to S varies as the magnetic field is applied at different orientations relative to the crystallographic axes. However, since the crystal field largely quenches the orbital angular momentum [91], the g factor anisotropy is expected to be small and insufficient to explain the observed anisotropy of the damping Experimental results Characterisation of static magnetic properties The sample magnetisation was measured by VSM and found to have values of 980, 1000 and 1000 emu/cm 3 at room temperature for A 300, A 400 and A 450 respectively. The magnetic anisotropy was investigated by means of MOKE magnetometry. Figure 4.7 shows static hysteresis loops obtained with a He-Ne laser for the three samples, with the field applied parallel to the easy, hard and intermediate axes. The raw data contains a component that is quadratic in the sample magnetisation [88]. The linear and quadratic magnetooptical (MO) effects can be separated by their respective symmetric and antisymmetric dependence on field polarity. A second loop is generated by forming the reflection the original loop about the zero field axis. The linear MO-effect is obtained from the difference of this loop and the original loop, while the quadratic MO-effect is obtained from the average of the two loops. The measured signal and separated linear and quartic components are all presented in Figure 4.7. No quadratic MO-effect was observed when loops were acquired with a 400 nm wavelength beam, and so equation (4.1) remains applicable in describing the results of TRMOKE measurements. The loops show a clear four-fold symmetry as the magnetic field is applied in different directions within the plane of the film, with the room temperature easy and hard axes lying parallel to the [110] and [100] axes of the Co 2 MnSi film respectively. Note that this is the reverse of the case for the Co 2 MnAl film. The magnetocrystalline anisotropy is reduced at higher annealing temperatures, with the hard axis saturation field falling from 260 Oe to 140 Oe then 80 Oe for samples A 300, A 400 and A 450 respectively. The easy

103 CHAPTER 4. OPTICALLY INDUCED FERROMAGNETIC RESONANCE A 3 0 0, [1 1 0 ] A 4 0 0, [1 1 0 ] A 4 5 0, [1 1 0 ] K e rr R o ta tio n (m d e g ) R a w lo o p L in e a r lo o p Q u a d ra tic lo o p A 3 0 0, 4 = o A 4 0 0, 4 = o A 4 5 0, 4 = o K e rr R o ta tio n (m d e g ) A 3 0 0, [1 0 0 ] A 4 0 0, [1 0 0 ] A 4 5 0, [1 0 0 ] K e rr R o ta tio n (m d e g ) M a g n e tic F ie ld (k O e ) M a g n e tic F ie ld (k O e ) M a g n e tic F ie ld (k O e ) Figure 4.7: Longitudinal MOKE loops obtained with a CW He-Ne laser. The columns, from left to right, for samples A 300, A 400 and A 450 while the rows, from top to bottom, are for field parallel to the [110], intermediate (φ 4 = 22.5 ) and [100] axes of the Co 2 MnSi films. Each plot includes the measured loop and the separated linear and quadratic components. The room temperature easy and hard axes are the [110] and [100] axes of the Co 2 MnSi films respectively. axis coercive field is about 15 Oe for all three samples. The saturation Kerr rotation at 633 nm wavelength also decreases with increasing annealing temperature, though the VSM measurement showed the magnetisation to be virtually unchanged. There is no evidence of any significant in-plane uniaxial anisotropy field. Ultrafast demagnetisation Figure 4.8 shows the ultrafast demagnetisation TRMOKE signal obtained within the first few picoseconds after excitation with a 0.6 µj pump pulse. The transient Kerr rotation signal (left hand column) reaches a maximum within about 650 fs, before decaying to about half the maximum value after the first few picoseconds. Plots of the TRMOKE signal on a logarithmic time scale (not shown) reveal that the decay can be well described

104 CHAPTER 4. OPTICALLY INDUCED FERROMAGNETIC RESONANCE 103 by the sum of two exponential terms. The demagnetisation was calculated for the time delay at which the exponential with the longer relaxation time became dominant. At this point the electrons and lattice are assumed to have the same temperature and the Kerr signal is assumed to be representative of the spontaneous magnetisation. When compared with a hysteresis loop measured with the same 400 nm wavelength probe beam (right hand column) the demagnetisation is found to be about 1.4 % for A 300, 1.0 % for A 400 and 0.9 % for A 450. The vertical lines indicate the time delay at which the demagnetisation was calculated. Notice that the MOKE loops in Figure 4.8 become more rounded as the annealing temperature is increased. With the stronger anisotropy field of the samples annealed at lower temperatures the intermediate axis loop more closely resembles that of the easy axis. K e rr ro ta tio n (m d e g ) 1.2 A p s A p s A p s T im e d e la y (p s ) F ie ld (k O e ) K e rr ro ta tio n (m d e g ) Figure 4.8: The transient Kerr rotation signal obtained from samples A 300, A 400 and A 450 close to zero time delay with φ 4 = 22.5 in the H L configuration. The vertical lines indicate the time delay at which the demagnetisation was calculated. The right hand column shows longitudinal MOKE loops measured at φ 4 = 22.5 with an s-polarised 400 nm probe beam.

105 CHAPTER 4. OPTICALLY INDUCED FERROMAGNETIC RESONANCE 104 Dependence of transient Kerr rotation signals upon the orientation of field Figure 4.9(a) shows the results of measurements performed on sample A 300, with a magnetic field of 885 Oe applied at difference orientations with respect to the crystallographic axes in the field geometry H L (refer to figure 4.1). The TRMOKE scans were fitted to equation (4.1) to extract the amplitude, frequency and relaxation rate, with a chirp parameter being used to allow for a change of frequency during the length of the scan. Figures 4.9(b)-(e) show the precession amplitude, frequency, relaxation rate and effective damping parameter respectively. The uncertainties in these fitted parameters are obtained in the same manner as for the Co 2 MnAl film from the earlier section. Note that the uncertainty in the relaxation time is largest when the amplitude of the MOKE signal is smallest, for φ 4 = 45, 135 and 225. Measurements made at different field values will be described in the next section. By simultaneously fitting the variation of frequency with field strength and orientation using equation (4.6), values of K 1 and g were determined and are presented in Table 4.1. As for the Co 2 MnAl film the uncertainties in the values of K 1 and g were obtained by fitting the frequency with the maximum and minimum values of M S given its 10 % uncertainty. The perpendicular anisotropy constant K u was set equal to zero during the fitting. The amplitude was fitted by equation (4.5) using the room temperature value of K (0) 1 obtained from static MOKE measurements by K (0) 1 = (H S M S )/2, which is equal to erg/cm 3 for sample A 300. The angular dependence of the relaxation rate was found to be well described by 1/τ = 1/ [A sin (4φ 4 ) + B], with A = ns and B = ns. The effective damping parameter in Figure 4.10(e) was obtained from the relaxation rate using equation (4.7). All parameter values in Figure 4.9 show a fourfold dependence upon the orientation of the in-plane field. The fourfold variation of the amplitude confirms that precession is induced by an ultrafast modification of the magnetocrystalline anisotropy. The frequency is a maximum when the static field is parallel to the [110] axis, indicating that this remains the easy axis at the elevated temperature in the TRMOKE measurements. When the field is applied parallel to the [110] easy (φ 4 = 45, 135 ) or [100] hard axes (φ 4 = 0, 90 ) the amplitude is zero, since no reorientation of the effective field occurs upon a reduction of M S or K 1. The precession undergoes a 180 phase change as the static field crosses either of these axes. The data is of sufficient quality that the amplitude in Figure 4.9(b) is seen to be a maximum when the static field is applied at 18.5 to the [100] axis rather than at 22.5 as one might initially expect. The canting angle φ was calculated as a function of

106 CHAPTER 4. OPTICALLY INDUCED FERROMAGNETIC RESONANCE 105 T ra n s ie n t K e rr ro ta tio n (m d e g ) T im e d e la y (n s ) 2.0 (a ) 1.5 (b ) o 8 3 o 7 3 o 6 8 o 6 3 o 5 8 o 5 3 o 4 8 o 4 3 o 3 8 o 3 3 o 2 8 o 2 3 o 1 8 o 1 3 o 8 o 3 o A m p litu d e (m d e g ) F re q u e n c y (G H z ) R e la x a tio n ra te (n s -1 ) D a m p in g p a ra m e te r In h o m o g e n e o u s b ro a d e n in g P h e n o m e n o lo g ic a l c u rv e A n g le 4 (d e g ) (c ) (d ) (e ) Figure 4.9: (a) Transient Kerr rotation signals obtained from A 300 with H = 885 Oe and at different φ 4 values. The experimental data are fitted to equation (4.1), with uncertainties included as error bars. The variation of (b) the fitted amplitude and (c) the frequency of precession are fitted to equations (4.5) and (4.6) respectively, with fitted parameter values given in Table 4.1. The solid line in (d) is a guide to the eye as described in the main text. The red line in (e) is a fit to an inhomogeneous broadening model (4.15) with fitted parameter values given in Table 4.2, while the dashed blue line in (e) is a phenomenological curve calculated from equation (4.16).

107 CHAPTER 4. OPTICALLY INDUCED FERROMAGNETIC RESONANCE 106 applied field orientation using the fitted values of the magnetic parameters (not shown) and the maximum angle was indeed found to occur for φ 4 = We observe in Figure 4.9(e) that the effective damping parameter is anisotropic, having a maximum value when the field is parallel to the [100] hard axis ( 0.018) that is roughly 2.5 times larger than the minimum value that occurs when the field is parallel to the [110] easy axis ( 0.007). The variation of the damping parameter is fitted by the inhomogeneous broadening model (equations (4.14) and (4.15)) with a constant offset, while the blue dashed curve is a phenomenological curve that has the algebraic form, α = C/ {1 D cos [4 (φ + φ 4 )]}, (4.16) where φ is calculated from equation (4.12). All fitted parameter values are shown in Table 4.2. Notice that the maximum frequency is obtained for φ 4 = 45 for both the Co 2 MnSi and Co 2 MnAl films, but there is a 45 phase difference between the peak damping parameter for the two films. For the Co 2 MnAl film the peak frequency and damping parameter coincide, while for Co 2 MnSi the peak damping parameter is found when the frequency is at a minimum. Dependence of transient Kerr rotation signals upon the field strength The dependence of the transient Kerr rotation signal upon magnetic field strength for A 300 is shown in Figure 4.10(a). Again each TRMOKE scan has been fitted to equation (4.1), with the dependence of the fitted amplitude, frequency, relaxation rate and effective damping parameter on the field strength shown in Figures 4.10(b)-(e) respectively. The fitting parameters are the same as those used to fit the variation of frequency with field orientation in the previous section. From Figure 4.10(b) the measured precession amplitude is seen to gradually decrease as the static magnetic field is increased from 0.5 to 2 koe. This is consistent with the reduced canting of the magnetisation from the external field at higher field values. The amplitude also decreases rapidly when the magnetic field is decreased from 0.2 to 0 koe, as the magnetisation approaches the easy axis. The curve generated from equation (4.5) describes the general trend but has a much sharper maximum. Good agreement is only obtained when the value of K (0) 1 is increased to a value much larger than that deduced from the static MOKE magnetometry measurements, as shown in Figure 4.10(b). This value of K (0) 1 also fits the variation of the amplitude with field orientation. In principle inhomogeneity of K 1 and M S might lead to broadening of the peak. Numerical calcula-

108 CHAPTER 4. OPTICALLY INDUCED FERROMAGNETIC RESONANCE k O e 1.7 k O e (a ) A m p litu d e (m d e g ) K 1 = (s ta tic ) K 1 = (b e s t fit) (b ) T ra n s ie n t K e rr ro ta tio n (m d e g ) k O e k O e 1.0 k O e 0.7 k O e 0.5 k O e k O e k O e F re q u e n c y (G H z ) R e la x a tio n ra te (n s -1 ) D a m p in g p a ra m e te r In h o m o g e n e o u s b ro a d e n in g A n is o tro p ic in trin s ic a lp h a (c ) (d ) (e ) T im e d e la y (n s ) F ie ld (k G ) Figure 4.10: (a) Transient Kerr rotation signals obtained from A 300 with φ 4 = The experimental data are fitted to equation (4.1). The field dependence of (b) the fitted amplitude and (c) the fitted precession frequency on the field strength are then fitted to equations (4.5) and (4.6) respectively, with fitted parameter values given in Table 4.1. The fitted relaxation rate is shown in (d) while the associated damping parameter is shown in (e). The red curve is a fit to the inhomogeneous broadening model (4.15) while the blue dashed curve in (e) is a phenomenological curve calculated from equation (4.16), with fitted parameter values given in Table 4.2.

109 CHAPTER 4. OPTICALLY INDUCED FERROMAGNETIC RESONANCE 108 tions showed that while the peak amplitude field value does depend upon K 1 and M S, reasonable choices of M S and K 1 do not produce broadening sufficient to reproduce the experiment. Note also that the fit to the frequency in Figure 4.10(c) is only accurate when the expression for φ in equation (4.12) is used. The effective damping parameter α appears to be independent of the applied field strength until the field is reduced to less than 0.2 koe. For fields greater than 0.2 koe, the value of α = is consistent with that found in the azimuthal scan shown in Figure 4.9(f) at φ 4 = Again the effective damping parameter is fitted to the inhomogeneous broadening model (red curve) while the blue dashed curve is obtained from equations (4.16) and (4.12). The inhomogeneous broadening model does not describe the field dependence of the effective damping parameter particularly well, producing a sharply peaked minimum that is not seen in the experimental data, and predicting an increase at larger field values while the data shows an approximately constant value. Dependence of transient Kerr rotation signals upon the pump pulse energy and spot size Measurements were performed for a range of pump pulse energies in order to detect the presence of damping mechanisms that depend upon the amplitude of precession. The average power of the pump beam was measured with a standard power meter to an accuracy of about 10 %. Figure 4.11 shows the variation of (a) amplitude, (b) frequency, (c) chirp parameter, and (d) relaxation rate with pump pulse energy for sample A 300. The amplitude increases linearly with pulse energy up to 0.9 µj, while the frequency decreases linearly. Two sets of data are presented for the frequency: values obtained from the fit to equation (4.1) and values obtained from FFTs of the TRMOKE scans. The FFT gives an average frequency over the entire scan period (2-3 ns), while the fit - when a chirp parameter is used - gives the frequency at the beginning of each scan. For the maximum pulse energy used the frequency obtained from the FFT is smaller by about 3 %, while that determined by the fitting is smaller by about 4 %, relative to the extrapolated value at zero pump energy. This can be understood as a thermal effect whereby the magnetic parameters (magnetisation and magnetocrystalline anisotropy) of the sample undergo a larger ultrafast modification at zero time delay when a higher pump pulse energy is used. The frequency also changes more rapidly in time, giving rise to an increased chirp parameter (Figure 4.11(c)). For the maximum pulse energy used, the chirp parameter of 0.06 GHz/ns implies an increase in frequency of 0.18 GHz, or about 2 %, during a 3 ns

110 CHAPTER 4. OPTICALLY INDUCED FERROMAGNETIC RESONANCE (a ) (b ) A m p litu d e (m d e g ) C h irp p a ra m e te r (G H z /n s ) (c ) P u ls e E n e rg y (µj ) F re q u e n c y (G H z ) R e la x a tio n ra te (n s -1 ) (d ) P u ls e e n e rg y (µj ) Figure 4.11: The dependence of (a) amplitude, (b) frequency, (c) chirp parameter, and (d) relaxation rate upon the energy of the pump pulse are shown for measurements made on sample A 300 with a field of 445 Oe applied parallel to the plane of incidence and at φ 4 = In (b) the circles were determined from fits to equation (4.1), while the squares were obtained from fast Fourier transforms. In all panels the solid lines are guides to the eye. scan. The relaxation rate (Figure 4.11(d)), and hence the effective damping parameter, are not affected by the pump pulse energy within the range of values used in the present experiments. A possible origin of inhomogeneity in all-optical TRMOKE is the spatially nonuniform intensity profile of the pump laser spot. The nonuniform pumping mechanism could lead to generation of spin waves that carry energy away from the probed region. If this is a significant factor then changing the size of the pump spot relative to the probe should result in a different value of the relaxation rate. In fact we found that doubling the pump spot diameter with a constant probe spot size made little difference to the observed relaxation rates. Therefore we can say that the nonuniform pump intensity has a negligible contribution to the total damping in this case.

111 CHAPTER 4. OPTICALLY INDUCED FERROMAGNETIC RESONANCE 110 Dependence of the precession frequency upon the annealing temperature Time resolved measurements were also made on samples annealed at 400 C (A 400 ) and 450 C (A 450 ). Annealing at higher temperatures is known to improve the site ordering of these films, and changes in the structure and electronic state are expected to influence the magnetic properties [62]. The static He-Ne MOKE loops in Figure 4.7 show a reduction in the magnetocrystalline anisotropy, K 1, with increasing annealing temperature. The smaller magnetocrystalline anisotropy in turn leads to a smaller amplitude precession in TRMOKE measurements. While smaller static field values were used to increase the precession amplitude, the values of 440 Oe for A 400 and 475 Oe for A 450 are still sufficient to produce a uniformly magnetized state. Time-resolved data for A 400 and A 450 are shown in Figures 4.12 and 4.13 respectively. The oscillation amplitude is expected to 6 (a ) O e 1 0 (b ) O O O e O T ra n s ie n t K e rr ro ta tio n (m d e g ) O e O e O e O e O e O e T ra n s ie n t K e rr ro ta tio n (m d e g ) O O O O 9 0 O 8 5 O 8 0 O O e 7 5 O O e O T im e d e la y (n s ) T im e d e la y (n s ) Figure 4.12: (a) TRMOKE signal as a function of applied field strength for sample A 400, with φ 4 = 22.5, and (b) TRMOKE signal as a function of field orientation, φ 4, with H = 440 Oe. The open circles are experimental data, while the red curves are fits to equation (4.1).

112 CHAPTER 4. OPTICALLY INDUCED FERROMAGNETIC RESONANCE (a ) (b ) O e O O e O O T ra n s ie n t K e rr ro ta tio n (m d e g ) O e O e O e O e O e O e T ra n s ie n t K e rr ro ta tio n (m d e g ) O O O O O O O e O e O O O e O O T im e d e la y (n s ) T im e d e la y (n s ) Figure 4.13: (a) TRMOKE signal as a function of applied field strength for sample A 450, with φ 4 = 22.5, and (b) TRMOKE signal as a function of field orientation, φ, with H = 475 Oe. The open circles are experimental data, while the red curves are fits to equation (4.1). decrease monotonically with increasing field strength, as a direct result of the smaller equilibrium canting of M relative to H. This trend is well produced by A 450, but for A 400 some variability in amplitude was noted for scans obtained hours apart. This may be due to inhomogeneity of the sample on length scales comparable to or greater than the spot size, and repositioning of the sample between scans. Again due to the reduced magnetocrystalline anisotropy, the amplitude of precession and hence the signal to noise ratio of the TRMOKE data is worse for A 400 and A 450 compared to A 300. For sample A 450 TRMOKE signals were recorded in the transverse field geometry (H T in Figure 4.1) as the field strength was varied. This yielded somewhat larger oscillatory Kerr signals, and explains why larger signals are seen for A 450 relative to A 400.

113 CHAPTER 4. OPTICALLY INDUCED FERROMAGNETIC RESONANCE 112 F re q u e n c y (G H z ) D a m p in g p a ra m e te r In h o m o g e n e o u s b ro a d e n in g m o d e l P h e o m e n o lo g ic a l c u rv e A n g le φ 4 (d e g ) (a ) (c ) (e ) (g ) A A A A A A F ie ld (k O e ) (b ) F it F it F it (d ) (f) (h ) Figure 4.14: The results of TRMOKE measurements on samples A 300, A 400 and A 450. (a) and (b) show the dependence of the precession frequency on field orientation and strength respectively. The remaining panels show the variation of the effective damping parameter with field strength and orientation for all three samples. The red curves are the fit to the inhomogeneous broadening model, while the blue dashed curves correspond to a phenomenological expression fitted to the data. Transient Kerr rotation signals were again fitted to equation (4.1), but with the chirp parameter set to zero due to the somewhat lower quality of the raw data. Figures 4.14(a) and (b) show the variation of precession frequency with field orientation and field strength respectively for all three annealing temperatures. Although the variation of the precession frequency in Figure 4.14(a) is much smaller for A 400 and A 450 compared to that observed for A 300, the fourfold symmetry is still clear (Figure 4.14(a)). The frequency versus field strength scans are nearly identical at high field for all three samples (figure

114 CHAPTER 4. OPTICALLY INDUCED FERROMAGNETIC RESONANCE (b)), indicating that M S is very similar for all three samples. The dependence of the effective damping parameter on the field orientation is shown in Figures 4.14(c), (e) and (g), and variation with field strength in (d), (f) and (h), for samples A 300, A 400 and A 450 respectively. The damping parameter values in Figure 4.14(e) and (g) show strong scatter near the easy and hard axis orientations due to the small amplitude of the Kerr rotation. The uncertainty in the damping parameter increases with increased annealing temperature as a result of the reduced amplitude of the MOKE signal. The fitted magnetic parameters and extracted damping parameters with there uncertainties are presented in Table 4.1, along with the values of the saturation magnetisation determined by VSM and hard axis saturation field H S from the conventional MOKE measurements. The dependence of the effective damping parameter upon H for H > 0.5 koe is quite different for A 400 and A 450 when compared to A 300. For A 300 the damping parameter appears to be constant above 500 Oe, while for A 400 and A 450 the damping parameter increases with field. The anisotropy of the damping parameter is rather similar for all three annealing temperatures. For all three samples the variation of damping with field orientation can be well fitted by the inhomogeneous broadening model with a constant offset, while the same model reproduces the trends in the field dependent data for all Table 4.1: The measured and fitted magnetic parameters from static and time-resolved MOKE. H S M S g K 1 2K 1 /M S α [110] α [100] (Oe) (emu/cm 3 ) (erg/cm 3 ) (Oe) ±0.003 ±0.005 A ± ± A ± ± A ± ± Table 4.2: Fitted parameter values from the inhomogeneous broadening model and phenomenological curve α constant M S K 1 K 1 /K 1 C D (emu/cm 3 ) (erg/cm 3 ) A ±6 0.17± % A ±9 0.09± % A ±9 0.11± %

115 CHAPTER 4. OPTICALLY INDUCED FERROMAGNETIC RESONANCE 114 but A 300. The parameter values obtained from fitting to the inhomogeneous broadening model are shown in Table 4.2. Due to their relatively weak influence on the total damping, the dispersion in the perpendicular anisotropy ( K u ) and the magnetisation orientation ( φ 4 ) were set equal to zero. The dispersion in the anisotropy constant, K 1, is found to be of similar magnitude, erg/cm 3, for all three samples, even though this represents a very large percentage change for A 450. The phenomenological expression (blue dashed curve in figures) yields a reasonable description of the angular variation of α for all three samples, however for samples A 400 and A 450 the increase of the effective damping parameter at higher fields is only reproduced by the inhomogeneous broadening model Discussion The static magnetic properties of the samples in the present study are seen to be distinctly different to those reported previously for nominally similar samples [88]. VSM measurements have shown that the value of the spontaneous magnetisation M S is close to that of the bulk material in all three samples and so appears to be unaffected by the annealing treatment. This finding is supported by the dependence of the precession frequency upon field strength shown in Figure 4.14(b). The curves for the three samples are almost exactly overlaid at high field values, suggesting that the effective demagnetizing field is very similar in each case. The film thickness of 30 nm is rather too large for surface anisotropy fields to be significant, while there is no suggestion from x-ray measurements of a tetragonal distortion in the direction normal to the film. It is therefore reasonable to conclude from the TRMOKE measurements that the spontaneous magnetisation is very similar in each case, and also that any diffusion from the Cr buffer layer must be weak. While the values of K 1 deduced from the MOKE hysteresis loops of Figure 4.7 are larger, the dramatic decrease of K 1 with annealing temperature observed by both static and time resolved MOKE is similar to that reported by Gaier et al. [88]. The variation of the precession amplitude with the orientation of the applied magnetic field shown in Figures 4.9, 4.12(b) and 4.13(b) confirms that magnetisation precession is induced by ultrafast optical modification of the magnetocrystalline anisotropy field. The amplitude is seen to vanish when the field is parallel to either the hard or easy axes, while the amplitude of precession decreases with annealing temperature due to the decreasing value of K 1. The experimental data of Figures 4.9 and 4.10 is well described by the simple model presented previously, with the exception of the dependence of the Kerr amplitude upon field strength shown in Figure 4.10(b). This is most likely due to the occurrence of

116 CHAPTER 4. OPTICALLY INDUCED FERROMAGNETIC RESONANCE 115 spatial non-uniformity of the magnetisation, which is not taken into account within the model, when the applied field is smaller than the anisotropy field. The values of 2K 1 /M S deduced from pump-probe experiments shown in Table 4.1 are significantly smaller than those deduced from MOKE magnetometry at room temperature. This may be attributed to the local increase in temperature induced by the pump pulse during the time resolved MOKE measurements. The pump-induced demagnetisation was deduced from Figure 4.8 for time delays at which non-thermal modification of the optical constants can be neglected and at which the electron and phonon systems can be assumed to have reached a common temperature. While the optically induced demagnetisation was found to be about 1 % for all three samples, the reduction of 2K 1 /M S deduced from the dependence of the precession frequency upon field orientation in Figure 4.14(a) was about 35 % for A 300 and A 400 and 49 % for A 450. The reduction of K 1 deduced for A 300 is also consistent with the dependence of the precession frequency upon pump pulse energy shown in Figure 4.11(b). The variation of the precession frequency is dominated by the variation of the 2K 1 /M S term within the expression for H β in equation (4.6). The 3 % reduction in the precession frequency at short delay times for pulse energy of 0.6 µj requires 2K 1 /M S to be reduced by 35 %. For bulk materials theory predicts [5] that K 1 (T ) M(T ) n, with n = 10, so that the pump induced demagnetisation should lead to a fractional change in 2K 1 /M S given by, ( ) ( ) K1 (T ) K1 (T ) / = (n 1) M(T ) M(T ) M(T ) M(T ). (4.17) A demagnetisation of about 1 % should then lead to a change in 2K 1 /M S of about 10 % that is significantly smaller than the observed values. This suggests the presence of other pump-induced contributions to the anisotropy energy, such as magneto-elastic anisotropy associated with thermal expansion [96] and magnetoelastic coupling [97], which has been inferred previously when larger values of n have been observed [9]. While the dependence of the frequency of precession upon field strength and orientation is generally well described by the model using constant values of M S, g and K 1 for a particular sample, Figure 4.14 shows that the damping parameter α must vary significantly for the model to reproduce the observed variation of the relaxation rates with field strength and orientation. It is first necessary to consider whether the variation of α is either an artifact associated with the TRMOKE measurement technique or specific to the experimental conditions employed. Figure 4.11 shows that while the amplitude of precession increases monotonically, the relaxation rate and hence α are constant as the

117 CHAPTER 4. OPTICALLY INDUCED FERROMAGNETIC RESONANCE 116 pump fluence is increased. This suggests that non-linear effects such as three and four magnon scattering do not contribute to the damping. Also the temperature dependence of the damping reported previously [98] for spin-valve samples cannot be significant in the present case. The intensity of the focused pump beam may be assumed to have a Gaussian radial dependence, which implies that the initial temperature change and hence the frequency of precession also depend upon the distance from the center of the pump spot. By weighting the signals obtained from annuli of different radius by the probe intensity, which is itself described by a Gaussian function of smaller width, a frequency distribution function may be obtained. The full width at half maximum (FWHM) of this curve may then be inserted into equation (4.14), from which it is found that dephasing of signals associated with different distances from the spot center should contribute less than 15 % of the total observed relaxation rate. The radial variation of the amplitude of precession could also lead to the propagation of long wavelength magnetostatic spin waves out of the probed region, leading again to an increase of the observed relaxation rate [80]. The effect is anisotropic with surface modes propagating perpendicular to the magnetisation with a group velocity that is an order of magnitude greater than that of the backward volume waves that propagate parallel to the magnetisation. A rough estimate suggests that the surface waves may propagate a distance up to about 30 µm within the 3 ns range of time delay used in the experiments. This effect may therefore have some small influence upon the relaxation rate determined with a probe spot of 80 µm diameter. However, the most direct evidence that inhomogeneous excitation does not significantly contribute to the observed relaxation comes from the observation that the relaxation rate was unaffected when the diameter of the pump spot was doubled. The phenomenological expression in equation (4.16) is seen to give a good description of the dependence of α upon field orientation, but a poor account of the dependence of α upon field strength within Figure The inhomogeneous broadening model is able to reproduce the dependence of α upon field orientation and the increase in α seen at large fields for A 400 and A 450. However it overestimates the variation of α at high fields for A 300. While the model shows an upturn in α at low field it is again questionable whether the model is applicable in this regime, since the static magnetisation may become spatially non-uniform, and so the lack of quantitative agreement is unsurprising. From Table 4.2 it is seen that the model is able to describe the data for all three samples if the constant intrinsic contribution to α increases slightly from to as T an is increased from 300 to 450 C. The fractional dispersion in M S is about 5 % for all three samples while

118 CHAPTER 4. OPTICALLY INDUCED FERROMAGNETIC RESONANCE 117 the fractional dispersion in K 1 is much larger. This seems reasonable since K 1 appears to differ greatly for the B2 and L2 1 phases, so there should be strong dispersion of K 1 for a film containing both phases. Although the absolute dispersion decreases with annealing, the fractional dispersion increases dramatically with annealing temperature due to the large reduction of the average value of K 1. An alternative explanation of the variation of the value of α may be provided by two magnon scattering from a four-fold network of misfit dislocations, as reported previously for epitaxial thin films [73, 74]. However further structural studies are required to confirm the presence of such dislocations in the present case, and further theoretical work is required to demonstrate that this mechanism yields the correct dependence of α upon the strength and orientation of the applied field. In those studies the Fe films were subjected to a lattice strain by a mismatch with an underlying Pd layer, giving rise to dislocations with the same rotational symmetry as the Fe films. While in this case the Co 2 MnSi films are well lattice-matched to the substrate, growth by sputter deposition may introduce a similar network of defects that are not fully removed by the annealing process. Comparing the values of α in Figure 4.14 and Table 4.2 with those reported by Yilgin et al., there are a number of significant differences. The values obtained from TRMOKE are larger than those from FMR, and in the TRMOKE measurements the inhomogeneous broadening model can largely account for the variation of the effective damping parameter without the need for an anisotropic intrinsic damping. It is possible that the TRMOKE and FMR techniques yield different values due to the different volumes of material sampled. However TRMOKE samples a small spot of 100 µm size while in FMR the entire sample is placed within the microwave cavity, so inhomogeneous broadening is expected to be more severe in the case of FMR [78]. The smaller values of α obtained by Yilgin et al. may in part be due to the different methods used to account for the contribution of inhomogeneous broadening to the FMR linewidth. While Cr diffusion from the buffer layer might influence the damping in the study of Yilgin et al., this seems less likely in the present study because the value of M S was unaffected by the annealing treatment. Finally, it should be noted that the beam from the regenerative laser amplifier system used in the present study may become very slightly divergent or convergent as the alignment of the amplifier is adjusted from day to day. The focusing of the pump and probe spots is performed with the optical delay line set for short time delays. However if the pump beam passing through the delay line is not exactly parallel then the size of the focused spot may increase when the path length is changed so that the amplitude of the oscillatory Kerr signal is reduced giving the

119 CHAPTER 4. OPTICALLY INDUCED FERROMAGNETIC RESONANCE 118 impression of a somewhat larger damping. The diameter of the pump spot would need to increase by approximately 50 % over the duration of the measurement to explain the difference in the values of α deduced from the TRMOKE and FMR studies. The present study has therefore shown that the site ordering that results from annealing Co 2 MnSi films can lead to a dramatic change in the value of K 1 while the values of M S, g and the intrinsic contribution to α are not greatly affected, even though the values of K 1 and α both originate from the spin-orbit interaction. While the slight variation of the fitted g factor in Table 4.1 with annealing temperature is probably not significant, the fact that the value is just less than 2 for all three samples suggests that in each case the orbital moment is small and anti-parallel to the spin moment. The small orbital moment also accounts for the relatively small values of α since the values of α and g - 2 are generally found to be correlated [99]. However the magnetocrystalline anisotropy depends instead upon the anisotropy of the orbital moment as it is aligned parallel to different crystallographic axes. Annealing presumably enhances the strength of the crystal field and leads to a reduction in both the size and anisotropy of the orbital moment, and hence to the observed reduction of the magnetocrystalline anisotropy. 4.6 Summary In summary, all-optical pump-probe measurements of precessional magnetisation dynamics have been presented for epitaxial Co 2 MnAl and Co 2 MnSi thin films in which precession of the magnetisation is induced by an ultrafast reduction of the magnetocrystalline anisotropy field. A simple model allows the values of the effective fields within the sample to be deduced from the dependence of the frequency of precession upon the strength and orientation of the applied magnetic field. The macrospin LLG model also allows an effective damping parameter α to be determined from the observed relaxation of the oscillatory Kerr rotation signal. A first study on a Co 2 MnAl film showed that the damping parameter in these TRMOKE measurements is not a constant value, but varies with strength and orientation of the applied static field. The data also revealed that the magnetocrystalline anisotropy can, due to its strong temperature dependence, be reversed under the action of the laser pulse heating. A study of Co 2 MnSi films with varied annealing temperature revealed that while the magnetocrystalline anisotropy constant is greatly reduced with increased annealing

120 CHAPTER 4. OPTICALLY INDUCED FERROMAGNETIC RESONANCE 119 temperature, the magnetisation remains almost unchanged, and therefore it is unlikely that the reduction in anisotropy is the result of diffusion from the Cr buffer layer. The damping parameter again exhibits a strong dependence upon the strength and orientation of the applied field. For the Co 2 MnAl and Co 2 MnSi films the peak frequency was observed when the static field was applied parallel to the [110] axis, and so the easy axis of magnetisation at the elevated temperature of the TRMOKE measurements is the [110] axis for all samples. On the other hand the peak damping parameter was found to occur when the static field was applied parallel to the [110] axis for Co 2 MnAl, but parallel to the [100] axis for Co 2 MnSi. This indicates that the damping parameter is not directly related to the frequency of precession in these films. This is supported by the observation that while the magneto-crystalline anisotropy is greatly reduced with increased annealing temperature of the Co 2 MnSi films the variation of the damping with field orientation is relatively unchanged. For the Co 2 MnSi films the dependence of α upon the field orientation is well described by an inhomogeneous broadening model in which there is a constant intrinsic contribution to the damping and strong dispersion in the value of the cubic magnetocrystalline anisotropy constant, K 1. The inhomogeneous broadening model provides a good description of the field dependence of the effective damping parameter for samples annealed at temperatures of 400 and 450 C, but not for that annealed at 300 C. This may imply that two magnon scattering from a four-fold network of misfit dislocations contributes to the observed damping behaviour. The strong dispersion of K 1, invoked within the inhomogeneous broadening model for samples of mixed phase, is a consequence of the large difference in the values of K 1 for the B2 and L2 1 phases. Annealing leads to an increased fraction of the L2 1 phase and a reduction in the measured K 1 value, while the intrinsic contribution to α increases slightly. These conclusions may be understood if the orbital moments are small for both phases, but the anisotropy of the orbital moment is reduced in the L2 1 phase relative to the B2 phase. Finally, this work demonstrates the potential of the optical pump-probe measurement technique for the study of dynamical magnetic properties in microscopic samples where the addition of planar waveguides for the delivery of pulsed magnetic fields is either undesirable or infeasible.

121 Chapter 5 Interfacial studies of Heusler alloy thin films 5.1 Introduction The tunneling magnetoresistance (TMR) of a magnetic tunnel junction (MTJ) is thought to depend largely upon the spin polarisation at the interfaces between the electrodes and the tunnel barrier [22, 100]. Therefore a great deal of effort is placed on improving the quality of interfaces of these multilayered structures by, for example, post deposition annealing and optimising tunnel barrier oxidation. Measurement techniques capable of characterising surface and interfaces are therefore required for investigation of these regions of thin films. In this chapter work performed using magnetic second harmonic generation (MSHG) and x-ray magnetic circular dichroism (XMCD) will be reviewed. The MSHG work was undertaken at the University of Exeter by myself, while the XMCD work was performed at the Advanced Light Source (ALS) by Dr N D Telling, Dr P S Keatley and myself. MSHG was proposed as a probe of surface magnetisation in 1989 [43, 44] and was first demonstrated in 1991 [45]. In that first experiment the second harmonic intensity from a nickel sample with a clean surface was found to vary by 25 % when the magnetisation orientation was reversed. The intensity change was found to decay exponentially as the surface became contaminated by CO absorption from the residual gas, demonstrating the high surface sensitivity of the tecnhique. Since then MSHG has been applied in many surface and interface studies. In 1995 Wierenga et al. used MSHG to measure surface hysteresis loops from fcc Co/Cu, with surface sensitivity demonstrated by the dependence

122 CHAPTER 5. INTERFACIAL STUDIES OF HEUSLER ALLOYS 121 on the Co thickness. Oscillations in the second harmonic intensity during growth of Co have been observed [101, 102] with the period corresponding to a single monolayer of growth. In 2004 H Yamada et al. [103] used MSHG to probe the magnetic properties at the interface between La 0.6 Sr 0.4 MnO 3 and a non-magnetic insulating layer. They found a magnetic dead layer at the interface with a SrTiO 3 insulating layer, while the interface with a LaAlO 3 layer showed interfacial ferromagnetism up to 250 C. The studies reported in this chapter were made on the same series of Co 2 MnSi films as investigated by optically induced ferromagnetic resonance in chapter 4. The full Heusler alloy Co 2 MnSi is a highly promising material for use in spintronics due to its predicted half-metallic electronic structure [23] and its high Curie temperature (985 K [91]). The films were fabricated at Tohoku University by Y. Sakuraba, Y. Ando and T. Miyazaki [87] where transport measurements were also performed on full MTJ stacks. Large TMR values of up to 570 % have already been observed at low temperature in MTJs with Co 2 MnSi electrodes and an amorphous AlO x barrier [60, 104]. The site-ordering is known to increase with annealing temperature, with optimum TMR found for T an =450 C [60]. It was found that the tunnel magnetoresistance was strongly dependent on temperature and on the annealing temperature of the ferromagnetic electrodes. MSHG and XMCD studies have been performed on the effect of annealing temperature and of ambient temperature on the surface region of the Co 2 MnSi Heusler alloy. In this chapter the results of these studies will be presented independently, with summaries and conclusions drawn at the end. 5.2 Magnetic Second Harmonic Generation Magnetic second harmonic generation is a magneto-optical effect that is interface sensitive for materials that have bulk inversion symmetry, as discussed in detail in chapter 3. A first study showed a strong dependence of the MSHG in a Ni 81 Fe 19 /AlO x structure upon the oxidation time of the Al over layer [105]. More recently the TMR and MSHG intensity were shown to have a qualitatively similar dependence upon temperature and interface composition in MTJ structures with La 1 x Sr x MnO 3 (LSMO) electrodes [103, 106]. Interface roughness has been shown to increase the nonmagnetic contribution to the second harmonic intensity [107], and periodic oscillations in MSHG asymmetry during growth of a Co film have been observed with maximum asymmetry for a complete monolayer [101, 102] with a corresponding oscillation coercive field of the films.

123 CHAPTER 5. INTERFACIAL STUDIES OF HEUSLER ALLOYS 122 It is reasonable to expect that due to their shared interfacial sensitivity there may exist a link between TMR and MSHG. In this section it will be shown that a strong correlation between the effect of annealing temperature on TMR and in the MSHG response for samples prepared under similar conditions has been found. Temperature dependent MSHG measurements will also be reported Experimental details The MgO(001)/Cr(40 nm)/co 2 MnSi(30 nm)/alo x (1.3 nm) samples were grown by inductively coupled plasma assisted magnetron sputtering at room temperature [60]. The Co 2 MnSi films form a cubic structure of (001) orientation with fourfold rotational symmetry, the hard and easy magnetic anisotropy axes lying parallel to the [100] and [110] crystal axes respectively [64]. Samples A x had varied Co 2 MnSi annealing temperature with x = RT (no anneal), 300, 400, 450, and 500 C, prior to deposition of the Al capping layer which was not oxidised (except for natural oxidation in the air). Samples B 50 and B were annealed at 450 C after which the Al layer was deposited and then plasma oxidised for 50 s. Sample B also had a second annealing treatment at 250 C after barrier oxidation. The Co 2 MnSi full Heusler alloy has a body-centred cubic structure in which the site occupation and ordering depends on the annealing temperature. X-ray diffraction has shown that in the as-deposited films the A2 phase is realised where the sites are randomly occupied by Co, Mn and Si atoms [87]. After annealing at 300 C the B2 phase forms where the Co atoms occupy the cubic corner sites and the Mn and Si atoms randomly occupy the body centres. At sufficiently high annealing temperature the highly ordered L2 1 phase is obtained where Mn and Si atoms occupy alternate body centre sites. For the films studied in this thesis the B2 phase was obtained for films annealed at 300 C and the L2 1 phase was obtained in progressively higher proportions at higher annealing temperatures. It is important to consider the symmetry of these various phases and how they may affect the interface sensitivity of MSHG. MSHG is surface sensitive when the bulk material has inversion symmetry, but whether this applies to the Co 2 MnSi films depends on the site ordering. In the A2 and B2 phases the unit cell may be chosen as the primitive bodycentred cubic cell, and for both phases inversion symmetry is allowed in the bulk since several sites are randomly occupied. In the L2 1 phase the same unit cell does not allow inversion symmetry since the body centre sites are alternately occupied by Mn and Si. In a semi-classical picture bulk SHG is still forbidden if the charge density seen by electrons

124 CHAPTER 5. INTERFACIAL STUDIES OF HEUSLER ALLOYS 123 near Mn and Si ions are similar, so that the potential does have inversion symmetry. The most reliable method is to test for interfacial sensitivity in every case. In this chapter a significant difference in the MSHG response from Co 2 MnSi films with and without plasma oxidation of the Al-O cap supports of strong interfacial of MSHG in this case. The experimental setup is shown in Figure A Ti:sapphire regenerative amplifier supplied 100 fs pulses of 800 nm wavelength and 0.5 µj energy at a 45 angle of incidence. The inset in figure 3.15 shows the relative orientation of the optical polarisation and applied magnetic field. H T refers to a field perpendicular to the plane of incidence, H L refers to a field in the plane of incidence, while both H L and H T lie in the sample plane. The four combinations of incident and collected polarisation states probe different components of the nonlinear optical susceptibility tensor that describes the MSHG [43, 50]. From here on we use the notation s, p to refer to incident fundamental polarisation, and S, P to refer to collected second harmonic polarisation. The collinear 800 nm and 400 nm components of the reflected beam were spatially separated using dispersive glass Brewster prisms, and the 400 nm light was detected using a photon counting system, with a background count rate of 20 counts/s and typical signal levels of 1000s counts/s Annealing temperature dependence Results In Figure 5.1 MSHG and linear magneto-optical Kerr effect (MOKE) hysteresis loops are shown for sample A 450 with field applied parallel to the [110] easy and [100] hard axes in the p-p configuration. The MSHG loops were acquired using a field H T, while the MOKE loops were acquired using a field H L, since these configurations are expected to be sensitive to the same component of the magnetisation. The linear MOKE and MSHG loops are seen to have a qualitatively similar shape, suggesting that the bulk and interfacial magnetisation reverse in a similar manner. The effect of annealing temperature and oxidation upon the MSHG response for all samples is shown in Figure 5.2. The left and right columns show results obtained with the sample magnetised parallel to the [100] and [110] axes of the Co 2 MnSi, respectively. All measurements were made with the field applied perpendicular to the plane of incidence (H T in Figure 3.15 inset). The first row (Figures 5.2(a) and 5.2(b)) shows the even MSHG intensity, which is defined to be the average intensity within the hysteresis loop. The second row (Figures 5.2(c) and 5.2(d)) shows the odd MSHG intensity, which is equal to the hysteresis loop height. The absolute second harmonic intensity is not normalised

125 CHAPTER 5. INTERFACIAL STUDIES OF HEUSLER ALLOYS 124 to the incident intensity of the fundamental light, and therefore will vary as the square of the intensity variation of the incident fundamental light. In addition the second harmonic yield was found to vary with position of the sample. The third row (Figures 5.2(e) and 5.2(f)) show the MSHG asymmetry, A = [I (+M) I ( M)] [I (+M) + I ( M)], (5.1) which has been suggested to be a more reliable measure of the magnetic contribution to the SHG yield [50], and which empirically is the most reproducible quantity when measurements are repeated. The asymmetry is normalised to the total SHG intensity, so it is not affected by intensity fluctuations of the laser source or by frequency or polarisation dependent properties of the optics. The asymmetry was also found to be repeatable from different regions of the sample. In the final panel (Figure 5.2(g)) we plot the difference in the MSHG asymmetry for M parallel to the [100] and [110] axes, which we refer to as the MSHG anisotropy, defined by, MSHG anisotropy = A ([110]) A ([100]). (5.2) Within each panel data are presented for the s-p and p-p configurations for all samples (see legend in lower-right of figure). No measurable S-polarised SHG was observed when the sample was magnetised parallel to either the [100] or [110] axes. 1.0 M S H G M O K E 0.5 M /M s (a ) (b ) F ie ld (k O e ) F ie ld (k O e ) Figure 5.1: Comparison of bulk MOKE and interface MSHG hysteresis loops for field parallel to (a) the [110] easy axis and (b) the [100] hard axis.

126 CHAPTER 5. INTERFACIAL STUDIES OF HEUSLER ALLOYS 125 E v e n M S H G (c p s ) M S H G a n is o tro p y M S H G a s y m m e ty O d d M S H G (c p s ) [1 0 0 ] a x is N o n -m a g n e tic [1 0 0 ] a x is M a g n e tic [1 0 0 ] a x is A s y m m e try (a ) (c ) A n n e a lin g te m p e ra tu re ( o C ) M S H G a n is o tro p y (g ) A n n e a lin g te m p e ra tu re ( o C ) [1 1 0 ] a x is N o n -m a g n e tic [1 1 0 ] a x is M a g n e tic (b ) (d ) (e ) [1 1 0 ] a x is (f) A s y m m e try A n n e a lin g te m p e ra tu re ( o C ) p -P s -P A x B 5 0 B Figure 5.2: (a) and (b) show the average MSHG intensity (even signal), and (c) and (d) the MSHG loop height (odd signal) with varied annealing temperature and oxidation. (c) and (d) are the MSHG asymmetry and (g) the MSHG anisotropy (defined in the main text). Apart from the s-p case in Figure 5.2(c), all odd and even MSHG intensities exhibit a pronounced peak at an annealing temperature of 450 C (sample A 450 ). No such peak is observed in the MSHG asymmetry plotted in Figures 5.2(e) and 5.2(f). Instead Figure 5.2(f) shows a general trend for the MSHG asymmetry to increase with increasing annealing temperature for M parallel to the [110] axis, while in Figure 5.2(e) the overall trend is for a slight decrease of the MSHG asymmetry with increasing annealing temperature

127 CHAPTER 5. INTERFACIAL STUDIES OF HEUSLER ALLOYS M S H G a s y m m e try A A fit A A fit B 5 0 B 5 0 fit B B fit Figure 5.3: Polar plot of MSHG asymmetry for samples A 300, A 450, B 50, and B, showing clearly the fourfold anisotropy of the MSHG. for M parallel to [100]. This implies that the difference in MSHG asymmetry for the easy and hard axes - the MSHG anisotropy - tends to increase for samples annealed at higher temperatures, and indeed shows a peak for an annealing temperature of 450 C, in Figure 5.2(g). The effect of oxidation (sample B 50 ) and post-oxidation annealing (sample B ) upon samples with a Co 2 MnSi annealing temperature of 450 C are also shown in Figure 5.2. From Figure 5.2(a) (d) the general trend is for both oxidation and the second anneal to reduce the SHG yield. However in Figure 5.2(e) (f) the effect upon the MSHG asymmetry is much less marked. Finally in Figure 5.2(g) the MSHG anisotropy is seen to first decrease with oxidation and then partially recover after the second anneal. The full angular dependence of the MSHG asymmetry for samples A 300, A 450, B 50 and B in the p-p case is shown in Figure 5.3. The samples were gradually rotated through an angle φ in the range of 0 360, about the normal to their plane, for the H T field orientation. The experimental data from each sample is well fit by a cos(4φ) function, confirming the fourfold symmetry of the interface.

128 CHAPTER 5. INTERFACIAL STUDIES OF HEUSLER ALLOYS 127 Discussion The strong effect of plasma oxidation of the Al cap on the SHG yield and magnetic signal indicates a high level of interface sensitivity in this MSHG study. Furthermore XAS and XMCD measurements (discussed in a later section) did not reveal any difference between samples B 50 and B, while the MSHG anisotropy shows a clear change between the two samples. A change in SHG yield following surface oxidation is often quoted as confirmation of interface sensitivity in SHG experiments, and in this case the same reasoning can be applied. No S-polarised SHG was observed in any measurement geometry. From symmetry analysis such as described in chapter 3 no S-polarised SHG is expected when the sample is magnetised parallel to the [100] Co 2 MnSi crystallographic axis, but when the magnetisation is parallel to the [110] axis some SH intensity is expected. It has been shown that S-polarised SHG can be hundreds of times weaker than P-polarised SHG [108], so in this case it is possible that S-polarised SHG was too weak to be detected. It is reasonable to expect that the strongest nonlinearity is perpendicular to the sample surface, which would give P-polarised second harmonic reflection. The peak observed in Figure 5.2(a) (d) in the odd and even MSHG yield for sample A 450 occurs at an annealing temperature of 450 C, which was previously found to yield the optimum degree of L2 1 ordering in x-ray diffraction (XRD) [87] and x-ray absorption spectroscopy (XAS) measurements. A multiplet structure observed in the associated x-ray magnetic circular dichroism (XMCD) spectra (see later) was suggested to be a signature of the half-metallic state [89]. This annealing temperature also yielded the maximum TMR [109], suggesting that the MSHG may be correlated with surface site ordering and spinpolarisation at the electrode/barrier interface. However repeated measurements of the MSHG yield generally show a monotonic decrease with time, which may be the result of accumulated laser damage or chemical reaction of the sample surface with the atmosphere. The MSHG asymmetry did not vary over time for a given configuration and sample, but no clear peak was observed for an annealing temperature of 450 C in Figures 5.2(e) and (f). On the other hand, the MSHG anisotropy has a maximum for an annealing temperature of 450 C in both the s-p and p-p configurations. Oxidation of the Al tunnel barrier is known to lead to the appearance of a multiplet structure in the Mn XAS spectra that signifies the formation of Mn oxide [89], possibly due to migration of oxygen at grain boundaries, which may be responsible for the dramatic decrease of the MSHG anisotropy. Post-oxidation annealing leads to a partial recovery

129 CHAPTER 5. INTERFACIAL STUDIES OF HEUSLER ALLOYS 128 of the MSHG anisotropy, which might be expected as oxygen returns from the Co 2 MnSi to the tunnel barrier where it is more strongly bound, and perhaps also as the interfacial roughness is reduced. Valev et al. [102] observed monolayer-period oscillations in the MSHG yield from a Mn/Co interface, with maximum yield for half-filled monolayers due to an increased interface roughness. They also concluded that the net interfacial magnetic moment is maximum for the flat interface since the MSHG asymmetry is maximum in this case. For the Co 2 MnSi/AlO x interface studied here the second anneal of sample B might be expected to reduce the even part of the MSHG intensity as the interface is smoothed, yet increase the MSHG asymmetry as a result of an increased interfacial magnetic moment. This is indeed observed in Figures 5.2(a), (b) and (g).

130 CHAPTER 5. INTERFACIAL STUDIES OF HEUSLER ALLOYS Temperature dependence of MSHG It has been observed that the temperature dependence of the TMR in MTJs with Co 2 MnSi electrodes is far stronger than that of MTJs with CoFeB electrodes [60]. The origin of this temperature dependence is not known, and x-ray measurements have shown that the near-interfacial moments are unchanged in this temperature range (see later section). In this section a study of the temperature dependence of the MSHG response of the Heusler alloy Co 2 MnSi is presented. MSHG has been successfully applied in temperature dependent studies of interfacial magnetisation. Valev et al. found a relationship between exchange bias in a CoO/Cu/Fe multilayer and the second harmonic Kerr rotation [110], while Ishii et al. observed an agreement between the spin-polarisation determined from TMR measurements and the square root of the MSHG intensity for magnetic tunnel junctions using (La,Sr)MnO 3 electrodes [103, 106]. The temperature dependent MSHG experiment presented in this section is effectively identical to that in the previous section but with the sample mounted inside an optical cryostat, as shown in Figure The inclusion of the cryostat dictated that the plane of incidence be rotated to the vertical in order to accommodate the rigid liquid-he transfer line. Also, dichroic mirrors replaced dispersive prisms in separating the reflected fundamental and second harmonic beams. This was done since no S-polarised SHG was recorded when the prisms were used and it was a concern that, due to their intrinsic polarisation-sensitive transmission, any S-polarised SHG was being attenuated. Two samples from the first study, B 50 and B, were studied as a function of temperature in the range K. Both samples had an initial anneal at 450 C and a 50 s Al oxidation, with sample B having a second anneal at 250 C and therefore most closely resembling the bottom electrode in the MTJs that showed strong TMR temperature dependence. Results Tests with a reference 400 nm wavelength beam showed very little polarisation dependence of the transmission of the dichroic mirrors, but still no measurable S-polarised SHG was observed. From the symmetry analysis and nonzero tensor elements discussed in chapter 3 one may expect that the S-polarised SH yield would be smaller than the P-polarised SH simply due to the lower number of tensor elements involved. It is noted that the S-polarised SHG may be significantly weaker than the P-polarised SHG [108], and therefore may not be discernible from the noise in these measurements.

131 CHAPTER 5. INTERFACIAL STUDIES OF HEUSLER ALLOYS 130 A b s o lu te M S H G A s y m m e try A b s o lu te M S H G A s y m m e try S a m p le B 5 0 p -P s -P (s ig n re v e rs e d ) (a ) S a m p le B p -P s -P (s ig n re v e rs e ) (c ) H [1 0 0 ] H [1 0 0 ] T e m p e ra tu re (K ) H [1 1 0 ] (b ) H [1 1 0 ] (d ) T e m p e ra tu re (K ) Figure 5.4: Temperature dependence of the MSHG asymmetry for samples B 50 ((a) and (b)) and B ((c) and (d)). The sign of the s-p data has been reversed for comparison with the p-p data. The points are experimental data and the lines are fitted as guides to the eye. The circled point has been disregarded in the fitting since the measured second harmonic yield was significantly lower than that for all other points. In Figure 5.4 the MSHG asymmetry for samples B 50 and B for field parallel to the [100] and [110] crystallographic axes in the s-p and p-p geometries is shown. The solid lines are included as a guide to the eye only. Note that one point in (c) for sample B is circled. The MSHG loop at this point showed significantly reduced second harmonic intensity compared to all other loops measured for that sample in that orientation. The data points are perhaps spaced too far apart on the temperature axis to know whether this is a true result or not, but for the current data that point appears to lie away from the general trend, and so is not included on the trend line. The absolute second harmonic intensity was found to be unreliable in the temperature dependent measurements, possibly as a result of sample movement with thermal expansion of the sample holder. The MSHG asymmetry however was reliable and repeatable. There is a clear difference in the MSHG

132 CHAPTER 5. INTERFACIAL STUDIES OF HEUSLER ALLOYS 131 response of the two samples. For sample B 50 the asymmetry is approximately constant at 0.4 with exception of the p-p case for field parallel to the [100] Co 2 MnSi axis. In that case the asymmetry falls to 0.3 at 292 K. For sample B (figure 5.4(c) and (d)) the picture is very different with a significant difference for the s-p and p-p cases for both sample orientations. For field parallel to the [110] Co 2 MnSi axis the MSHG asymmetry is larger than for sample B 50 and slightly decreases with increasing temperature for p-p. With field parallel to the [100] axis there is a significant difference in the asymmetry recorded in the s-p and p-p cases with a strong temperature variation particularly in the s-p case. It is noted that the 50 K temperature steps are insufficient to identify any complex variation of the asymmetry with temperature, so the analysis is restricted to trends over the K range. M S H G a n is o tro p y (a ) T e m p e ra tu re (K ) S a m p le B 5 0 p -P s -P (x -1 ) (b ) S a m p le B p -P s -P (x -1 ) T e m p e ra tu re (K ) Figure 5.5: Temperature dependence of the MSHG anisotropy for Co 2 MnSi samples (a) B 50 and (b) B. The solid lines are fitted as a guide to the eye, with the circled point has been disregarded in the fitting. Figure 5.5 shows the MSHG anisotropy determined from the data in Figure 5.4 and shows very clearly a difference between the two samples, with the anisotropy greatly enhanced for sample B compared to sample B 50. Temperature variation for sample B 50 in the p-p geometry shows an increase from 0.05 to 0.15 from K. For sample B there may be no temperature variation for p-p but there is a decrease from from K for s-p.

133 CHAPTER 5. INTERFACIAL STUDIES OF HEUSLER ALLOYS 132 Discussion The MSHG asymmetry can be increased by an increased magnetic contribution to the second harmonic intensity, a reduced nonmagnetic contribution or a combination of both. With the second anneal of sample B it is reasonable to expect a reduction of the interface roughness compared to sample B 50 and therefore an increase of the MSHG asymmetry. For field parallel to the [110] Co 2 MnSi axis the MSHG asymmetry is larger for sample B compared to sample B 50, as expected, however for field parallel to the [100] axis in the s-p geometry the asymmetry is lower for sample B. There is also a large difference in the MSHG asymmetry recorded by the p-p and s-p measurements in Figure 5.4(c). A p-polarised incident fundamental beam has an electric field component perpendicular to the sample surface while an s-polarised incident fundamental beam does not. It might be expected that the p-polarised incident fundamental is more sensitive to the magnetic asymmetry normal to the sample surface, and therefore that the MSHG asymmetry would be higher in the p-p case than in the s-p case. In the previous section the variation of the MSHG anisotropy with annealing temperature was found to vary similarly with the TMR, and a correlation between the two parameters was proposed. The MSHG anisotropy is far higher for sample B than B 50, indicating the importance of the second anneal following barrier oxidation. Sample B most closely resembles the bottom electrode in the MTJ that showed a strong dependence of TMR on temperature. For sample B the p-p MSHG anisotropy is temperature independent, while for s-p it decreases linearly from 0.35 to 0.15 from K. In this same temperature range the TMR has been found to fall from 570 % to 67 % [60] which, assuming identical spin polarisation in each Co 2 MnSi electrode, corresponds to spin polarisations 0.86 and 0.50, a 42 % reduction. Over the same temperature range the MSHG anisotropy in the s-p geometry is also reduced by about 42 %. This is a promising first result, and certainly warrants further investigation. Given the number of temperature points measured here and the potential for error, measurements must be repeated with high temperature resolution and on a broader range of samples to confirm whether this correlation between MSHG and TMR is real. With a suitable semi-classical model the interpretation of the MSHG data could be improved and a correlation between the MSHG response and TMR better understood. MSHG continues to be promising as a highly interface sensitive measurement tool.

134 CHAPTER 5. INTERFACIAL STUDIES OF HEUSLER ALLOYS X-ray magnetic circular dichroism Soft x-ray spectroscopy with photon energies scanned over the the core electron binding energies, typically several hundred ev for transition metals, allows determination of element specific magnetic moments. In chapter 3 x-ray magnetic circular dichroism (XMCD) was introduced as an element specific probe of magnetisation that can be used to measure the size and direction of magnetic moments. Additionally by orienting the x- rays at a narrow angle of incidence to the sample surface and recording the electrical drain current the measurements have near-interfacial sensitivity. This was illustrated very nicely in 1999 by R Nakajima et al. [111] on a sample consisting of a wedge shaped layer of Fe (0 3.5 nm) on top of a layer of layer of Ni (5 nm). As the x-rays were directed towards the thicker end of the Fe wedge the electron yield at the Fe resonant energy increased while at the Ni resonant energies the signal decreased in magnitude. The Ni signal dropped from its maximum to 1/e of this value with an Fe thickness of 2 nm. Additionally the fine structure in the x-ray absorption (XAS) and x-ray magnetic circular dichroism spectra can reveal localisation of electron states [112, 113], and hence the degree of spin-polarisation and half metallicity in the sample. XAS and XMCD have been employed here to study the near-interfacial region between ferromagnetic Co 2 MnSi and an Al capping layer. In the following sections I will discuss the results of XAS and XMCD on a series of Co 2 MnSi Heusler alloy films with varied annealing temperature and capping layer thickness. I will also discuss the temperature dependence of the interfacial Co and Mn moments obtained by sum-rule analysis of the XMCD spectra. The measurements were all performed at the Advanced Light Source synchrotron in Berkeley, California, with principal investigator Dr N D Telling. In this section the results of studies into the effect of annealing temperature and ambient temperature on the near interfacial moments of Co 2 MnSi films will be reviewed. Dr Telling was accompanied by Dr P S Keatley for investigations of a series of samples with varied annealing temperature, whilst I am a co-author of the temperature dependence of interface moments published by Dr Telling [93] Experimental details When performed in the total electron yield geometry the drain current through the sample that arises from the ejection of secondary electrons is recorded. Since the escape

135 CHAPTER 5. INTERFACIAL STUDIES OF HEUSLER ALLOYS 134 depth of the secondary electrons is limited the signal is sensitive to a region 2 3 nm from the surface of the capping layer. The technique is described in greater detail in chapter 3. The samples investigated were the same films studied by magnetic second harmonic generation in the previous sections and by optically induced ferromagnetic resonance in chapter 4, with the addition of a series of samples with varied thickness of the Al capping layer. 30 H CP x-rays e - Figure 5.6: Schematic of sample orientation in total electron yield XMCD measurement. The circularly polarised (CP) x-rays are incident at 30 to the sample plane, with the saturating field applied along the x-ray propagation axis. In most cases the sample surface was inclined by 30 to the incident x-ray beam, indicated in Figure 5.6, where smaller angles give a greater interface sensitivity but lower intensity XMCD signal. XMCD spectra were obtained with fixed helicity circularly polarised x-ray photons by reversing a 500 G field applied parallel to the propagation axis of the incident x-rays Results Figure 5.7 shows XAS measured at the Co L 2,3 edges for Co 2 MnSi films in the asdeposited state and annealed at up to 450 C. The spectra show a shoulder after the L 3 peak that grows with increased annealing temperature, which correlates with the increase in the degree of L2 1 site ordering that has been shown by x-ray diffraction [87]. It was suggested by Dr. Telling that the origin of this shoulder could be photoelectron scattering from the sublattice, since the estimated photoelectron wavelength of 5.9 Å is close to the lattice parameter of the ordered L2 1 structure (5.65 Å). Sum-rule analysis of the XMCD spectra showed that the total moment per 3d hole for Co approximately doubles from 0.18 to 0.35 µ B for as-deposited and annealed films, while for Mn the increase is slightly larger at 0.18 to 0.4 (Figure 4 in reference [89]).

136 CHAPTER 5. INTERFACIAL STUDIES OF HEUSLER ALLOYS 135 Figure 5.7: X-ray absorption spectra at the Co L 2,3 edges for Co 2 MnSi films with varied annealing temperature. Reproduced from reference [89] Figure 5.8: XAS and XMCD spectra measured at the Mn L 2,3 edges with varied annealing temperature. (a) shows the spectra from the as-deposited film, while (b) shows the spectra from the film annealed at 450 C. The inset shows increasing multiplet structure in the L 3 XMCD peak with increased annealing temperature. Reproduced from reference [89]

137 CHAPTER 5. INTERFACIAL STUDIES OF HEUSLER ALLOYS 136 Figure 5.9: (a) shows the XMCD spectra measured at the Co L 2,3 edges for as-deposited Co 2 MnSi (A RT ) and a film annealed at 450 C (A 450 ) and a reference Co film capped with Al. (b) are the derivatives of the XMCD spectra in (a). The arrows mark the multiplet features. Reproduced from reference [89] Possible evidence of the half-metallic nature of these Co 2 MnSi films was found in the XMCD spectra measured at the Mn L 2,3 edges, shown in figure??. Multiplet structure can be indicative of localised moments, but while it is a strong feature in the XMCD spectra it is weak in the corresponding XAS spectra. Half-metallicity is characterised by localisation of one spin band only, and since XAS is not spin sensitive the localisation of only one spin band may not show as a strong effect. A similar feature is seen for Co, shown in figure 5.9, where the derivatives of the XMCD spectra are also included to show the multiplet structure more clearly. It was also observed that the multiplet features in the Co XMCD spectra were reduced following plasma oxidation of the Al capping layer (figure 8 in reference [89]). This suggests that the near-interfacial half-metallicity is reduced by barrier oxidation. A sample with a 1 nm Mg layer between the Co 2 MnSi and Al cap showed clear multiplet structure after oxidation, indicating that this layer prevents the loss of half-metallicity and may help maintain spin-polarisation at the interface. To investigate whether the large decrease of TMR with increasing temperature is the result of a change of the interfacial magnetisation, XAS and XMCD spectra were recorded

138 CHAPTER 5. INTERFACIAL STUDIES OF HEUSLER ALLOYS 137 Figure 5.10: XAS measured at (a) Mn and (b) Co L 2,3 edges with varied Al capping layer thickness. From top to bottom the Al cap thickness is 2, 3, 3.5 and 4 nm. The insets show the x-ray absorption branching ratio as a function of Al cap thickness. Reproduced from reference [93] as a function of temperature. In this study the sensitivity to the Co 2 MnSi surface was improved by increasing the thickness of the Al capping layer. The Co 2 MnSi films were annealed at 450 C prior to deposition of the Al capping layer which was allowed to oxidise naturally in air. Figure 5.10 shows the XAS measured at the (a) Mn and (b) Co L 2,3 edges, where from top to bottom the Al cap thickness is 2, 3, 3.5, and 4 nm. There is a weak multiplet structure in the Mn XAS that increases with the thickness of the capping layer. The multiplet structure is characteristic of a localised Mn moment which may result from the formation of MnO at the interface. The slight shift of the L 3 peak supports the formation of MnO, as the peak energy is shifted from that of metallic Mn. The increased multiplet structure with thicker capping layer indicates greater sensitivity to a thin layer of MnO formed at the interface between the Co 2 MnSi film and the cap. The relative proportion of metallic Mn and MnO contributing to the XAS signal is shown by the x-ray absorption branching ratio, inset of figure The XA branching ratio is given by, B = I(L 3 )/ [I(L 2 ) + I(L 3 )], where I(L 3 ) and I(L 2 ) are the integrated intensities of the L 3 and L 2 XAS peaks [114]. The branching ratio is larger in a metal-oxide than in a metal because there is increased 3d spin-orbit interaction and 3d localisation. The increase in the Mn branching ratio with Al cap thickness indicates an increased contribution of MnO in the XAS, confirming the enhanced interface sensitivity. Figure 5.10(b) shows the XAS for Co L 2,3 edges which are almost unaffected by the thickness of the Al cap, and the inset shows almost no change of the branching ratio. This indicates that there is no significant oxidation of the Co.

139 CHAPTER 5. INTERFACIAL STUDIES OF HEUSLER ALLOYS 138 Figure 5.11: Relative total moments of (a) Mn and (b) Co in Co 2 MnSi obtained by sum-rule analysis of the XMCD spectra. The open red circles are data obtained from the sample with the 4 nm Al cap and the black crosses are the data obtained from the sample with a 1.3 nm Al cap. The open triangles are data obtained from a disordered Co 2 MnSi film with a 1.3 nm Al cap. Reproduced from reference [93] Having shown that the interface sensitivity is enhanced with a thicker capping layer, the temperature dependence of the interface moments was studied for the film with the thickest, 4 nm Al cap. Figure 5.11 shows the relative (a) Mn and (b) Co moments obtained from sum rule analysis of the XMCD spectra. Measurements with a 4 nm and 1.3 nm cap are shown for comparison of the interface and near-interface moments, and for a disordered (un-annealed) film with a 1.3 nm cap. Both L2 1 ordered films show no variation of the Mn or Co moments, while in the disordered film the Mn and Co moments both increase with temperature Discussion The decrease of Mn and Co moments with decreasing temperature in the disordered film can be explained by an increase in the Mn-Mn antiferromagnetic coupling. The antiferromagnetic coupling will dominate the ferromagnetic ordering when the temperature is reduced below the Néel temperature with a reduction in the net magnetic moment [87, 115]. In L2 1 ordered films the Mn-Mn nearest neighbour coupling is reduced, and since there is no variation of the interfacial moments it appears that the L2 1 ordering must extend to the surface of the Co 2 MnSi film.

140 CHAPTER 5. INTERFACIAL STUDIES OF HEUSLER ALLOYS Summary The interfacial region of Co 2 MnSi Heusler alloy films has been investigated using magnetic second harmonic generation and x-ray magnetic circular dichroism. The interfaces are vitally important in the performance of magnetic tunnel junctions, and so there is a need to employ techniques that allow investigation of this region in isolation from the bulk material. The observed qualitative correlation between MSHG anisotropy and TMR is likely due to the shared interface sensitivity of each effect. MSHG could be applied as an effective technique in the identification and improvement of interfaces in MTJs. The large decrease of TMR with increased temperature observed for MTJs with Co 2 MnSi electrodes motivated an investigation of the MSHG anisotropy with temperature. The MSHG anisotropy was indeed found to depend on temperature for a Co 2 MnSi film with fabrication conditions similar to those found in the MTJs. Further work on the interpretation of the MSHG data is required to develop the technique. XMCD can be applied as an interfacially sensitive probe when the total electron yield measurement geometry is used, and it has been shown that by increasing the thickness of the capping layer sensitivity to thinner interfacial regions could be achieved. Measurements of XMCD spectra from L2 1 ordered films showed no temperature dependence of the interfacial Mn and Co moments. Therefore it is unlikely that the large decrease in TMR observed in MTJs is the result of a reduction in interfacial magnetisation at higher temperatures. There is perhaps some discrepancy between the MSHG and XMCD results on the same sample series. XAS and XMCD studies did not reveal any significant differences between samples B and B [89]. In addition, magnetometry and ferromagnetic resonance (FMR) measurements revealed that the magnetisation and magnetocrystalline anisotropy decrease, while the damping parameter increases, as the films are annealed at temperatures greater than 300 C [64]. While further work is required to explain these observations, it is important to remember that MSHG, total electron yield XAS/XMCD, and magnetometry/fmr, probe different regions of the sample, namely the interface, a near interfacial region of a few nm thickness, and the entire volume of the film. MSHG is therefore expected to be most relevant in understanding the variation of measured TMR values, even though ab-initio calculations of the MSHG are challenging and it is unclear whether any of the experimentally determined quantities can be directly related to either the spin

141 CHAPTER 5. INTERFACIAL STUDIES OF HEUSLER ALLOYS 140 polarisation at the Fermi level or to the net interfacial magnetic moment.

142 Chapter 6 Ultrafast demagnetisation and elastic oscillations in patterned CoNi/Pt multilayers 6.1 Introduction The future of magnetic recording media requires advances in reading and writing speeds as well as increased storage density. The latter can be improved by sub-micro scale patterning of media and use of perpendicular anisotropy materials where the remanent magnetisation is oriented perpendicular to the plane of the film [116]. To increase write speeds in particular it will be necessary to employ precessional magnetisation switching and ultrafast magnetisation dynamics with timescales less than 1 picosecond. In 1996 Beaurepaire et al. reported sub-picosecond demagnetisation of a Ni film after excitation by a femtosecond laser pulse measured in a time-resolved magneto-optical pump-probe experiment [15]. Ultrafast magnetisation dynamics have subsequently been studied by a number of time-resolved techniques, including time-resolved magnetic second harmonic generation [16 18], two-photon photoemission [117] and time-resolved x-ray absorption spectroscopy [118]. In some cases the transient magnetisation reached its minimum before thermalisation of the electron system was completed. Ultrafast magnetic phase transitions following pulsed optical excitation have also been reported, with CoPt 3 films being driven from a ferromagnetic to a paramagnetic state [119] and from antiferromagnetic to ferromagnetic in an FeRh film [120], with, in the former case, complete demagnetisation being observed on a timescale comparable to the laser pulsewidth. On longer

143 CHAPTER 6. CoNi/Pt MULTILAYER FILMS 142 timescales it has been reported that by patterning an Fe film the magnetic anisotropy was modified in such a way that optically induced precession was observed in the patterned film but not for the continuous film under the same conditions. These observations are of great interest since such fast demagnetisation occurs on much shorter timescales than the typical timescale for spin-lattice energy relaxation associated with demagnetisation of the order of several picoseconds. Therefore there must be a separate energy channel involved in this ultrafast demagnetisation. Such ultrafast control of magnetisation presents a path to greatly increasing the speed of operation of data storage devices. The response of a sample to an incident ultrafast laser pulse is usually described by a three temperature model [15] with interactions between electron, lattice and spin systems taking the system back to thermal equilibrium. Absorption of a femtosecond optical pulse induces a non-equilibrium electron population that thermalises to a Fermi-Driac distribution by electron-electron interactions on a sub-picosecond timescale. On picosecond timescales the hot electron gas passes energy to the lattice by electron-phonon interactions. Transient temperatures T e and T l can be assigned to the electron and lattice systems respectively, and the evolution of these temperatures can be investigated by time-resolved reflectivity measurements. Additionally a temperature T s can be assigned to the spin system, where modification of T s would lead to an ultrafast demagnetisation. The temperature of the spin system may be modified by electron-spin and lattice-spin interactions, with different characteristic relaxation times for the two processes. Absorption of an optical pulse should not directly affect the magnetisation since optical transitions conserve spin (in the dipole approximation), but spin-dependent electron scattering in the hot electron phase could alter the spin populations. Ultrafast demagnetisation cannot arise from spinlattice interactions which have a much longer characteristic timescale. The microscopic mechanism of ultrafast electronic demagnetisation remains unknown, with suggestions including direct electron-spin interaction [15] and Stoner excitations [117] where an electron is excited from a spin-up to a spin-down state in a ferromagnetic spin-split band, or that the magnetisation is directly related to the electron temperature [17]. Koopmans et al. [35] suggest that a purely electronic demagnetisation process is unlikely since total angular momentum of the electron system must be conserved if interactions with other systems are neglected. They note that if there exists a direct link between the magneto-optical response and the magnetisation it would be necessary that the magneto-optical rotation and the ellipticity have a similar dependence on time delay. However they observe a very different response in the two signals in the first hundreds

144 CHAPTER 6. CoNi/Pt MULTILAYER FILMS 143 of femtoseconds following excitation, with small differences lasting up to 1.5 ps. From this they conclude that the loss of magneto-optical contrast cannot be directly related to an ultrafast magnetisation effect, and instead the initial response may be accounted for by state-filling effects. It is common practice to measure demagnetisation no earlier than 1.5 ps following pulsed laser excitation in case the signal at shorter time delays is complicated by the nonthermal electron distribution. Co/Pt multilayers are excellent candidate materials for magnetic recording media, and by alloying the Co layers with Ni the Curie temperature can be reduced [121]. Due to the interface anisotropy films with the correct thickness of CoNi layers have a perpendicular anisotropy with remanent magnetisation normal to the plane of the film. In an earlier study with lower laser pulse energies [122] full demagnetisation of a CoNi/Pt film was inferred from TRMOKE signals by taking into account the Gaussian intensity distribution of the focused laser spots, with maximum demagnetisation achieved within 300 fs. In this chapter the results of static and time-resolved magneto-optical Kerr effect (MOKE) measurements of continuous film and patterned CoNi/Pt multilayer films are presented. Full demagnetisation is observed directly in TRMOKE scans and in MOKE hysteresis loops. The dynamics of continuous and nanoscale patterned films are compared, and the effect of circularly polarised pump light on the dynamic magnetisation is considered. Additionally a strong oscillatory reflectivity is observed for the patterned film, with frequency determined by the periodicity of the array. 6.2 Experimental Details The CoNi/Pt multilayer films were fabricated at Leeds University by Dr Gavin Burnell by magnetron sputtering, with stack sequence Si(001) / [Co 25 Ni 75 (x Å)/Pt(8 Å)] 20, where the thickness of the CoNi layers x was 3.0, 4.5 and 6.0 Å. The films were annealed by Dr Burnell at Exeter with the resulting films showing strong perpendicular anisotropy. A film with x = 4.5 Å was patterned using nanosphere lithography by Evgeny Sirotkin and Dr Feodor Ogrin at the University of Exeter [123]. The patterned film consists of a hexagonal array of dots with 390 nm nearest neighbour centre-to-centre separation determined by the diameter of the nanospheres and dot diameter of 350 nm determined by the milling time. Figure 6.1 shows scanning electron microscope (SEM) images, obtained by Evgeny Sirotkin, of the patterned film (a) with and (b) without the nanospheres on the surface of the film.

145 CHAPTER 6. CoNi/Pt MULTILAYER FILMS 144 The static magnetisation properties of the films were studied by MOKE using an intensity stabilised He-Ne laser with a polar magnet to apply a field of up to ±10 kg perpendicular to the film plane. Figure 6.2(a) shows the setup used to measure polar MOKE, with a non-polarising beamsplitting cube to allow normal incidence at the sample which gives the maximum polar MOKE signal (see chapter 3 for more information). Timeresolved measurements were performed using an amplified Ti:sapphire ultrafast pulsed laser system setup as shown in figure 6.2(b). All measurements used different wavelength pump and probe beams. The 800 nm wavelength pump beam was focused at normal incidence on to the sample, while the frequency-doubled 400 nm wavelength probe beam was incident at approximately 15 from the normal. A nonzero angle of incidence of the probe provides some sensitivity to the in-plane magnetisation, which is required if magnetisation precession is to be detected for out of plane saturation magnetisation. The optical aperture of the polar magnet allows a maximum incidence angle of about 15. The 800 nm wavelength pump beam was focused to 120 µm diameter using a f = 150 mm lens, while the 400 nm probe was focused to 15 µm with a 10 beam expander to reduce beam divergence and an f = 63 mm doublet lens. The overlap of the focused pump and probe beams was set using a CCD beam profiler and was optimised in all experiments by small adjustments of the pump lens to maximise the lock-in signal at zero time delay. The probe beam polarisation was maintained as s while the pump polarisation was varied between s and p polarisation using a combination of polariser and (a) Nanospheres on surface (b) Nanospheres removed Figure 6.1: Scanning electron microscope images of the patterned CoNi/Pt film. In (a) the nanospheres used in lithography are on the surface of the magnetic dots, while in (b) they have been removed.

146 CHAPTER 6. CoNi/Pt MULTILAYER FILMS 145 quarter-wave plate. More details of the MOKE and TRMOKE techniques can be found in chapter 3. The main source of error in the accuracy and repeatability of these measurements comes from the alignment of the sample and focusing optics. The spot sizes are measured using a CCD beam profiler before the sample is placed at pump-probe overlap position. With short focal length lenses the depth of focus can be very small, less than a mm, and therefore some variation of the spot size when changing or rotating the sample is expected. Measuring with a time delay of up to 3.5 ns requires a linear delay stage with 600 mm of travel, and over such a range it is possible for the pump and probe spot overlap on the sample to change which can modify the measured relaxation rate. However this is not a significant issue for scans with less than 1 ps delay, such as those used to investigate ultrafast demagnetisation. The uncertainty in the incident power of the pump beam has been measured as 5 %, with long term drifts corrected for by variable neutral density filters. The effect of the varying probe beam intensity on the AC Kerr rotation and reflectivity can be reduced by normalising to the DC intensity of the probe beam measured by the bridge detector. This has been found very effective at removing background in both signals. 6.3 Experimental Results Static MOKE hysteresis loops Figure 6.3 shows polar-moke loops obtained for the annealed CoNi/Pt continuous films with the central (black) curve for x = 3.0 Å, the middle (red) curve for x = 4.5 Å and the outer (green) curve for x = 6.0 Å. Table 6.1 lists the coercive field and saturation (a) 633 nm He-Ne (beam blocked) to bridge detector polar magnet H (b) probe, 400 nm pump, 800 nm to bridge detector polar magnet H Figure 6.2: (a) static and (b) time-resolved MOKE setups based around the polar electromagnet. In (a) normal incidence is used to maximise the polar MOKE signal, while in (b) the probe is incident at 15 in order to provide some sensitivity to in-plane magnetisation.

147 CHAPTER 6. CoNi/Pt MULTILAYER FILMS 146 Kerr rotation for each film. The coercive field increases with the thickness of the CoNi layers, while the saturation Kerr rotation angle decreases. Polar MOKE loops for the patterned film are shown in Figure 6.4, plotted with the continuous film hysteresis loop for comparison where both films have x = 4.5 Å. Two loops for the patterned film are shown, one where the nanospheres were left on the film surface and one after removal of the nanospheres. It is perhaps surprising that the patterned film with nanospheres on the surface gives a larger Kerr rotation than the continuous film. Anti-reflection coatings can enhance MOKE, and in this case it appears that the nanospheres act as an anti-reflective coating. The patterned film with the nanospheres removed shows a weaker Kerr rotation than the continuous film, which is expected due to the lower areal coverage of magnetic material, all other factors being constant. The coercive field of the patterned film is lower than that of the continuous film, at 1.8 kg compared with 2.2 kg. All data presented in [ (x ) ( )] K e rr ro ta tio n (m d e g ) Figure 6.3: Polar MOKE loops of continuous CoNi/Pt films with varied CoNi layer thickness, measured by intensity stabilised CW He-Ne laser. Table 6.1: Coercive field (H C ) and saturation Kerr rotation (θk s ) extracted from polar MOKE hysteresis loops measured with a CW He-Ne laser for varied CoNi layer thickness in CoNi/Pt multilayers (figure 6.3). CoNi thickness (Å) H C (kg) θk s (mdeg)

148 CHAPTER 6. CoNi/Pt MULTILAYER FILMS (a ) P a tte rn e d (w ith s p h e re s ) C o n tin u o u s film 1.0 (b ) K e rr ro ta tio n (m d e g ) P a tte rn e d (n o s p h e re s ) M /M S W ith s p h e re s N o s p h e re s F ie ld (k G ) F ie ld (k G ) Figure 6.4: Polar MOKE loops of patterned CoNi/Pt with 4.5 Å thick CoNi layers measured by intensity stabilised CW He-Ne laser. The corresponding continuous film loop is included for comparison. In (a) the absolute Kerr rotation is shown while in (b) the loops are normalised to M/M S. The two loops for the patterned film show the MOKE signal with and without nanospheres on the surface of the CoNi/Pt array. the remainder of this chapter was taken from the sample with the nanospheres removed for consistency between continuous film and patterned samples Ultrafast demagnetisation Time-resolved measurements with small time delay were made to study the demagnetisation achieved by ultrafast heating following absorption of an intense femtosecond laser pulse. Figure 6.5 shows (a) the TRMOKE and (b) the TR-reflectivity signals obtained from the continuous film sample with varied pump fluence at 10 kg applied field. The time axis is split to show in detail the ultrafast response and the subsequent relaxation, with data plotted up to a time delay of 90 ps for direct comparison with the data from the patterned films in figure 6.7. All TRMOKE (TR-reflectivity) data are the difference (average) of scans taken at opposite external field in order to remove nonmagnetic contributions to the polarisation rotation signal. The TRMOKE data have been fitted by a sum of three exponential decay functions (red lines in the figure) with typical relaxation times of the fastest and slowest decaying functions of 5 ps and 1.3 ns. The third exponential decay time increases exponentially from ps with pump fluence increased from mj/cm 2. Once saturation of the TRMOKE signal has been achieved a flat

149 CHAPTER 6. CoNi/Pt MULTILAYER FILMS (a ) 8.8 m J /c m 8.0 m J /c m 7.1 m J /c m (b ) K e rr ro ta tio n (m d e g ) m J /c m 4.4 m J /c m 3.5 m J /c m 2.7 m J /c m R e fle c tiv ity (% ) m J /c m m J /c m T im e d e la y (p s ) T im e d e la y (p s ) Figure 6.5: (a) TRMOKE and (b) TR-reflectivity with varied pump fluence from continuous film CoNi(4.5 Å)/Pt multilayer with external field ±10 kg applied perpendicular to the film. Data is plotted up to 0.09 ns time delay for direct comparison with the patterned film in figure (a ) 1.2 (b ) K e rr ro ta tio n (m d e g ) g ra d = 1 1 P e a k re fle c tiv ity (% ) g ra d = P e a k T R M O K E L o n g re la x a tio n a m p litu d e P u m p flu e n c e (m J /c m 2 ) P u m p flu e n c e (m J /c m 2 ) Figure 6.6: (a) Peak Kerr rotation and (b) peak reflectivity as a function of pump fluence from time-resolved measurements of a continuous film CoNi/Pt with CoNi thickness 4.5 Å, extracted from figure 6.5. In (a) the amplitude of the long relaxation exponential function fitted to the TRMOKE data is shown also (circles, red line).

150 CHAPTER 6. CoNi/Pt MULTILAYER FILMS 149 region of the Kerr rotation signal appears which in this case extends to 3.5 ps delay for the highest pump fluence used (8.8 mj/cm 2 ) (in a later measurement at the same fluence, shown in figure 6.9, the saturation extended for 150 ps). The increased relaxation time of this exponential function reflects the duration of this saturation region. The combined amplitude of these fitted functions, which is the peak amplitude at approximately 600 fs delay, is plotted as a function of pump pulse fluence in figure 6.6(a). Figure 6.6(b) shows the peak reflectivity signal extracted directly from the TR-reflectivity plots. The peak height of the TRMOKE signal is saturated for pump pulse fluences greater than 4 mj/cm 2, while the peak reflectivity signal continues to rise. Also plotted in figure 6.6(a) is the amplitude of the longest decay ( 1.3 ns) exponential which continues to rise when the peak TRMOKE signal has saturated. The TRMOKE peak rise time is 680 fs while the rise time of the initial peak of the TR-reflectivity signal is faster at 460 fs, with both unaffected by pump pulse fluence. Figure 6.7 shows (a) TRMOKE and (b) TR-reflectivity with varied pump fluence for the patterned film. The TRMOKE data is fitted in the same way as that for the continuous film sample. A similar saturation of the TRMOKE signal at 4 mj/cm 2 is observed while the TR-reflectivity peak continues to rise. Figure 6.8 shows (a) the peak Kerr rotation and (b) the peak reflectivity obtained from the time-resolved scans. While the TRMOKE signal saturates at about the same fluence as the continuous film, the peak reflectivity and amplitude of the longest decay exponential fitted to the TRMOKE data increase with pump power approximately twice as steeply for the patterned film. The rise time of the of the TRMOKE peak is 850 fs and the rise time of the peak TR-reflectivity signal is 650 fs, both longer than for the continuous film. The demagnetisation was also studied by static and AC-MOKE loops as a function of time delay and pump fluence. In standard static MOKE loops the heating by the pump pulse is revealed by a reduction of the saturation Kerr rotation and of the coercivity. In AC-MOKE loops the intensity of the pump beam is modulated and lock-in detection is used so the loops obtained represent the pump-induced change of the magnetisation. The advantage of the latter technique is much improved signal to noise ratio, allowing the coercivity to be accurately determined as a function of pump fluence. Figure 6.9 shows M/M S measured by TRMOKE and MOKE hysteresis loops at varied time delay with an 8.8 mj/cm 2 pump fluence, and the two curves agree very well. A dashed line has been added to indicate more clearly the region of full demagnetisation, which in this case extends for 150 ps, far longer than seen in previous measurements. A 10 beam

151 CHAPTER 6. CoNi/Pt MULTILAYER FILMS (a ) 5.3 m J /c m 2 6 (b ) m J /c m 2 5 K e rr ro ta tio n (m d e g ) m J /c m 2.7 m J /c m 2.4 m J /c m R e fle c tiv ity (% ) ,2 m J /c m m J /c m T im e d e la y (p s ) T im e d e la y (p s ) Figure 6.7: (a) TRMOKE and (b) TR-reflectivity with varied pump fluence from a patterned CoNi/Pt multilayer with CoNi thickness of 4.5 Å, with external field ±7.5 kg applied perpendicular to the film to saturate the magnetisation (a ) 1.2 (b ) K e rr ro ta tio n (m d e g ) g ra d = P e a k re fle c tiv ity (% ) g ra d = P e a k T R M O K E L o n g re la x a tio n a m p litu d e P u m p flu e n c e (m J /c m 2 ) P u m p flu e n c e (m J /c m 2 ) Figure 6.8: (a) Peak Kerr rotation and (b) peak reflectivity as a function of pump fluence from time-resolved measurements of patterned CoNi/Pt with CoNi thickness 4.5 Å, extracted from figure 6.7. In (a) the amplitude of the long relaxation exponential function fitted to the TRMOKE data is shown also (circles, red line).

152 CHAPTER 6. CoNi/Pt MULTILAYER FILMS T R M O K E S ta tic M O K E lo o p s M /M S T im e D e la y (p s ) Figure 6.9: M/M S at varied time delay measured by TRMOKE and time-delayed MOKE loops for continuous film CoNi/Pt with a 8.8 mj/cm 2 pump beam. In this scan full demagnetisation is observed to extend for 150 ps after the peak signal, far longer than in figure (a ) (b ) K e rr ro ta tio n (m d e g ) N o p u m p 1.3 m J /c m 5.3 m J /c m 2 2 S a tu ra tio n M O K E ro ta tio n (m d e g ) F ie ld (k G ) P u m p flu e n c e (m J /c m 2 ) Figure 6.10: (a) MOKE hysteresis loops measured with the 400 nm probe beam for continuous film CoNi/Pt, with varied pump pulse fluence at the time delay corresponding to the peak TRMOKE signal ( 700 fs). (b) Saturation Kerr rotation from MOKE loop as a function of pump pulse fluence.

153 CHAPTER 6. CoNi/Pt MULTILAYER FILMS 152 expander was in the probe path to help focus to a smaller spot size by reducing beam divergence, but also gives a very narrow depth of focus. It is possible that the probe spot size could vary fairly significantly, at its smallest being 10 µm diameter (found by scanning pinhole measurements, see chapter 3). It should be noted that the saturation (a ) (b ) m J /c m S a tu ra tio n K e rr ro ta tio n K e rr ro ta tio n (m d e g ) m J /c m 2.7 m J /c m 1.8 m J /c m 1.3 m J /c m 0.5 m J /c m 0.0 m J /c m F ie ld (k G ) S a tu ra tio n K e rr ro ta tio n (m d e g ) C o e rc iv e fie ld P u m p flu e n c e (m J /c m 2 ) C o e rc iv e fie ld (k G ) Figure 6.11: (a) AC-MOKE hysteresis loops from continuous film CoNi/Pt with varied pump pulse fluence. (b) Saturation Kerr rotation (circles) and coercive field (squares) as functions of the pump pulse fluence. K e rr ro ta tio n (m d e g ) (a ) 6.2 m J /c m 4.4 m J /c m 2.7 m J /c m 1.8 m J /c m 0.9 m J /c m 0.0 m J /c m F ie ld (k G ) S a tu ra tio n K e rr ro ta tio n (m d e g ) (b ) S a tu ra tio n K e rr ro ta tio n C o e rc iv e fie ld P u m p flu e n c e (m J /c m 2 ) C o e rc iv e fie ld (k G ) Figure 6.12: (a) AC-MOKE hysteresis loops from patterned CoNi/Pt film with varied pump pulse fluence. (b) The saturation Kerr rotation (circles) and coercive field (squares) as functions of the pump pulse fluence.

154 CHAPTER 6. CoNi/Pt MULTILAYER FILMS 153 Kerr rotation obtained in static and time-resolved MOKE measurements do not agree. In TRMOKE measurements the signal saturates at about 115 mdeg, while in MOKE and AC-MOKE the saturation Kerr rotation is approximately 140 mdeg. The origin of this discrepancy is not yet known. Figure 6.10(a) shows MOKE loops measured by the 400 nm wavelength probe beam at the time delay corresponding to the maximum of the TRMOKE signal, with 6.10(b) a plot of the saturation Kerr rotation as a function of pump fluence. With increased pump fluence the saturation Kerr rotation is reduced reaching zero at 4 mj/cm 2, in agreement with the previous TRMOKE measurements. Figure 6.11(a) shows hysteresis loops measured by AC-MOKE with varied pump pulse fluence. With no pump pulse the AC-MOKE loop is a flat line while with full demagnetisation the AC-MOKE loop height is the full height of the equilibrium MOKE loop. From Figure 6.11(b) the coercivity is observed to collapse to zero at 3 mj/cm 2, before full demagnetisation is achieved. Figure 6.12(a) shows the AC-MOKE loops recorded for the patterned film with 6.12(b) showing the extracted saturation Kerr rotation and coercivity. The coercivity collapse and MOKE saturation are observed at approximately the same pump fluence as for the continuous film. Measurements were also made with a circularly polarised pump. For the continuous and patterned films no difference was found between TRMOKE and TR-reflectivity measured with a p-polarised or a circularly polarised pump Reflectivity oscillations from patterned CoNi/Pt film Very strong oscillations have been observed in the TR-reflectivity of the patterned film with frequency that is independent of pump fluence, field strength and pump polarisation. Figure 6.13 shows TR-reflectivity data from the patterned CoNi/Pt film up to 3.25 ns time delay with a 3.5, 4.4 and 5.3 mj/cm 2 pump fluence. The amplitude of the oscillations increases with pump fluence while the frequency, including a clear beating, is unchanged. Figure 6.14(a) shows TR-reflectivity of the patterned film with varied field strength, and once again the mode frequencies remain unchanged. However the field strength does appear to have an effect on the amplitude of the reflectivity signal. Figure 6.14(b) shows a plot of peak reflectivity signal as a function of field strength, with the arrow indicating the direction of the field sweep. The amplitude of the TR-reflectivity oscillations varies in the same way as the peak signal.

155 CHAPTER 6. CoNi/Pt MULTILAYER FILMS (a ) r e fle c tiv ity ( % ) m J /c m m J /c m T im e d e la y ( n s ) G H z F F T p o w e r (x 1 0 ) 5.3 m J /c m (b ) 9.8 G H z F re q u e n c y (G H z ) 3 0 Figure 6.13: (a) TR-reflectivity from the patterned CoNi/Pt film with varied pump fluence, averaged from scans at ±7.5 kg, and (b) the corresponding Fourier transforms k G k G k G f le c t iv it y ( % ) f le c t iv iv t y ( % ) re -2.8 k G k G T im e d e la y ( n s ) k G (b ) r e (a ) P e a k F ie ld ( k G ) Figure 6.14: (a) TR-reflectivity from the patterned CoNi/Pt film with varied field strength with a 5.3 mj/cm2 pump beam. (b) shows a change in the amplitude of the peak TRreflectivity signal for field between +0.9 kg to kg. The amplitude of the TR-reflectivity oscillations varies in the same way. Fourier transforms (not shown) reveal peaks at 9.8 and 7.6 GHz that are unaffected by field strength.

156 CHAPTER 6. CoNi/Pt MULTILAYER FILMS 155 A v e ra g e K e rr ro ta tio n (m d e g ) (s -p o l) A v e ra g e re fle c tiv ity (a rb ) (a ) T im e d e la y (n s ) 5 0 (b ) T im e d e la y (n s ) Figure 6.15: (a) average TRMOKE and (b) average TR-reflectivity of scans made at opposite applied field with rotated polarisation axis of the linearly polarised pump for the patterned film. The angle shown is the rotation away from p-polarisation. Figures 6.15 and 6.16 show average TRMOKE and average TR-reflectivity for scans made at opposite applied field as the plane of polarisation of the linearly polarised pump is rotated. In figures 6.15(b) and 6.16(b) the TR-reflectivity signal is unchanged by the plane of pump polarisation. In figures 6.15(a) and 6.16(a) there a peak at ps delay that grows in amplitude with increasing angle of pump polarisation rotation away from p. There is also an oscillation in the average TRMOKE signal with amplitude that depends on the angle of the pump polarisation. Figures 6.16(c) and (d) are the Fourier transforms of the signals in (a) and (b) respectively. The reflectivity shows a strong peak at 9.8 GHz and a weaker peak at 7.6 GHz, and the amplitude and frequencies of these modes do not change with pump polarisation. The TRMOKE Fourier transforms shows peaks at 9.8, 8.3 and 6.5 GHz, with the amplitude of the 6.5 GHz peak strongly dependent on pump polarisation. The 9.8 GHz mode is likely to be the result of reflectivity breakthrough in to the rotation signal, but there are no peaks in the reflectivity signals at 6.5 or 8.3 GHz. Taking the average of the TRMOKE signal with opposite fields removes all contributions whose sense reverses with field orientation. (By contrast, all TRMOKE data shown so far

157 CHAPTER 6. CoNi/Pt MULTILAYER FILMS A v e ra g e K e rr ro ta tio n (m d e g ) A v e ra g e re fle c tiv ity (% ) A v g K e rr ro ta tio n F T p o w e r (x ) A v g re fle c tiv ity F T p o w e r (x ) Figure 6.16: (a) average TRMOKE and (b) average TR-reflectivity for the patterned CoNi(4.5 Å)/Pt film for scans made at ±2.7 kg field with rotated polarisation axis of the 5.3 mj/cm 2 linearly polarised pump. (c) and (d) are the corresponding Fourier transforms for (a) and (b) respectively. has been the difference of scans made at opposite field, in order to remove nonmagnetic contributions to the polarisation rotation.) Figure 6.17 shows similar data taken at zero applied field again with Fourier transforms of the time-resolved data. For pump polarisation rotated from 30 to +30 the TR-reflectivity Fourier transforms are unchanged with a strong peak at 9.8 GHz while the TRMOKE Fourier transforms show a peak at 6.5 GHz with amplitude dependent on pump

158 CHAPTER 6. CoNi/Pt MULTILAYER FILMS º 9 7 p-pol º º º º Time delay (ns) (c) 9.8 GHz 6.5 GHz (b) 8 R e fle c tiv ity ( % ) K e r r r o ta tio n ( m d e g ) (d) 9.8 GHz 7.6 GHz Time delay (ns) R e f le c tiv ity F T p o w e r ( x 1 0 ) p-pol 0 K e r r r o ta tio n F T p o w e r ( x 1 0 ) -30º -10º (a) Frequency (GHz) Frequency (GHz) Figure 6.17: (a) TRMOKE and (b) TR-reflectivity scans at zero field with rotated polarisation axis of the 6.2 mj/cm2 linearly polarised pump for the patterned CoNi/Pt film. (c) and (d) are the corresponding Fourier transforms for (a) and (b) respectively. polarisation rotation. since the frequency of the oscillation in the TRMOKE signal does not change with field strength it is unlikely to be a magnetic resonance mode excited by optical absorption. In both figure 6.16 and figure 6.17 the pump fluence was sufficient to fully demagnetise the film, though measurements with a weaker 1.8 mj/cm2 pump (not shown) also show a TRMOKE oscillation at 6.5 GHz.

159 CHAPTER 6. CoNi/Pt MULTILAYER FILMS Discussion Time-resolved MOKE and MOKE hysteresis loops of continuous and patterned CoNi/Pt films have revealed a complete demagnetisation by ultrafast laser pulse heating in less than 1 ps. The continuous and patterned films reach full demagnetisation at the same pump fluence of approximately 4 mj/cm 2. It has been a concern that for time delays less than the electron thermalisation time the magneto-optical signal may not truly represent the magnetisation as the magneto-optical response of the nonthermal electron system may differ from that of the thermalised system [35]. With this in mind several authors measure demagnetisation at a time delay of 1.5 ps, allowing for the thermalisation to complete [124]. This procedure was followed in chapter 4 on the study of optically-induced ferromagnetic resonance in Heusler alloy films. However in this case the TRMOKE rotation is the same at longer time delay, up to 150 ps in one case (figure 6.9) as it is at 0.5 ps delay for a pump fluence of 8.8 mj/cm 2. Furthermore if the non-thermal electrons did contribute to the magneto-optical signal the peak height should continue to increase with pump pulse fluence and not reach a saturation. The TR-reflectivity measurements show a peak signal that continues to increase with pump fluence when the TRMOKE signal has saturated, indicating that the film temperature continues to rise. Thus it is safe to assume that the MOKE signal at sub-picosecond time delays does correspond to the magnetisation of the film. The rise time of peak TR-reflectivity signal is found to be faster than the rise time of the peak TRMOKE signal for both the continuous and patterned film. However both are longer for the patterned film than for the continuous film. It is not understood why patterning increases the rise time of the magnetic and reflectivity signals. Strong reflectivity oscillations following ultrafast pulsed laser excitation have been observed for the patterned film, with a strong 9.8 GHz mode and a weaker 7.6 GHz mode. Reflectivity oscillations from patterned media on a silicon substrate have been observed by Comin et al. [125, 126], and were attributed to the excitation of a surface acoustic wave (SAW) in the substrate by the elastic interaction between the metallic array and the substrate with wavevector, q, determined by the array spacing, D, by q = 2π/D. To confirm the same mechanism in the data presented here ore measurements are required on patterned films with different array periodicity. Comin et al. also observed an oscillation in the transient magneto-optical signal that has a slightly different period to the reflectivity oscillation. They found that the frequency of the magneto-optical oscillation did not change with field strength and so was

160 CHAPTER 6. CoNi/Pt MULTILAYER FILMS 159 not the result if a pump-induced resonance. They suggested that magnetoelastic coupling may be the origin of the magnetic signal. This explanation may also fit the observations in this chapter, though in this case the TRMOKE oscillations are only found when the pump polarisation is rotated away from s or p. The dependence on pump polarisation indicates a birefringence effect, where the pump induces a transient change in refractive index along an axis determined by its polarisation. The data in this chapter is insufficient to determine whether the periodicity of the pump polarisation dependence is 90 or 60, and therefore whether the birefringence is directly pump induced or due to an interaction with the CoNi/Pt hexagonal array. In order to understand the origin of the oscillations in the transient Kerr rotation and reflectivity measurements are required on arrays with different array spacing and dot size. Measurements with rotated pump polarisation must be performed over 360 to confirm the periodicity of the birefringence effect. A model based on magnetoelastic interactions has to be developed that could be tested against the data presented here. 6.5 Summary All-optical pump-probe measurements of the MOKE and reflectivity of continuous and patterned CoNi/Pt multilayer films have been presented. Complete demagnetisation has been observed in less than 1 ps following absorption of an ultrafast laser pulse, revealed by saturation of the peak TRMOKE signal with increasing pump fluence and by vanishing MOKE rotation in static hysteresis loops. Comparison of the continuous and patterned film has revealed that complete demagnetisation is achieved at the same pump fluence for both, but the rise time of the peak TRMOKE and TR-reflectivity signals is longer for the patterned film. A strong oscillatory response has been observed in the TR-reflectivity of the patterned film. The modes of this oscillation are unaffected by pump fluence, field strength and pump polarisation, with the periodicity determined by the array spacing. Rotation of the linearly polarised pump has revealed an oscillatory mode in the Kerr rotation that is not present in the reflectivity signal. The origin of this mode is not clear, though it is possibly the result of a magneto-elastic interaction. Further measurements are required to determine the origin of this interesting effect.

161 Chapter 7 Ferromagnetic exchange springs 7.1 Introduction Composites can be used to extend and tailor the properties of a material, combining the properties of each component. In the case of permanent magnets, for example, the design goal is to maximise the saturation magnetisation and the coercive field maximising the key figure of merit, the energy product (BH) max [127]. Usually this is achieved by combining the high anisotropy of a rare-earth element with the high saturation magnetisation of a transition metal, as for example in NdFeB and SmCo [128]. Kneller and Hawig [129] suggested producing composites of a hard and soft magnetic materials that are coupled by an exchange interaction. These materials are called exchange springs or exchange hardened magnets. The hard material donates its strong magnetic anisotropy to the composite, while the soft material provides the high saturation magnetisation. Exchange spring materials also display interesting magnetisation reversal behaviour. M Sawicki et al. [130] investigated magnetisation hysteresis in multilayers of antiferromagnetically coupled DyFe 2 /YFe 2 bilayers. In these samples the DyFe 2 layers have strong anisotropy while the YFe 2 layers are magnetically very soft. The magnetisation of the hard layer remains closely aligned with its easy axis while the magnetisation of the soft layer can rotate to follow an applied field. The moments at the interfaces are exchange coupled and therefore domain walls form at the interfaces in the soft layers. These domain walls resemble a coiled spring, and through their action the magnetisation curves of these materials are fully reversible for external fields weaker than the switching field of the hard layer. The authors found that the bending field required to rotate the magnetisation of the soft layers was dependent on the thickness of the hard and soft layers. The same group also showed that the coercivity of the multilayer could be modified by varying the relative

162 CHAPTER 7. MAGNETIC EXCHANGE SPRINGS 161 thicknesses of the component layers [131] and that the exchange spring can even be used to generate negative coercivity [132]. While several studies have been made on the magnetisation curves of multilayered exchange spring materials, there has been little or no research on the dynamic behaviour in such films. In this chapter static and time-resolved magneto-optical Kerr effect (MOKE) measurements of a DyFe 2 /YFe 2 multilayer film are presented. The reversible and irreversible magnetisation mechanisms are discussed with reference to static MOKE measurements, and it is shown that a magnetisation precession can be induced by an intense laser pulse when the system is magnetised in a wound exchange-spring state. A possible mechanism responsible for inducing precession by the action of the torque from the exchange spring is described. Understanding the mechanism that leads to precession in this case is not trivial, and measurements of reference DyFe 2 and YFe 2 films are shown that may aid the picture. The data presented here serves as a successful proof of concept for using time-resolved magneto-optics to investigate exchange coupled multilayers. 7.2 Sample and Experimental Details DyFe 2 /YFe 2 multilayers have been fabricated by molecular beam epitaxy at Oxford University [133], with in this case the sample consisting of 40 repeats of a [DyFe 2 (20 Å)/YFe 2 (80 Å)] bilayer. The film was grown on a sapphire (1120) substrate with a 1000 Å niobium buffer layer and a 20 Å iron seed layer. The layers form in the C15 MgCu 2 - type cubic Laves phase where the rare earth atoms are located on sites of the face-centred cubic diamond structure and the Fe atoms form tetrahedra around the rare earth atoms. Both substances have a high Curie temperature in excess of 600K [130]. Reference films plane Figure 7.1: Crystallographic axes orientations of [ DyFe 2 (20 Å)/YFe 2 (80 Å) ] exchange spring multilayer and DyFe 2 (2000 Å) and YFe 2 (1000 Å) films.