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1 ELECTRON TUNNELING AND SPIN DYNAMICS AND TRANSPORT IN CRYSTALLINE MAGNETIC MULTILAYERS Radovan Urban B.Sc., Charles University, Prague, 1995 M.Sc., Charles University, Prague, 1997 THESISUBMITTED IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY IN THE DEP.4RTMENT OF Radovan Urban 2003 SIMON FRASER UNIVERSITY July 2003 All rights reserved. This work may not be reproduced in whole or in part, by photocopy or other means, without permission of the author.

2 APPROVAL Name: Degree: Title of Thesis: Examining Committee: Radovan Urban Doctor of Philosophy Electron tunneling and spin dynamics and transport in crystalline magnetic multilayers J. F. Cochran (Chpir) - B. Heinrich (Senior Supervisor) R. F. Frindt (Supervisor) ~Aheinfein (Internal Examiner) I P. E. Wigen (Exte Date Approved:

3 PARTIAL COPYRIGHT LICENSE I hereby grant to Simon Fraser University the right to lend my thesis, project or extended essay (the title of which is shown below) to users of the Simon Fraser University Library, and to make partial or single copies only for such users or in response to a request from the library of any other university, or other educational institution, on its own behalf or for one of its users. I further agree that permission for multiple copying of this work for scholarly purposes may be granted by me or the Dean of Graduate Studies. It is understood that copying or publication of this work for financial gain shall not be allowed without my written permission. Title of Thesis/Project/Extended Essay Author: - (signature) (name) (date)

4 Abstract This thesis reports on electron transport and the magnetization dynamics of crystalline multilayers grown on Fe-whiskers(001) and clean GaAs(001) wafers by means of molecular beam epitaxy (MBE). The high quality magnetic multilayers with well defined interfaces are required to allow one to compare quantitatively the experimental results with the theoretical predictions. The electrical properties of crystalline Fe/MgO/Fe-whisker structures were characterized by in-situ scanning tunneling spectroscopy. For most of the scanned area, the tunneling I-V characteristics have revealed a tunneling barrier of 3.6 V which corresponds to the perfect MgO layer. At negative bias voltages, the localized spikes in the tunneling current have been observed indicating ballistic transport in crystalline tunnel junctions. Kerr microscopy has shown, that the magnetization of Fe-whisker and Fe film are coupled via stray field of the Fe-whisker domain wall. Atom force microscope (AFM) operating in an external magnetic field was used to measure tunneling magnetoresistance (TMR). In some cases, the TMR reached nearly 100 % at RT. The spin dynamics were studied in the ultrathin Fe films grown directly on (4 x 6) reconstructed GaAs(001) wafers. FMR was used to determine the static and dynamic magnetic properties of Fe/Cr and Fe/Au multilayers. For Fe films covered by Cr, the extrinsic relaxation term has shown evidence of two-magnon scattering. The in-plane Gilbert damping includes both intrinsic and extrinsic contributions to the Gilbert damping parameter. In the Fe/Au/Fe multilayers, where the static interlayer exchange coupling is negligible, the magnetizations are still coupled through the normal metal (NM) spacer by emitting and absorbing non-equilibrium spin currents. Ultrathin Fe layers in double layer structures, Fe/Au/Fe, acquire an additional interface Gilbert damping compared to Fe/Au samples. The additional non-local Gilbert damping can be described by the

5 spin-pump and spin-sink concepts. The second ferromagnetic (FM) layer acts as a spin momentum sink. A semi-classical model of the spin momentum transfer in FM/NM structures was formulated. The model is based on the Landau-Lifshitz equation of motion and the exchange interaction in FM, and the spin diffusion equation in the NM spacer. The internal magnetic field is treated by employing Maxwell's equations. The theoretical calculations are tested against the experimental results.

6 Dedication To my wife Klara and to my parents

7 Acknowledgements It has been a privilege for me to complete my Ph.D. degree under the guidance and supervision of Prof. Bret Heinrich. His enthusiasm for exploring new physical ideas was inspiring. His knowledge, expertise, and patience were essential for completing this work. I very much enjoyed discussing experimental and theoretical aspects of our work, always learning something new. I have benefited tremendously from many opportunities he has given to me. I would like to thank Prof. John F. Cochran for his assistance in measuring and interpreting Brillouin light scattering data. I wish to thank the members of my supervisory committee, Prof. Daryl Crozier and Prof. Robert Frindt for their guidanance and advice during the course of this work. I would also like to thank Prof. Jurgen Kirschner for giving me the opportunity to visit and work for nine months at the Max-Planck-Institute fiir Mikrostruktur Physik (MPI) in Halle, Germany. It was a great pleasure to perform the STM measurements with Dr. Manfred Klaua and Dr. Jochen Barthel. Their skills and knowledge were inspirational. My thanks also go to Dr. Wulf Wulfhekel for his help and assistance in collecting and interpreting the STM/AFM images and tunneling spectra. I am indebt to Dr. Rudolf Schiifer from the Institute for Metallic Materials Dres- den, Germany for his assistance with the MOKE microscopy studies presented in this work. His knowledge of micromagnetism and magnetooptics was invaluable. I thank Dr. Peter Grutter and Dr. Xiaobin Zhu from McGill University, Montrhal, Qukbec for inviting me to use a custom built AFM for the electron transport properties of the magnetic tunnel junctions as a part of the Canadian Institute for Advanced Research (CIAR) collaboration. Especially I would like to thank Dr. Ken Myrtle for his great help in mastering experimental apparatus and for his assistance in the matter of equipment.

8 vii I extend my thanks to my fellow graduate and post-graduate colleagues for their help during the course of my Ph.D. program. Especially, I wish to thank Dr. Ted Monchesky for helping me to master the MBE and the growth of Fe-whiskers. It was a pleasure to work long hours together with Dr. Ted Monchesky, Dr. Axel Enders, Mr. Georg Woltersdorf, and Mr. Bartek Kardasz. Their knowledge and different backgrounds were inspirational. Nearly last, but not least, I would like to thank my wife Klara for encouragement and patience during the course of my work. I thank you for your moral support. Finally, Klara and I vastly enjoyed spending time with our good friends Janice and Selwyn, Paola and Wolfgang, Junas and Cristina, Ted and Nicole, and Axel and Suzi. Thank you all!

9 Contents.. Approval 11 Abstract Dedication Acknowledgements Contents List of Figures List of Tables List of Symbols iii v vi viii xi xv xvi 1 Introduction 1 2 Theoretical background 2.1 Ultrathin magnetic medium Exchange interaction Landau-Lifschitz equation of motion Spin dynamics and relaxation mechanisms Gilbert damping Eddy currents Tw~magnon scattering Micromagnetism and domain structure Tunneling magnetoresistance Julliere's and Slonczewski's model viii

10 2.4.2 Tunneling of the band electrons Experimental apparatus Fe whisker growth and preparation MBE apparatus Scanning tunneling microscopy Atom force microscope with conducting tip Ferromagnetic resonance Magnetooptical Kerr effect Kerr microscopy Fe/MgO/Fe whisker(001) tunnel structures Theoretical considerations Growth and structure of Fe/MgO/Fe-whisker tunnel junctions Growth of MgO on an Fe-whisker(001) template Growth of Au/Fe on MgO/Fe-whisker(001) template In situ transport properties STM spectroscopy of the MgO/Fe-whisker system STM spectroscopy of Au/Fe/MgO/Fe-whisker Magnetic properties Magnetic studies using MOKE microscopy Magnetization reversal in the Fe/MgO/Fe-whisker Magnetic stray field interaction Magnetotrasport studies using AFM I-V measurement in external magnetic field Charging effects Fe/Cr and Fe/Au multilayers Growth and structure of M/Fe/GaAs(001); M = Au and Cr Magnetic properties of Fe/GaAs(001) Two-magnon scattering in Cr/Fe/GaAs Out-of-plane FMR linewidth Two-magnon contribution to the FMR linewidth... 90

11 5.4 Non-local damping in Au/Fe/GaAs and Au/Fe/Au/Fe/GaAs Experimental evidence for non-local damping Spin-pump model of the non-local damping... 6 Semiclassical theory of the spin transport 6.1 Landau-Lifshitz-Gilbert equation of motion for FM and NM Boundary conditions Results and discussion Single magnetic layer Spin pumping effect FM/NM bilayer... 7 Conclusions A Magnetic anisotropies A.1 Parallel configuration... A.2 Perpendicular configuration... A.3 Effective magnetic anisotropy... B Jones formalism B. 1 Polarization of the light... B.2 Jones vector... B.3 Transformation of Jones vectors on optical elements... B.4 Calculating MOKE signal... Bibliography 131

12 List of Figures 2.1 A coordinate system for the FMR experiment A graphical representation of the three-particle collision A schematic diagram of the two-magnon scattering process A coordinate system used to describe the mutual orientation of M, H. k7 and the sample plane Calculated 2D spin-wave manifold for three different orientations of M with respect to the sample plane The Landau structure of the Fe whisker (001) Domain and domain wall images of Fe-whisker(001) A schematic diagram of the apparatus used to prepare Fe-whiskers A schematic diagram of UHV system A sketch of the modified e-beam MgO furnace A schematic atomic energy level diagram for Auger and photoemission processes The Ewald sphere construction for the RHEED geometry Bragg and anti-bragg condition for a thin film grown on a flat substrate RHEED intensity oscillation for an atomic layer grown on a flat substrate (layer-by-layer growth) The Ewald sphere construction for the LEED geometry A sketch of a typical STM set up A schematic band diagram of the metallic sample and the STM tip separated by the vacuum barrier A schematic diagram of an interferometer technique to monitor the displacement of the flexible cantilever Block diagram of the FMR experiment... 41

13 xii 3.13 A schematic diagrams of the in-plane and out-of-plane TEOl2 cylindrical cavities The measured FMR signal as a function of the applied field Three basic configurations of the Kerr effect A graphical representation of the Kerr effect Experimental set up for measuring longitudinal and transversal component of MOKE signal Two orientations of the sample, the optical plane of incidence. and the external magnetic field A sketch of a common high lateral resolution Kerr microscope The complex penetration function as a function of the depth RHEED. LEED. and STM images of the clean Fe-whisker(001) surface 54 The reconstruction of the Fe/MgO interface from the surface X-ray diffraction (SXRD) experiments The RHEED intensity oscillations of a 6 ML MgO film deposited on the clean Fe-whisker(001) surface at RT STM topographic images of 6 ML MgO grown on Fe-whisker(001) at RT 57 The LEED patterns for MgO layers grown on a Fe-whisker template. 58 A schematic diagram of the MgO LEED pattern with the additional diffraction spots The tilt angle J as a function of the MgO thickness dmgo The RHEED patterns of 20 ML Fe grown on MgO/Fe-whisker(001). 61 A schematic diagram of the electronic band structure of the Fe/MgO interface The STM morphology of 3.8 ML MgO on Fe(001) A schematic electronic band diagram of Fe-whisker/MgO/vacuum/PtIrtip junction for different values of VB The experimental values of the MgO tunneling barrier height as a function of the MgO film thickness The STM morphology of 7 ML MgO grown on Fe(001) The tunneling spectra observed in the 20 Au/20 Fe/5 MgO/Fe-whisker(001) sample using STM Magnetocrystalline anisotropies Fe grown on MgO(001) wafers as a function of l/dfe... 69

14 xiii MOKE measurements on the Au/Fe/MgO/Fe-whisker sample in the longitudinal configuration The depth-selective MOKE image of the Au/Fe/MgO/Fe-whisker structure... MOKE images of the Au/Fe/MgO/Fe-whisker structure for different values of the external dc field A low magnification image of the domain pattern of the 20 A420 Fe/20 MgO/Fe-whisker(001) structure A schematic diagram of the interaction of the domain wall stray field with the magnetization of the Fe film The AFM I-V characteristics of Au/Fe/MgO/Fe-whisker for different values of the external dc field The AFM images of Au/Fe/MgO/Fe-whisker AFM image of a Au/Fe/MgO/Fe-whisker structure taken at positive sample bias voltage The RHEED intensity oscillations of a 16 ML Fe film deposited on 4 x 6-GaAs(001) at RT FMR lines for two different in-plane angles c p between ~ the direction of the external dc field and a cubic axis Magnetocrystalline anisotropies Fe grown on GaAs(001) wafers and covered by Au and Cr as a function of l/dfe The FMR linewidth AH as a function of microwave frequency f FMR field and FMR linewidth at f = 24 GHz as a function of the polar angle OH for the 20 Cr/15 Fe/GaAs(001) sample The FMR linewidth for the parallel FMR configuration for the 20 Cr/15 Fe/GaAs(001) sample as a function of microwave frequency The 2D spin-wave manifold as a function of kll, $k, and OH The extrinsic FMR linewidth AH,,, as a function of the microwave frequency f compared to the theory by Arias and Mills The additional FMR linewidth AH,,, as a function of microwave frequency f compared to the general twemagnon scattering theory The additional FMR linewidth as a function of the out-of-plane angle OH The FMR field and FMR linewidth as a function of c p for ~ the 20 Au/40 Fe/40 Au/16 Fe/GaAs(001) structure at f = 36 GHz

15 xiv 5.12 The FMR field and FMR linewidth for the 16 ML Fe film as a function of (PH at f = 36 GHz The dependance of the additional FMR linewidth on l/dfe and microwave frequency f A cartoon representing the dynamic coupling between two magnetic layers which are separated by a non-magnetic spacer The measured field dependance of the FMR signal for 20 Au/40 Fe/40 Au/16 Fe/GaAs(001) at 24 GHz A schematic coordinate system Spin currents at the FM/NM interface The effective demagnetizing field perpendicular to the sample plane as a function of l/dfe The FMR linewidth as a function of dfe The FMR linewidth including the spin pump contribution as a function ofd Fe The total FMR linewidth in da, Au/16 Fe/GaAs(001) samples as a function of the gold thickness measured at f = 24 GHz The total FMR linewidth in Auldpd Pd/Fe/GaAs(001) samples as a function of the palladium thickness measured at f = 24 GHz... A.l Coordinate system... B.l Optical parameters of the elliptically polarized electromagnetic wave. B.2 Transformation of the Jones vector by the polarization optical element.

16 List of Tables Experimental data of electron and spin diffusion length measured by GMR.... Contribution of the eddy currents to the FMR linewidth The importance of the temperature profile over the Fe boat for the whisker growth The values of the interface uniaxial perpendicular anisotropy Kti for thin Fe layers The measured values of the anisotropy constants for Au/Fe and Cr/Fe grown on GaAs(001) The AH(0) and effective Gilbert damping GeR for the three principal in-plane and perpendicular orientations of the 20 Cr/15 Fe/GaAs(001) structure x 2 Jones matrixes for different o~tical elements in Cartesian base.

17 List of Symbols lattice constant exchange stiffness Hamaker constant magnetic induction vector velocity of light in free space (= 3 x 10'' cm/s) diffusion coefficient elementary charge (= l9 C) energy or energy density energy band gap electric intensity vector electron g-factor (for free electron g = ) Gilbert damping parameter Ferromagnetic resonance field magnetic intensity vector imaginary unit unit vectors in Cartesian coordinate system intensity of the electromagnetic field tunneling current exchange integral wave vector four-fold in-plane anisotropy constant uniaxial in-plane anisotropy constant uniaxial surface perpendicular anisotropy constant magnetization unit vector rf component of magnetization xvi

18 xvii magnetization vector saturation magnetization normal unit vector complex index of refraction (= n - i ~ ) spin polarization unit vector of the in-plane uniaxial axis Fermi velocity bias voltage electrical impedance nabla operator Laplace operator dimensionless Gilbert damping parameter (= GI y M,) spectroscopic splitting factor skin depth exchange length Kronecker symbol half width in a half maximum ferromagnetic resonance linewidth peak-to-peak ferromagnetic resonance linewidth Kerr ellipticity angle permittivity of vacuum Fermi energy Kerr rotation Landau-Lifschitz damping parameter spin diffusion length magnetic moment Bohr magneton electrical conductivity Pauli susceptibility transversal susceptibility complex Kerr effect electron orbital relaxation time electron spin-flip relaxation time angular frequency

19 Chapter 1 Introduction Understanding of magnetization dynamics and electron transport in magnetic mul- tilayers is of considerable interest. They determine the performance of spintronics devices such as magnetic random access memories (MRAM). The static and dynamic magnetic properties play an important role in device applications. The magnetocrys- talline anisotropies determine the equilibrium directions of the magnetization vector, and the magnetic damping parameter determines the time which is necessary to switch the magnetization from one equilibrium direction into another. The spin dependant tunneling allows one to employ the spin of electrons in electronics - spintronics. There is still a lack of in-depth understanding of the spin dependant transport. This is caused by its sensitivity to structural imperfections and defects. Multilayer films with well defined interfaces are required to make a meaningful quantitative comparison between the experiment and the theoretical modelling. The goal of this work is to prepare high quality crystalline multilayers to inves- tigate electron tunneling, and spin dynamics and transport in the simplest possible magnetic multilayers. To realize this goal two different systems were chosen: (i) Fe/Cr, Fe/Au and Fe/Au/Fe multilayers deposited directly onto clean GaAs(001) wafers, and (ii) Fe/MgO/Fe crystalline tunnel junctions grown onto Fe-whisker(001) templates. All ultrathin layers are deposited by means of molecular beam epitaxy (MBE). Iron has been chosen for its large magnetic moment and low Gilbert damping parameter. It is also well lattice matched to GaAs(001). The lattice mismatch between Fe (a = A) and GaAs (a12 = A) is only 1.4%. Both overlayer materials, Au and Cr, are well lattice matched to Fe; the lattice mismatch is within 0.7%. It has been demonstrated in numerous experiments, that the magnetic intrinsic

20 CHAPTER 1. INTRODUCTION 2 damping in metallic ferromagnets is described by Gilbert damping. However, the spin relaxation can be strongly effected by crystalline defects or interface roughness. Gold represents a noble metal with a single spherical Fermi surface with no magnetic ambitions. On the other hand, chromium represents an intrinsic antiferromagnet with ferromagnetically aligned (001) planes. At an ideally flat Cr/Fe interface, the atomic moments of Fe and Cr couple antiferromagnetically. In real Fe/Cr multilayers accompanied by interface roughness, the frustration between ferromagnetic and anti- ferromagnetic interactions results in unexpected and interesting magnetic properties. It will be demonstrated, that in the Fe/Cr structures a significant increase of the magnetic damping due to two-magnon scattering is observed. Magnetic double layers, where two ferromagnetic (FM) layers are separated by a non-magnetic (NM) spacer, provide a special case where the dynamic interaction between the itinerant electrons and the magnetic moments in ultrathin films offers new exciting possibilities. It will be shown, that even in the absence of static inter- layer exchange coupling, the magnetizations are still dynamically coupled through the NM spacer by emitting and absorbing non-equilibrium spin currents. The damping parameter is not only determined by the magnetic properties of the thin film, but is also affected by the surrounding magnetic and non-magnetic layers. This dynamic coupling is a new concept which can have a strong effect on spin relaxation in hybrid magnetic devices. The majority of the tunneling magnetoresistance (TMR) experiments are carried out using polycrystalline or amorphous magnetic multilayers. The tunneling process in these magnetic tunnel junctions (MTJs) is governed by a random hopping be- tween the defect states inside the tunneling barrier. The band structure properties of the magnetic electrodes and the tunneling barrier are washed out and a significant decrease of the magnetoresistance with increasing applied voltage is observed. The crystalline Fe/MgO/Fe(001) MTJs provide a model system to investigate the TMR effect. The lattice mismatch between the (100) direction of MgO and the (110) di- rection of Fe is 3.5%. The theoretical predictions by Butler et al. [I] and Mathon and Umerski [2] based on first principle calculations suggest, that for a 12 ML thick MgO layer, the conductance in the parallel orientation of the magnetic moments is 2-3 orders of magnitude higher than that for the antiparallel orientation. We have employed Fe-whiskers which provide atomically flat surfaces with terraces extend- ing over several pm allowing one to deposit high quality crystalline MTJs where the

21 CHAPTER 1. INTRODUCTION 3 predictions of the ballistic tunneling can be tested. The lateral dimensions of Fe-whiskers do not allow one to use a "cross" geometry or lithography, which are typically used in giant magnetoresistance (GMR) or TMR experiments. In this work, scanning tunneling microscopy (STM) and atom force microscopy (AFM) with conducting tip were employed to investigate local tunneling in Fe/MgO/Fe-whisker(001) structures. The AFM tip allows one to create a controllable ohmic contact to the top metallic electrode allowing one, in principle, to measure the local TMR in Fe/MgO/Fe-whisker(001) tunnel junctions. The thesis is organized as follows: Chapter 2 includes the important theoretical concepts to provide a background which is relevant for this work. Chapter 3 provides an overview of the different experimental techniques which were used in this work. It covers: (i) the MBE apparatus for preparing high quality magnetic multilayers, (ii) ferromagnetic resonance (FMR), magnetooptical Kerr effect (MOKE), and Kerr microscopy to study magnetic properties of multilayered structures, and (iii) scanning tunneling microscopy (STM) and atom force microscopy (AFM) to investigate electron transport properties of the MTJs. The results of the structural, electrical, and magnetic properties of crystalline tunnel junctions based on Fe/MgO/Fe-whisker(001) structures are discussed in Chapter 4. It will be shown, that in the crystalline multilayers, ballistic transport can be realized. The results of the spin dynamics and transport in Fe/Cr and Fe/Au multilayers grown on GaAs(001) wafers are discussed in Chapter 5. In the Fe/Cr structures, the extrinsic contribution caused by two-magnon scattering at interfaces was observed. The Fe/Au/Fe structures provided a clear demonstration of spin transport in magnetic multilayers. In Chapter 6, the concepts of spin pump and spin sink are extended for thick ferromagnetic (FM) and normal metal (NM) layers. A semi-classical model based on the Landau-Lifshitz-Gilbert equation of motion and the exchange interaction in a FM layers, and the spin diffusion equation in the NM spacer is formulated. A quantitative comparison between the model calculations and the experimental results is presented.

22 Chapter 2 Theoretical background This Chapter is devoted to the theoretical aspects which are important in this work. First, the magnetic properties of thin ferromagnetic films are discussed in the limit of an infinite exchange interaction; all magnetic moments across the film thickness are parallel to each other. This is often referred to as the ultrathin limit. The ferromagnetic resonance (FMR) condition and FMR linewidth are derived for the ultrathin limit including magnetocrystalline anisotropies. In the second part, properties of magnetic domains and their boundaries (domain walls) are discussed with extra attention to the Landau domain structure of Fe-whiskers. At the end of the Chap ter, the tunneling magnetoresistance (TMR) of magnetic tunnel junctions (MTJs) is discussed. The Julliere and Slonczewski models are compared to the full free-electron model. The role of the electronic band structure in MTJs will also be mentioned. 2.1 Ultrathin magnetic medium In ultrathin films all magnetic moments across the layer thickness are parallel to each other. This is only true for infinite exchange stiffness. It will be shown, that this is well satisfied for thin magnetic films of a few nanometers in thickness. Ultrathin magnetic layers are often called giant magnetic molecules [3] since they have unique magnetic properties which are different from those observed in bulk materials.

23 CHAPTER 2. THEORETICAL BACKGROUND Exchange interaction We will assume a simple Heisenberg exchange interaction. The total energy of two interacting spins pi and /+ is given by where g is an electron g-facotr, pg is the Bohr magneton, pi,j are atomic moments at sites i and j, and Ji,j is an exchange integral. If the direction of the atomic moments changes slowly through the crystal one can expand Eq. 2.1 in Taylor series. In the simple cubic crystal with the lattice constant a, the total energy associated with the magnetic moment p interacting with its 6 nearest neighbors, can be written as [4] where J represents the exchange integral between the nearest neighbors. The linear term of the Taylor expansion is absent due to cubic symmetry (contributions from the left and right are equal with the opposite sign). Eq. 2.2 can be rewritten in terms of the energy density I, = Ea/a3 and the magnetization vector M = p/a3 where M, is the saturation magnetization, and A is an exchange stiffness. The effective field due to exchange interaction, H z, is found to be [5, 41 Note, that in the ultrathin limit there is no variation of the magnetization across the film thickness and Eq. 2.6 reduces to the well-known expression [6, 31 Using Eq. 2.3 and 2.7 one can evaluate the effective exchange field for the simple cubic lattice and write it as [7]

24 CHAPTER 2. THEORETICAL BACKGROUND Figure 2.1: (a) A coordinate system for an arbitrary in-plane angle; x-axis is parallel to the direction of the saturation magnetization and z-axis is perpendicular to the sample plane. (b) The perpendicular FMR configuration. The direction of the saturation magnetization and the external dc field are oriented perpendicular to the sample plane. (c) The in-plane FMR configuration. The static part of the magnetization vector and the external dc field are confined to the sample plane. The ultrathin limit is well satisfied for films which are thinner compare to the exchange length 6,,. From a simple magnetostatic argument, he, is given by [7] For iron, A = 2 x erg/cm and M, = 1.7 koe which yields be, = 3.3 x cm. This corresponds to 23 ML Landau-Lifschitz equation of motion The magnetization dynamics in the classical limit can be described by the well-known Landau-Lifhsitz (LL) equation of motion [8, 31 where y is the absolute value of the gyromagnetic ratio and X is the LL damping constant. The first term on the right-hand-side is a precessional torque and the second term represents the LL relaxation term [8]. The effective field, HeE, is given

25 CHAPTER 2. THEORETICAL BACKGROUND by the magnetization derivative of the magnetic Gibbs (free) energy density & The Gibbs energy & contains the Zeeman energy of the external dc and rf magnetic fields, the magnetocrystalline anisotropy energy, and the demagnetizing energy which is associated with the magnetization component perpendicular to the film surface for a magnetization density that is uniform in the sample plane. In the static case, the magnetization vector M is parallel to the static part of the effective field Heff. For more details see Appendix A. For small damping (all = X/7Ms << 1) the LL damping term can be replaced by the Gilbert relaxation torque [9, 101, resulting in the Landau-Lifshitz-Gilbert (LLG) equation of motion where G represents the Gilbert damping parameter and 6i = M/Ms is the magneti- zation unit vector. In Gilbert's original work [lo] the damping parameter was derived in a tensor form. However, the Gilbert damping term is usually used as an isotropic relaxation parameter. Note, that the Gilbert damping term in the LLG equation of motion, Eq. 2.13, can be expressed using the effective damping field, ~z~ H =--- G G 852 eff r2ms at ' The effective damping field is proportional to the time derivative of the instanta- neous magnetization direction, a%/&, and inversely proportional to the saturation magnetization Ms. Parallel configuration : The external dc magnetic field H and Ms lie in the sample plane, Fig. 2.1~. The LLG equation of motion can be solved in the small angle approximation; Iml << Ms, where m represents the rf component of the magnetization vector, see Fig. 2.la. The total magnetization M = m + Ms = (M,, my, m,), where Ms and m are the longitudinal and transversal components of the magnetization. The external dc field is oriented along the x-axis and the driving microwave field is parallel to the y-axis. The LLG equation of motion 2.12, using effective field evaluated

26 CHAPTER 2. THEORETICAL BACKGROUND 8 in Appendix A, (see Eq. A.9-A.11) and for a time dependance exp(iwt), results in where HII is the projection of the external dc field into the direction of the saturation magnetization, 47r Meff = 47r M, - 2KiI/Ms, a~ = G/y M, is the dimensionless Gilbert parameter, Kt, is the surface uniaxial perpendicular anisotropy, and Kll and KUI are the in-plane four-fold and uniaxial anisotropy constants, respectively. Angle y~ represents the in-plane angle between the direction of the saturation magnetization and the crystallographic [loo] direction and cp is the angle between the saturation magnetization and the in-plane uniaxial anisotropy axis. The transversal susceptibility, XI = y, can be expressed as where A, and A, represent the effective anisotropy fields in the plane perpendicular to M, and Beff is the effective magnetic induction of the sample. The resonance condition is satisfied when the real part in the denominator in Eq is equal to zero This expression is valid only for a homogeneous precession. One can generalize this equation by assuming that the rf magnetization can be described by plane waves with

27 CHAPTER 2. THEORETICAL BACKGROUND 9 the wave-vector k. These excitations are called spin-waves or magnons, see e.g [ll]. A more detailed description will be given in Section The resonance linewidth defined as a half width of the absorption line at half maximum, HHWHM, can be found by putting the real and imaginary parts of the denominator in Eq equal to each other assuming that the function in the nu- merator is slowly varying within the linewidth. The resulting linewidth AHHWHM is given by Perpendicular configuration : The external dc magnetic field and Ms are oriented perpendicular to the sample plane, see Fig. 2.lb. The FMR resonance condition and the FMR linewidth are derived in a similar way as for the parallel configuration. The resonance field HFMR and linewidth AHHWHM are found to be where KII is the four-fold perpendicular anisotropy, see Appendix A. Note, that for both, the parallel and perpendicular configuration, the FMR linewidth follows the same expression regardless of the ellipticity of the rf precession [6]. Within the Gilbert phenomenology, the FMR linewidth is strictly proportional to the microwave frequency w and inversely proportional to the saturation magnetization Ms. 2.2 Spin dynamics and relaxation mechanisms The FMR linewidth can contain contributions which are sample dependant and there- fore can be avoided by preparing high quality crystalline samples. Two-magnon scat- tering or broadening due to sample inhomogeneities belong to this category. These contributions are called extrinsic. On the other hand, there are physical precesses which are unavoidable, such as electron scattering from phonons and magnons. For thick metallic layers one cannot avoid the energy dissipation by eddy currents. These processes are intrinsic and determine the value of the Gilbert damping parameter [12, 131. From the experimental point of view, the intrinsic value of the magnetic relaxation is given by the smallest measured FMR linewidth satisfying Eq and 2.25.

28 CHAPTER 2. THEORETICAL BACKGROUND 10 H. Suhl [14] summarized the intrinsic relaxation mechanism : "Ultimately, intrinsic damping of the magnetic motion comes about by coupling of the magnetization to nonmagnetic degrees of freedom which themselves are subject a to loss mechanism." Gilbert damping The physical processes responsible for the relaxation in metals have been extensively studied for the last four decades. The LLG equation of motion (see Eq. 2.12) which is the phenomenological description of the magnetization dynamics predicts a linear dependance of the FMR linewidth on the microwave frequency. In the 1970s it was shown that the intrinsic magnetic relaxation in metals is different from that in mag- netic insulators. In metals, the precession of the magnetization is accompanied by electron-hole pair excitations. The Gilbert damping coefficient G in metals is caused by incoherent scattering of electron-hole pair excitations by phonons and magnons. The electron-hole pair excitations are either accompanied by a spin-flip or the spin remains unchanged. The spin-flip excitations are caused by the exchange interaction between the magnons and itinerant electrons (s-d exchange interaction [15]). The non-spin-flip excitations are caused by the spin-orbit interaction which leads to a dy- namic redistribution of electrons in the electron k-momentum space [16]. Both of these processes contribute to the magnetic damping in metals and they will be discussed separately. Spin-flip scattering. The spin-flip model of magnetic relaxation was proposed by Heinrich et al. [15]. It is based on the s-d exchange interaction between the s,p- like electrons which are moving through the lattice (itinerant electrons) and localized d-spins. One should keep in mind, that in solids, there is no real distinction between s,p- and d-electrons (see e.g. [17]). The transverse interaction Hamiltonian involving the rf component of magnetiza- tion is described by a three-particle collision term where N is the number of atomic sites, S is the spin of d-electrons, J(q) is the s-d exchange interaction constant, a and a+ annihilates and creates electrons with wave-vector k and the appropriate spin (T, L), and b annihilates the magnon with wave-vector q. The subscripts T and 1 signs represent the majority and minority

29 CHAPTER 2. THEORETICAL BACKGROUND Figure 2.2: A graphical representation of the three-particle collision. spins, respectively. The Eq represents a three-particle collision in which an electron-hole pair is created or annihilated due to the interaction with a magnon, see Fig The total spin angular momentum of this process is conserved and therefore the itinerant electron flips the spin during the scattering event. The scattering of the electron-hole pair does not lead to magnetic damping for long wavelength spin waves (q -+ 0). One needs to include the finite life-time of the electron-hole pair excitation. That can be formally done by introducing an imaginary term for the electron-hole pair energy [15] where rsf is the effective life-time of the electron-hole pair excitation. r,f is given by the incoherent scattering with phonons and magnons which flips the spin of electron. The Gilbert damping can be calculated by evaluating the rf susceptibility using the Kubo Green function formalism [18, 151. The calculation was performed in the random-phase approximation (RPA)[18] by using a Green function G,,,, which was defined by [15, 191 where 8(t - t') is the Heaviside step-function (8 = 0 for t < t' and 8 = 1 for t 2 t'), (...) denotes averaging over a grand-canonical ensemble, and [...] is the commutative bracket. The infinite chain of high-order Green functions is terminated using con- traction over b- and a-operators [15] after introducing one additional Green function, Fk,kl,q, defined by [15, 191 The effective damping field due to the spin-flip scattering, H:;~, is given by the

30 CHAPTER 2. THEORETICAL BACKGROUND imaginary part of the Green function G,,,, and can be expressed as [15, 191 where the summation is carried out over all available states at the Fermi surface, S = M,(T)/M,(O) is the reduced spin S, and n is the density of states (DOS). The factor gpb = yh was used to convert energy into an effective field. Note, that the Lorentzian factor in Eq represents the probability of achieving particular scattering event in which energy is conserved ( h k = ~,+k,l- E,,J). that IT,^)^ can be neglected compared to (hk Eq can be simplified by realizing, + E ~,T - E,+~,J)~ [12]. Assuming the sharp Fermi distribution (Idn/d~l = S(E~ - EF), where EF is the Fermi energy) the Gilbert damping field can be rewritten as In FMR the response of the sample is given by the nearly homogeneous mode, q t 0. In this case, the energy of the spin-flip electron-hole pair excitation is dominated by the exchange energy, h, + &k,f - &kfq,l M &k,t- Ek+q,l = -2s J(o), [12]. Using NSgPB = M, (assuming unit volume), H:if can be expressed as Note, that Eq is proportional to w/m, which is a signature of the Gilbert damping, see Eq Comparing Eqs and 2.14 one can express the Gilbert damping parameter as where xp is the Pauli susceptibility of itinerant electrons and is derived from where n(&f) is density of itinerant electrons per spin at the Fermi level [20, 211. The spin-flip relaxation time ~~f is enhanced compare to the orbital relaxation time re, of electron. One can evaluate r,f from the spin-flip diffusion length XSd which can be

31 CHAPTER 2. THEORETICAL BACKGROUND 13 measured by means of a current-perpendicular to the plane giant magnetoresistance (CPP-GMR) experiment [22, 23, 241 where UF is the Fermi velocity and A* is an effective electron mean free path defined by [23, 241 where is the electron mean free path for majority and minority spins. In the free electron model the effective electron mean free path can be estimated by [24] where p is resistivity of the material and n is the total density of conduction electrons for both spins. The electron relaxation time, rel, and spin-flip relaxation time, rsf, were determined from GMR experiments for Co and Permalloy (Py). The results are summarized in Tab Non-spin-flip scattering. In the seventies, Kamberskf proposed a different model for relaxations in metals using a spin-orbit interaction Hamiltonian [26, 271. The same Harniltonian was used earlier by Brooks [28] for calculations of the magnetocrystalline anisotropies and electron g-factors for cubic crystals. In Kambersk9's model of the spin-orbit coupling, the electronic energy levels of the crystal depend on the direction of the magnetization, %(t) = MIM, as proposed by Clogston [29] and recently discussed by Suhl [14]. The precessing magnetization distorts periodically the Fermi surface; often it is referred to it as a breathing Fermi surface. The electron occupation number nk,, relaxes towards the instantaneous equilibrium value material A* [nm] Asd [nm] re1 [lo-15s] rsf [IO-~~S] Cobalt Permalloy (Fez2Ni78) Table 2.1: Experimental data of electron and spin diffusion length measured by GMR. The presented numbers are obtain at 77 K. The data for Co were taken from [23] and for Permalloy from [25, 241. The Fermi velocity was assumed to be 1.2 x lo8 cm/s for both materials.

32 CHAPTER 2. THEORETICAL BACKGROUND 14 by the scattering of electrons by phonons. The magnetic damping results from the phase lag between the changes of %(t) and the population response [16, 271. The total electron energy density E can be written in the form [27] where R is the volume of the sample and ~ k,, is the energy of the appropriate electron state. The summation is carried out over available states in the first Brillouin zone. The variation of the total energy density with respect to the magnetization direction %(t) results in the effective field The non-equilibrium populations nk,, can be approximated by where f (E~,,, 5%) represents the Fermi function and rk,, is the life-time of the appro- - priate electronic state. Since the Fermi function is time dependant, f (E~,,, m(t)), the out-of-phase part of the effective field can be obtained using Eq Note, that the relaxation effective field in Eq is proportional to the time deriva- tive of the direction of the magnetization vector, d%/dt, and inversely proportional to Ms. This is the hallmark of the Gilbert damping, see Eq Comparing Eq and the Gilbert effective field in 2.14, one can obtain the expression for the Gilbert damping parameter G [27] where &(E~,~ - E ~ M )-8 f (E~,,, %)/d~~,, and using the same T for all spin states. Since no spin-flip scattering is involved the electronic life-time T is equal to the electron orbital relaxation time re* [16, 121.

33 CHAPTER 2. THEORETICAL BACKGROUND Eddy currents A contribution to the FMR linewidth due to eddy currents can be considered as an intrinsic property of the material. It starts to play a role when the thickness of the ferromagnetic layer dfm is comparable to the skin-depth 6 defined usually as [30, 311 where c is the velocity of light in free space, w is the angular frequency, and a is the conductivity of the material in CGS/esu units. It was pointed out by Kittel and Herring [32] and Ament and Rado [33] that for thick magnetic films the eddy current leads to a finite FMR linewidth even in the absence of the damping. This effect is often called the exchange conductivity mechanism. Ament and Rado have shown [33], that in the limit where 47rMS >> H,,,, w/y, the resonance line broadening due to the eddy current loss is proportional to m; A is the exchange stiffness, see Eq In the limit where dfm >> 6 the additional linewidth due to eddy currents can be estimated from transversal susceptibility including the exchange field, see Eq The susceptibility XI, for the parallel MR configuration, can be written (see Eq neglecting crystalline anisotropies, Gilbert damping, and including exchange field) as XI = - Ms - Beff (:) - k2 Beff H - (Beff + H) z ' where k is the spin-wave wave-vector. Note, that we included the exchange field only in the denominator. One needs to assume, that the function in the numerator does not change much within linewidth; it does not have a resonant character. The value of the k-vector can be found solving Maxwell's equations and using the transversal susceptibility XI from Eq. 2 k = - The value of lc2 can be evaluated at the resonance ((~/y)~ = BeffH, see Eq. 2.22) and is equal to

34 CHAPTER 2. THEORETICAL BACKGROUND 16 f [GHz] 4nMs [kg] H,,, [koe] AHfU" [Oe] AHeSt [Oe] Table 2.2: Contribution of the eddy currents to the FMR linewidth. The column AHeSt shows the values obtain from Eq The full theory calculation, AH^"", solves numerically LLG equation of motion including the exchange interaction field. The conductivity and exchange stiffness corresponds to Fe : a = 1 x 1017 s (in CGS/esu units), A = 2 x lom6 erg/cm. The real part of k2 shifts the resonance field and the imaginary part corresponds to the FMR linewidth. Substituting k2 from Eq into Eq one is able to calculate the effective FMR linewidth due to eddy currents Beff + H FMR Beff This results is in agreement with the predictions of Ament and Rado 133, 341. In addition, our result predicts weak dependance on the saturation magnetization M, which is governed by I This dependance is very weak since in our case 4nM, >> HFMR, see last two lines in Tab The numerical results in Tab. 2.2 show, that the estimate using the simple argument reproduces the full calculation quite well. The estimated values of the FMR linewidth are % smaller compared to the full theory Two-magnon scattering In a wide range of metallic amorphous ribbons [35], films [36], and metallic multilayers [37, 3, 381 the FMR linewidth, AH, above 10 GHz is not only proportional to the microwave angular frequency w, as expected from Gilbert damping (see Eq. 2.23), but also possesses a zero frequency offset AH(0)

35 CHAPTER 2. THEORETICAL BACKGROUND Figure 2.3: A schematic diagram of the two-magnon scattering process. Homogeneous magnon W ~=O is scattered into the finite wave-vector magnon wklfo which is degenerate in frequency. A zero frequency offset is caused by magnetic inhomogeneities and therefore its origin is extrinsic. The Gilbert parameter Geff was used to express the fact that the slope of the FMR linewidth in Eq can, in general, include both intrinsic, Gint, and extrinsic, GeXt, contributions. From an experimental point of view, it is a reasonable assumption that for samples where AH(0) = 0, the effective Gilbert damping Geff equals to the intrinsic Gilbert parameter Gint. The two-magnon scattering process has been used extensively to describe extrinsic contributions to damping in ferrites [39, 40, 41, 42, 431. The systematic studies by LeCraw and coworkers [41] have revealed that the FMR line broadening was strongly dependant on a polishing procedure of the ferrite samples, and therefore related to sample defects. Later, Sparks, Loudon, and Kittel [42] developed the two-magnon scattering theory to account for an additional (extrinsic) contribution to the FMR linewidth. Patton's group pioneered the use of two-magnon scattering in metallic films [44]. Structural defects may scatter the energy from the homogeneous mode, k = 0, into the finite wave-vector magnon which is degenerate in frequency, see Fig This is a magnetic analogue of the elastic scattering of electrons in metals by lattice defects [45]. Magnons are scattered strongly by larger defects such as polishing pits or microscopic variations of the magnetic anisotropies [46, 451. The dispersion relation for spin-waves (spin-wave manifold) can be evaluated by solving the LLG equation of motion (see Eq. 2.12) with an effective field including the exchange field HE; (Eq. 2.8) and dipolar field HZ;, see e.g. 147, 481 where m = mo exp(ikr) is the rf magnetization. In ultrathin films the Ic wave-vectors

36 CHAPTER 2. THEORETICAL BACKGROUND Figure 2.4: A coordinate system used to describe the mutual orientation of M, H, k, and the sample plane. are confined to the film plane [46, 491. For a simple film which is described by the effective magnetization 4rMeff the magnon energies are given by the Damon Eshbach modes which are described for the parallel configuration in [46], and for an arbitrary out-of-plane (polar) angle in [50], see Fig (2rM,kd(cos?,hk sin $k sin 6 '~))~, (2.51) where HI, is the projection of the external dc field into the direction of the saturation magnetization (= H cos(om - OH)), Gk is the angle between the spin-wave wavevector k and the in-plane direction of the dc magnetization, and OH and OM are the polar angles between the direction of the external dc field and the magnetization vector with respect to the sample plane, respectively, see Fig There are two special cases: (a) = 0": spin-wave propagating along the in-plane projection of the saturation magnetization (kl 1 M,) corresponding to the lowest spin-wave frequency and (b) Gk = 90": spin-wave propagating perpendicular to the in-plane projection of the saturation magnetization (k 1 M,), which represents the upper bound of the spin-wave frequency. The dispersion relation for the intermediate angles lies between these two limits resulting in the spin-wave band (manifold). The spin-wave manifold depends on the orientation of external dc field with respect to the sample plane, see Fig In the parallel FMR configuration, see Fig. 2.5a, the dipolar field produces a term

37 CHAPTER 2. THEORETICAL BACKGROUND k [I 0' ~ ~ ' ' 1 k [I 0' ~ ~ ' ' 1 k [I 0' ~ ~ ' ' 1 Figure 2.5: Calculated 2D spin-wave manifold (Eq. 2.51) for three different orientations of M with respect to the sample plane : (a) OM = 0" (parallel configuration), (b) OM = 35"' and (c) OM = 90" (perpendicular configuration). The dotted line represents the magnons with non-zero k-vectors which are degenerate in frequency with the homogeneous mode (I kl = 0). The magnetic parameters correspond to Fe: 47rMs = 21.4 kg, 47rMeff = 16.0 kg, g = 2.09, and A = 2 x 10W6 erg/cm. The thickness of the layer was 15 ML. which is linear in k [51]. For qk = 0, this initial slope is negative. With increasing k, u(kll) decreases and eventually at k = ko crosses the angular frequency of the homogeneous mode, see Fig. 2.5a. Therefore, in the parallel configuration one expects an additional broadening of the FMR line due to the two-magnon scattering. In the perpendicular FMR configuration, see Fig. 2.5c, the spin-wave manifold is dominated by the positive term proportional to k2. The FMR field falls to the bottom of the band and therefore there are no magnons degenerate with the homogeneous precession. Therefore, in the perpendicular configuration there is no additional broadening by the twemagnon process. Recently, Arias and Mills [46, 491 developed the theory to evaluate the contribution to two-magnon scattering for ultrathin films for the in-plane FMR configuration. In the following text, external dc field and the saturation magnetization vector are parallel to the x-axis. The sample normal is parallel to the z-axis. They have used Green's functions defined as where t represent the Hermitian adjoint operator and a and p range over y and z.

38 CHAPTER 2. THEORETICAL BACKGROUND The two-magnon scattering Hamiltonian was written as [46] where V&(k;, kll) represents the matrix elements of the two-magnon interaction. One can find solution for the averaged Green's function Syg(krl = 0, W) [46] where The total FMR linewidth can be expressed as The first term corresponds to the Gilbert damping and the second one represents the extrinsic contribution due to two-magnon scattering. To evaluate the two-magnon contribution to the FMR linewidth one has to evaluate the matrix elements V&. Arias and Mills have used three different models for two-magnon scattering : (a) change in the Zeeman energy, (b) change in the dipolar energy, and (c) the variation in the direction of the anisotropy axis over the surface of a defect. They have shown, that only the variation of the uniaxial perpendicular surface anisotropy results in a measurable effect. After complicated mathematical steps, Arias and Mills derived an analytical expression for the additional FMR linewidth due to two-magnon scattering

39 CHAPTER 2. THEORETICAL BACKGROUND 2 1 where a and c are the lateral dimensions of the defects, and b is the defect depth. Parameter p represents the fraction of the surface covered by defects. Averaged values (alc) and (cla) were evaluated under the assumption that a and c were randomly distributed from 1 to Na and Nc, respectively. Then 2.3 Micromagnetism and domain structure The static magnetic configuration of thin ferromagnetic layers as well as bulk crystals has been studied by numerous imaging techniques for decades. However, most of the existing imaging techniques provide information from a thin slice of the ferromagnetic body close to the surface. The inner magnetic configuration is based on micromagnetic simulations. For further reading see e.g. [52, 531. In the further reading an Fe-whisker will be called a single crystal of iron with square or rectangular cross-section of about (200 x 200) pm and 5 to 10 mm in length. These samples are prepared by chemical vapor transport using the reduction of FeC12 or FeB2 in a hydrogen atmosphere [55], for more details see Section 3.1. Fewhiskers provide defect-free atomically smooth surfaces extending over several pm. The magnetic contrast is strong and it is possible to obtain magnetic images from all sides of the crystal [53]. The understanding of micomagnetism was significantly advanced by the studies of domain patterns of Fe- [56, 57, 58, 591 and Co-whiskers [60] and pure Ni-platelets [61]. Figure 2.6: The Landau structure of the Fe whisker (001).

40 CHAPTER 2. THEORETICAL BACKGROUND,- a'.' ",.'.,, ,. Figure 2.7: Domain and domain wall images of Fe-whisker(001) using : (a) magnetic force microscopy (MFM) and (b) magnetooptical Kerr effect (MOKE) microscopy. The contrast in (a) is given by the out-of-plane component of the magnetization vector; black and white segments of the domain wall (DW) correspond to the magnetization vector pointing upwards and downwards, respectively. Therefore, one is.sensitive the internal rotation of the Bloch wall. The characteristic kinks of the domain wall are caused by the Bloch lines. In MOKE imaging, figure (b), one is sensitive to the in-plane component of the magnetization vector; black and white segments of DW correspond to the magnetization pointing up and down, respectively. Therefore, one images the in-plane rotation of the N6el cap. The Bloch lines can be distinguished by kinks of the Bloch wall (marked by "BL" for clarity). The MFM image was taken from [54] with permission of Xiaobin Zhu...

41 CHAPTER 2. THEORETICAL BACKGROUND 2 3 Iron has a positive cubic anisotropy, K1 > 0, (easy axis along (100) directions). The strong shape uniaxial anisotropy of the Fe-whisker, see Fig. 2.6, keeps the magnetization aligned along the whisker length. The magnetization ground state of the (001) surface of the Fe-whisker is shown in Fig. 2.6, see e.g. [52, 53, 621. It consists of magnetic domains magnetized along the whisker axis (longitudinal direction) separated by 180" domain wall (DW). The longitudinal domains might by interrupted by diamonds, see Fig. 2.6, which are magnetized in the transversal direction (perpendicular to the whisker axis). The 180" domain wall along the whisker length is a so-called vortex wall, which is derived from the symmetric Bloch wall [53]. Inside the vortex wall, the magnetization rotates in the plane of the wall (Bloch-like). There are two possible orientations of the magnetization inside the Bloch wall; the magnetization direction pointing upwards (towards the whisker surface) or downwards (away from the whisker surface). The boundary between two such segments is called a Bloch line (BL) and it creates a kink at the surface, see Fig At the surface of the bulk material, the magnetization tilts towards the sample plane and appears like a common Nkel wall (the magnetization vector rotates perpendicular to the domain wall plane). Creating the vortex state at the surface, the stray field of the domain wall is reduced depending on the reduced anisotropy parameter Q = 2K1/(4rM:), where K1 is the strength of the cubic anisotropy energy [53]. With increasing Q, the vortex character of the wall diminishes until it reaches a Bloch character for high Q. For Fe-whisker Q FZ 0.02 and therefore the vortex character should be well pronounced. This was confirmed by surface-sensitive techniques like magnetooptical Kerr effect (MOKE) [53, 631 and scanning electron microscopy with polarization analysis (SEMPA) [64, 651, see Fig. 2.7b. However, the stray field compensation at the surface of the Fe-whisker is not complete. The out-of-plane component of the magnetization can be observed by the Bitter technique [58] or magnetic force microscopy (MFM) [54], see Fig. 2.7a. 2.4 Tunneling magnetoresistance The tunneling magnetoresistance (TMR) is characterized by the change of resistance or conductance depending on the mutual orientation of magnetic moments of two ferromagnetic layers (F) separated by an insulator (I)

42 CHAPTER 2. THEORETICAL BACKGROUND 24 where Gp,~p is the conductance for parallel and anti-parallel configuration and RP,AP represents the resistance for parallel and anti-parallel configuration. The maximum TMR effect can reach 100 %. The first spin-dependent transport measurement in F/I/F structures was reported by Julliere in 1975 [66]. Using a Co/Ge/Fe junction, Julliere observed a change of the resistance ratio of nearly 14% at 4.2 K. The effect decreased to less then 1% when a few mv bias voltage was applied. Over time numerous results by different groups using mainly A1203 as a tunnel barrier and Fe, Co, or permalloy (Py) as electrodes have exhibited the tunneling characteristics. Miyazaki et al. [67] have observed a resistivity change of 2.7% and 3.5% at RT and 77 K, respectively using Py/Al-A1203/Fe structures. Later, Moodera et al. [68, 691 have used Co/A1203/Py and Co/A1203/CoFe tunnel junctions. They have measured a TMR ratio of 16% and 24% at RT and 77 K, respectively. Recently, Bowen et al. [70] have observed a TMR ration of 60 % at 30 K in epitaxial Fe/MgO/FeCo(001) structures grown on GaAs (001) templates. Even though there are many experimental results showing tunneling characteris- tics in TMR structures, the basic understanding of tunneling processes is still unclear. This is partly due to the fact that the vast majority of TMR experiments have been carried out using polycrystalline or amorphous multilayers. For such structures, it is impossible to compare measured data with the theoretical predictions based on first principle calculations Julliere's and Slonczewski's model A simple theory of TMR was proposed by Julliere [66]. It follows the previous analysis by Tedrow and Meservey [71] who have studied the tunneling process in SC/I/F, where SC represents a superconductor. They found that the conductivity a of the structure is 0 = ups (ev + ph) + (1 - a)ps (ev - ph), (2.62) where p, is the SC density of states and a is the fraction of tunneling electrons in the F whose magnetic moments are parallel to the applied field,

43 CHAPTER 2. THEORETICAL BACKGROUND 2 5 where p~,l represent the density of states for the majority and minority carriers, re- spectively. The spin-polarization P is defined by In Ni, P = 7.5% [71]. Julliere has extended this formalism for F/I/F tunnel junctions and defined the TMR ratio by where P and PI are the tunneling spin-polarizations in each magnetic layer at the Fermi level. In this simple model the band structure is completely ignored. The tunneling conductance is distributed over the whole Fermi surface corresponding to the complete diffuse scattering limit. Slonczewski evaluated the TMR using a free-electron model and the Landauer- Biittiker formula [72, 731 for the tunneling conductance [74] where kii represents the component of the wave-vector parallel to the F/I interface and T (kll) is the transmission probability. No diffuse scattering in the barrier region is considered and therefore kll is conserved. He obtained an expression for the tunneling conductance [74] where KO is the decaying wave-vector in the barrier at kii = 0 and d is the barrier thickness. Eq is obtained from Eq by integrating over kll and keeping only the leading term in lid. Slonczewski's result for the conductance ratio is similar to that of Julliere's formula with a renormalized spin polarization Peff defined as where P is defined by Eq and ktll is the majority and minority wave-vector evaluated at kll = 0, respectively. The dependance on kt,1 reflects the fact, that the height of the tunneling barrier is spin-dependant.

44 CHAPTER 2. THEORETICAL BACKGROUND MacLaren et al. [75] have calculated TMR using the full free-electron model and compared their results to Julliere's (Eq. 2.64) and Slonczewski's (Eq. 2.68) model. They have shown, that Julliere's model does not describe the conductance ratio well for any barrier thickness and height. Slonczewski's approach provides much better agreement. The disagreement between the results of MacLaren et al. and Slonczewski's theory increases for thin insulator thicknesses and large barrier heights. The difference arises from neglecting the terms in the integral 2.66 which are a higher power that lid Tunneling of the band electrons In addition, MacLaren et al. [75] have evaluated the TMR ratio in Fe/insulator/Fe considering the complete band structure of Fe. They used the layered Korringa-Kohn- Rostoker (LKKR) approach [76, 77, 781 within the local spin density approximation to evaluate the electronic structure of the ferromagnetic electrodes. The barrier was considered to have a uniform potential V. According to their calculation, for a given barrier height the TMR is almost independent of the barrier thickness which is consistent with the Slonczewski and the free-electron models. In fact, the current distribution across the Brillouin zone (BZ) of the free-electron model is similar to the one for the majority channel in the parallel configuration. It has a Gaussian-like shape with the maximum in the middle of the BZ (k = 0). The current distribution for the minority channel shows a completely different profile with four maxima for k # 0. The theoretical predictions of the TMR ratio are much larger than experimental results observed so far. The detailed study of MacLaren and coworkers [75] has shown that the band structure of the electrodes plays an important role in the tunneling processes. The detailed analysis of the crystalline Fe/MgO/Fe(001) tunnel junctions will be presented in Chapter 4. It will be shown that the full band structure of the electrodes and the tunneling barrier plays an important role in TMR studies.

45 Chapter 3 Experiment a1 apparatus In this Chapter the experimental systems which are relevant to this work we will described. The apparatus and the procedure for the growth of Fe-whiskers is presented. Ultrathin magnetic multilayers were prepared in an UHV system which is equipped with characterization tools to monitor the sample preparation process : Auger electron spectroscopy (AES), X-ray photoemission spectroscopy (XPS), ultraviolet photoemission spectroscopy (UPS), reflection high energy electron diffraction (RHEED), and low energy electron diffraction (LEED). Electron transport studies were partly carried out in UHV, scanning tunneling microscopy (STM), and partly in ambient conditions using atom force microscopy (AFM). The magnetic properties were studied by means of ferromagnetic resonance (FMR), magnetooptical Kerr effect (MOKE), and MOKE microscopy. 3.1 Fe whisker growth and preparation Fe-whiskers represent unique substrates for growth of high quality thin film structures. Whiskers provide flat surfaces having large atomic terraces. Fe-whiskers are grown by chemical vapor transport using the reduction of iron chloride (FeC12) in a H2 atmosphere [79]. A schematic diagram of the apparatus is shown in Fig Ultra high purity hydrogen (UHP Ha) passes an OX1 clean gas purifier to remove residual gases such as 0 2 and N2. The hydrogen gas then passes into a quartz tube which is placed inside a three-zone LINDBERG tube furnace which allows one to control a temperature profile inside the furnace during growth. The outgoing gas bubbles through water in a glass jar. The number of bubbles per time determines the gas flow

46 CHAPTER 3. EXPERIMENTAL APPARATUS three-segment tube furnace Fe boat with FeCI, powder A flow (bubble) meter 4 "\ cool TC, TC, traps Figure 3.1: A schematic diagram of the apparatus used to prepare Fe-whiskers. The quartz tube with iron chloride (FeC12) is placed in the three-zone tube furnace and filled with Hz. The flow-rate is measured at the output by bubble meter. The temperature gradient across the sample area is measured by two A1-Cr thermocouples. through the system; 1 bubble corresponds approximately to 1 cm3. The water level controls the pressure inside the quartz tube and is kept at = 500 Pa above atmospheric pressure. Nitrogen is used to remove the Hz before opening the system. Iron chloride powder (FeC12, Aldrich, 98%, mesh -80) is packed inside a boat made of 1 mm thick Fe sheet, which was cleaned by sand-paper and acetone and annealed in Hz atmosphere at 735 "C for hours. The amount of iron chloride inside the boat can vary according to the size of the boat (about 50 g). A full boat is placed in the first half of the furnace between two furnace zones in order to create a temperature gradient across the boat, see Fig The whole system is purged by hydrogen. After 1 hour the furnace is switched on and the temperature is raised by 100 C every 15 minutes until it reaches 500 C. During this period of the growth process, the hydrogen flow is kept at 5-10 cm3/s. The temperature is further increased in smaller steps (= 10 C) and the front side of the boat (TC1) is kept about C cooler than the end of the boat (TC2). The H2 flow-rate is reduced to 1-2 cm3/s. The temperature at the beginning of the boat is kept close to the melting point of the FeC12 (685"C). Gradually increasing temperature over the boat length promotes whisker growth close to the middle of the boat. The growth of Fe whiskers using 50 g of FeC12 requires about hours. At the end of the growth the H2 flow-rate is increased to 5-10 cm3/s and temperature is

47 CHAPTER 3. EXPERIMENTAL APPARATUS 29 TC1 ["C] TC2 ["C] Result Good growth Too slow growth; reaction temperature is too low; not many whiskers and often contaminated by residual chemicals High vapor pressure of FeC12 towards the end of the boat Fe crystals are deposited on the tube wall Fast reaction in the front of the boat liquid FeClz pours out of the boat resulting in low whisker yield Table 3.1: The importance of the temperature profile over the Fe boat for the whisker growth. raised to 725 "C across the whole boat. This procedure ensures that all chemicals are reacted; no residuals are left on the Fe-whisker surfaces. After 20 minutes, the furnace is switched off and cooled down. When room temperature is reached, the quartz tube is purged using nitrogen gas and opened to retrieved the Fe-whiskers. Using this procedure one can prepare Fe whiskers which are about 1 cm long and ( ~ m in ) cross ~ section. The majority of whiskers have (001) orientation, but (110) and (111) orientation might be found as well. High quality Fe-whiskers can be kept in a sealed glass container for several years without appreciable oxidation. A thin oxide layer is created at the surface which passivates the surface and prevents further deterioration of the sample. The surface can be very effectively cleaned in an UHV apparatus by using Ar+ sputtering. 3.2 MBE apparatus All samples discussed in this work were prepared by molecular beam epitaxy (MBE). The MBE system consists of three separate UHV chambers with their individual pumping modules, see Fig. 3.2.

48 CHAPTER 3. EXPERIMENTAL APPARATUS Analysis chamber sources Figure 3.2: A schematic diagram of UHV system. Samples were mounted on molybdenum sample holders which were equipped with an alumel-chrome1 thermocouple for measuring the substrate temperature. The samples were then inserted into the MBE system via a loading chamber which was pumped down using a turbo molecular pump to a pressure = lo-* Torr. The sample holder was then transferred into the intro chamber which operates at a base pressure of 1 x lo-'' Torr. The analysis chamber was equipped with an Ar+ sputter gun to clean the sample surface and with AES, XPS, and UPS to monitor the surface contamination of samples. The growth chamber contained eight different thermal sources. It was also equipped with RHEED to monitor surface quality in real time during the sample growth. The ultrathin metallic and oxide layers were prepared using molecular beam sources which are based on thermal evaporation. While metals are relatively easy to evaporate from different thermal sources, the molecular source for high band gap insulators, such as magnesium oxide (MgO), deserves special attention. The construction of this source is based on electron beam heating. The electrons (provided by a hot filament) are accelerated towards the target which is held at a high positive

49 CHAPTER 3. EXPERIMENTAL APPARATUS Figure 3.3: A sketch of the modified e-beam MgO furnace. MgO rod is attached to the positive high voltage rod. A thin tungsten loop with four pins surround the MgO rod. The tungsten filament provide the electrons which are accelerated towards the MgO rod. The income flux of negatively charged particles is compensated by the emission of secondary electrons which are attracted by high voltage and carried away. voltage with respect to the filament. Since MgO is an insulator the construction of the source needs to be such as to avoid charging of the target. There are thin tung- sten wires placed around the MgO rod and kept at a high positive potential (1.5 kv). The secondary electrons emitted from the MgO rod were drained by the high voltage anode and prevented the rod from becoming charged. The composition of the sample surface was monitored by means of Auger Elec- tron Spectroscopy (AES), X-ray Photoemission Spectroscopy (XPS), and Ultraviolet Photoemission Spectroscopy (UPS), see Fig In all these techniques, outgoing electrons are detected by a hemispherical electron analyzer. The electron energy spec- trum is surface and element sensitive. The surface sensitivity is a consequence of a Auger E, electron lekw photoelectron E< \, X-ray E2" ElS =T-/ incident - e e K yyt E'" - 1 *K Figure 3.4: A schematic atomic energy level diagram for Auger and photoemission processes.

50 CHAPTER 3. EXPERIMENTAL APPARATUS 32 relatively short electron mean free path which ranges between 1-2 nm for different electron energies 180, 811. The element sensitivity is due to the specific atomic levels. Auger electrons are emitted by a three-electron process : (i) the deep level hole (K shell in Fig. 3.4) is created by the primary electron beam, (ii) the hole is filled by another electron from an outer shell (L shell in our example), (iii) the energy released by this process is given to the third electron (from the L shell) which leaves the sample and is detected by the analyzer, see Fig The energy is described by three indexes e.g. EKLL. Note, that the energy of outgoing Auger electrons is independent of the energy of the primary beam. The XPS technique is based on the photo-electric effect discovered by Heinrich Hertz in and later confirmed by Philip Lenard [83]. Electrons are excited by an X-ray beam at the well-defined energy h, (Mg Ka : ev, A1 Ka : ev). The kinetic energy of the outgoing photo-electron, EK, is simply given by where hu is the energy of the X-rays and EB is the binding energy of the appropriate electron level. This means that the position of the XPS lines depends on the X-ray energy. Note, that in the XPS spectra one observes the Auger electrons as well. The combination of AES and XPS can be used to distinguish different chemical states for the given element. The UPS technique is equivalent to XPS except that it uses ultraviolet light (20-40 ev) instead of X-rays. The source of photons is a gas discharge lamp producing discrete low energy lines (E(Hel) = 21.2 ev, E(HeI1) = 40.8 ev) with linewidths of a few mev. UPS is widely used to study the valence electron band structure of metals and semiconductors close to the Fermi level. Atomic surface quality was monitored by means of Reflection High Energy Elec- tron Diffraction (RHEED). A collimated high energy electron beam (typically 10 kev) is focused at the sample surface under a grazing incident angle (usually about lo with the respect to the sample surface). In non-relativistic limit, the electron wavelength Xel is related to the beam energy E (in ev) by where p is the momentum of the electron, h is Planck constant, me is the mass of electron, and e is the absolute value of the elementary charge. At 10 kev, the electron

51 CHAPTER 3. EXPERIMENTAL APPARATUS specular spot fluorescent screen Figure 3.5: The Ewald sphere construction for the RHEED geometry. wavelength is 1.22 x 10-l1 m which is small compared to the lattice constant of metals (Fe : 2.87 A, Au : 4.08 A). This means that the electron beam is diffracted from the crystal lattice the same way as light diffracts from an optical grating. Since the angle of incidence is small the electron beam penetrates only a few atomic layers, making this technique surface sensitive. In order to understand the RHEED pattern it is useful to use the Ewald sphere construction, see Fig The grey sphere represents the Ewald sphere which is a surface of constant wave-vector k corresponding to the energy of the incident elec- tron beam, 10 kev. The black rods represent a two-dimensional surface reciprocal lattice. The wave-vectors of the diffracted electron beams, kf, are determined by the intersections of the reciprocal lattice rods with the Ewald sphere. The difference k - ki, where ki is the wave-vector of the incident beam, is an integer multiple of the in-plane reciprocal lattice vector G of the 2D lattice. The angle of the diffracted beams is determined by the atom periodic separation in the direction perpendicular to the beam. The scattered electron beams create an image on the fluorescent screen. The top middle spot corresponds to the specular reflection. The side spots are the 1st order diffraction spots.

52 CHAPTER 3. EXPERIMENTAL APPARATUS A Figure 3.6: Bragg and anti-bragg condition for a thin film grown on a flat substrate. Number of atomic layers Figure 3.7: RHEED intensity oscillation for an atomic layer grown on a flat substrate (layer-by-layer growth). The angle of the incident beam is set for the anti-bragg condition.

53 CHAPTER 3. EXPERIMENTAL APPARATUS 35 The intensity of the specular spot is used to monitor the growth of thin epitaxial layers. The presence of two exposed layers at the surface results in an interference between two beams reflected from the bottom filled and the top unfinished layer, see Fig The path difference between the two beams is equal to 2A. There are two limiting cases : (i) 2A = nxel; n E N corresponds to a constructive interference (Bragg condition) and (ii) 2A = (2n+1)/2Xe1; n E N corresponds to a destructive interference (anti-bragg condition). From a simple kinematical argument the total field E(q) of the reflected beam (neglecting spatial and time-dependent parts) is given by where q is the coverage of the top layer (q E (0, I)) and cp is the phase difference between the wave reflected from the top and bottom atomic layer. The intensity variation I(t) which is observed on the fluorescent screen is given by The intensity variation for Bragg and anti-bragg diffraction conditions are following : Bragg : cp = 2nz : I(t)=l, n N, anit-bragg : cp= (2n+l)z : I(t) =4q2-4q+1, nen. (3.5) For the Bragg condition there is no variation in the RHEED intensity with the sample coverage, while in the anti-bragg condition the electron beam intensity varies periodically having a parabolic profile between two maxima corresponding to the finished layers. In real samples the RHEED intensity oscillations are smeared out by growth imperfections and the parabolic cusps become rounded, see Fig Low Energy Electron Diffraction (LEED) was used in addition to RHEED to investigate the quality of the surfaces. The electron beam (typically ev) is oriented perpendicular to the sample plane. The back scattered electrons create a diffraction pattern on the fluorescent screen. The Ewald sphere construction is shown in Fig As for RHEED, the intersection of the reciprocal rods with the Ewald sphere determine the direction of the diffracted beam. The LEED diffraction patterns reflect the symmetry of the surface structure. The lateral separation of the diffracted spots is inversely proportional to the size of the surface unit cell. Although the diffraction pattern gives the basic symmetry of the 2D reciprocal lattice it does not

54 CHAPTER 3. EXPERIMENTAL APPARATUS sphere 2D :ipn _- lattice Figure 3.8: The Ewald sphere construction for the LEED geometry. determine the exact positions of atoms at the surface. The intensity measurements of diffracted spots as a function of the electron energy, I(E), together with a dynamic theory of electron diffraction is required to construct the atom distribution at the surface. For a comprehensive discussion see e.g. review by K. Heinz Scanning tunneling microscopy The first scanning tunneling microscope was designed and build by Russell Young and coworkers between 1965 and 1971 at the National Institute of Standards and Technology (NIST). Pioneering work in field of tunneling microscopy was done by Gerd Binning and Heinrich Rohrer [85] in They were awarded the Nobel prize in STM is a surface sensitive technique for measuring the surface topology of different materials. An UHV-STM system is a convenient tool for studying the surfaces of deposited thin metallic and insulating layers. The STM images and STM spectroscopy data were obtained using the Omicron

55 CHAPTER 3. EXPERIMENTAL APPARATUS preamplifier reference current piezocrystal controller Figure 3.9: A sketch of a typical STM set up. The sharp STM tip is mounted on an xypiezoelectric scanning tube. The tunneling current is amplified and is part of the feed back loop. The feed-back loop maintains a constant tunneling current by adjusting the sample-tip separation using the z-piezoelectric translation stage. The voltage on the z-piezoelectric crystal contains the information about the surface topology and is recorded by the PC computer. system [86] during my stay at the Max-Planck Institute in Halle, Germany. Good vibration isolation is achieved using a magnetic eddy current damping system. In all experiments, a platinum-iridium (PtIr) tip was used. The tunneling microscope (see Fig. 3.9) is based on an atomically sharp conducting tip which is brought close to the sample. A bias voltage between the tip and the investigated surface ranges from hundreds of millivolts to several volts. A tunneling current can be measured for the sample-tip separation on the order of a few nm. A typical sample-tip current of the order of na is used as a feedback signal to maintain a constant separation between the sample and the tip. To understand the tunneling process we will use a simple picture of two metallic electrodes separated by a rectangular barrier. The solution of Schrodinger's equation inside the barrier can be written in the form where K, is defined by

56 CHAPTER 3. EXPERIMENTAL APPARATUS sample vac tip Figure 3.10: A schematic band diagram of the metallic sample and the STM tip separated by the vacuum barrier. The band diagram corresponds to the positive sample bias voltage VB. where E is the energy of an electron participating in tunneling and Vbar is the height of the vacuum barrier. Therefore, the transmission probability T, or the tunneling current IT, depends exponentially on the separation d of the electrodes A change of 1 A of the tip-sample separation results in an order of magnitude change of the tunneling current IT. The electronic structure of surfaces can be studied using tunneling spectroscopy. The tunneling current IT is recorded as a function of the applied bias voltage V for a constant tip-sample separation. Selloni et al. [87] has shown that the I(V) dependence can be expressed as where T(E, V) is the transmission probability which is function of the bias voltage and energy of the tunneling electron, and p(e) is a local density of states (LDOS) of the sample assuming constant LDOS of the tip, see Fig Atom force microscope with conducting tip Atom force microscopy (AFM) is another scanning probe technique used to study the sample topology. The AFM with conducting tip was used to establish a reliable

57 CHAPTER 3. EXPERIMENTAL APPARATUS 39 ohmic contact between the AFM tip and the top metallic film. I-V characteristics were measured in the external magnetic field. A flexible cantilever with a sharp tip is used as a force sensor. If the tip is brought close to the sample surface (typically hundreds of Angstroms) the tip-sample inter- action changes the state of the force sensor (deflection or change in the resonance frequency). The total force between the tip and the sample involves (a) electrostatic interactions, (b) van der Waals interaction, (c) short range interaction, and (d) cap- illary forces [54]. In our case, the AFM images were acquired in non-contact mode in which the short ranged interaction and capillary forces can be neglected. The van der Waals force FvdW and force gradient F$dW between a spherical tip and a semi-infinite sample can be written as [88, 541 where R is the tip radius, AH is the Hamaker constant [89](typically 1 ev for metals), and d is the tip-sample separation. For example, for R = 10 nm and d = 50 nm, the van der Waals force is approximately 1 nn and the force gradient will be 1 x N/m. The electrostatic force Fel and the force gradient FL, between tip and sample can be written as [54] where c is the velocity of light in free space and V is the bias voltage between the tip and the sample. Assuming R = 10 nm, d = 50 nm, and V = 100 mv, the force due to the electrostatic interaction is 0.5 nn and the force gradient is 1 x N/m. These values are comparable to those caused by the van der Waals interaction. However, the strength of the electrostatic force rises by 2 orders of magnitude for a bias voltage of 1 V, and becomes the dominant interaction between the tip and the sample surface. The AFM experiments were performed at McGill University in Montrkal, Qukbec using a custom-built AFM. A detailed description and discussion can be found in numerous theses, see e.g. [54]. The AFM images were taken in non-contact ac mode

58 CHAPTER 3. EXPERIMENTAL APPARATUS laser Figure 3.11: A schematic diagram of an interferometer technique to monitor the displacement of the flexible cantilever. to reduce environmental noise and to increase the signal-to-noise ratio. The cantilever resonance frequency changes due to the tip-sample interactions. In a linear approximation, the frequency shift 6 f is given by [54] where FA is a force gradient along the normal direction of the cantilever, kc is is a spring constant of the cantilever, and fo is an a resonance frequency of the cantilever where m* is an effective mass of the cantilever. The cantilever resonance frequency shift is obtained by a frequency modulation technique [go]. The phase relation between the drive signal and the cantilever oscillation is kept at a constant value by means of a phase locked loop (PPL) from Nanosurf [91]. Therefore, the cantilever is always driven at its new resonance frequency [go]. The deflection of the cantilever beam was detected by a fiber optics interferometer [92]. The light (A = 785 nm) is guided towards the polished back-side of the cantilever,.. see Fig Part of the total incoming intensity is reflected from the end of the.. waveguide (Il), and interferes with the beam reflected from the cantilever (Iz), see Fig and details in [54]. The total intensity I reaching the detector depends on the fiber-cantilever separation. A typical fiber-cantilever separation A is less than 5 pm.

59 CHAPTER 3. EXPERIMENTAL APPARATUS Microwave diode detector 9- in signal signal Lock-in amplifier reference out Microwave Low frequency modulation coil Figure 3.12: Block diagram of the FMR experiment. 3.5 Ferromagnetic resonance Ferromagnetic resonance (FMR) operates in the range of microwave frequencies [93, 94, 61. The FMR technique is based on measuring microwave losses in magnetic samples as a function of the external dc magnetic field. This technique is suitable for measuring the static (effective and saturation magnetization, magnetocrystalline anisotropies) and dynamic (damping and electron g-factor) magnetic properties of magnetic materials. The block diagram of the FMR apparatus used in our laboratory is shown in Fig Klystrons are used as a source of microwave radiation [94] operating in the frequency range from 10 to 72 GHz. The studied sample is mounted inside a microwave resonant cavity (see Fig. 3.13) which is placed between the pole-pieces of a Varian electromagnet (Model V 3800). The Varian electromagnet can reach magnetic fields up to 2.5 T. Cylindrical cavities with the TEol, mode are used; subscripts represent the number of half wavelength variations in the standing wave pattern in the angular, radial, and longitudinal direction, respectively [94]. The cavity is coupled to the

60 CHAPTER 3. EXPERIMENTAL APPARATUS waveguide (a) in-plane configuration U qua* rod (b) out-of-plane configuration Figure 3.13: A schematic diagram of the (a) in-plane and (b) out-of-plane TEOl2 cylindrical cavity. The dotted line represents the rf magnetic field distribution inside the cavity. rectangular wave-guide by a small coupling hole, see Fig For the in-plane FMR measurements (the external dc field is applied in the sample plane), the studied sample (size about (2 x 3) mm) is mounted on the top wall of the cavity, the thin magnetic film facing the wall, see Fig. 3.13a. The Q-factor in this configuration reaches For the out-of-plane FMR measurements (the external dc field is applied at angle OH with respect to the sample plane), the thin quartz rod is inserted through the middle of the bottom of the cavity, see Fig. 3.13b. The sample was mounted on the flat face of the quartz rod. For the TEol, mode the electric rf field is zero on the axial axis of the cavity and therefore the insulating rod does not significantly perturb the standing-wave pattern inside the cavity. The Q-factor in this configuration reached This set-up allowed us to measure the FMR field and the FMR linewidth continuously from the in-plane to the perpendicular orientation. The reflected power from the microwave cavity is monitored by a microwave diode detector. It can be shown [95] that the reflected microwave power is proportional to

61 CHAPTER 3. EXPERIMENTAL APPARATUS 43 the absorption of microwaves in the ferromagnetic sample. The absorbed power P is proportional to where X: is the imaginary part of the rf transversal susceptibility defined in Eq. 2.17, XI = X; +ix;. The imaginary part of the transversal susceptibility can be expressed, neglecting the in-plane anisotropies, as where HII is the projection of the external dc field into the direction of the saturation magnetization, BeE = HII + 4rMeff, and ac represents the dimensionless Gilbert damping parameter. The FMR absorption line has a lorentzian profile as a function of the applied field H (Fig. 3.14). It is characterized by the resonance field HFMR and the resonance linewidth AHHWHM (half width at the half maximum) or AH,-, (peak- to-peak), see Fig For a Lorentzian lineshape one can evaluate the relationship between the AHHWHM and AHp-, AH,-, 2 = - AHHWHM z AHHWHM fi. (3.18) In the following text, AH is used for simplicity. If not specified otherwise AH = AHHWHM. The signal-to-noise ratio is improved by using a small ac modulation of the ex- ternal field. The amplitude of the modulation has to be much smaller than the FMR linewidth. The measured signal corresponds to the field derivative of the imaginary part of the transversal susceptibility dx:/dh, see Fig The sensitivity of the FMR apparatus is great enough to detect the FMR signal from a few atomic layers of the ferromagnetic specimen. It has been shown in the previous Chapter that the resonance condition for the in-plane FMR configuration is given by Kul 1 + c0s4(p~) + -(I + COS 2 ~ ) Ms

62 CHAPTER 3. EXPERIMENTAL APPARATUS DC applied field [koe] Figure 3.14: The measured FMR signal as a function of the applied field. The top panel shows the absorption line which is proportional to the imaginary part of the transversal susceptibility xu. The bottom panel corresponds to the measured FMR signal detected by the lock-in technique. The external field was modulated ba a small ac field (z 3-5 Oe) at the modulation frequency of 150 Hz. The measured signal is proportional to dxm/dh. where Kill and KuII represent the strength of the in-plane four-fold and uniaxial anisotropy, respectively. 47rMefi is the effective demagnetizing field which is associated with the magnetization component perpendicular to the film surface, c p is ~ the angle between the direction of the saturation magnetization and the cubic axis, and cp is the angle between the saturation magnetization and the in-plane uniaxial axis. The magnetic anisotropy constants can be determined by measuring the resonance field HFMR as a function of the angle c p ~. The FMR measurements at different mi- crowave frequencies are required to determine the effective demagnetizing field 47rMefi and the electron g-factor g.

63 CHAPTER 3. EXPERIMENTAL APPARATUS Figure 3.15: Three basic configurations of the Kerr effect : (a) polar, (b) longitudinal, and (c) transversal. 3.6 Magnetooptical Kerr effect Magnetooptical Kerr Effect (MOKE) is a common technique used to investigate the static and dynamic properties of ferromagnetic samples. This effect is named after John Kerr who observed a rotation of the plane of polarization of the linearly polarized light when reflected from a polished iron plate in the field of a permanent magnet [96]. It is sensitive enough to detect one atomic layer of an iron film. This is very useful in studies of the magnetic properties of ultrathin samples. The Kerr effect can be measured using different configurations depending on the mutual orientation of the sample plane, the direction of an external magnetic field, and the plane of incidence of the polarized light, see Fig In general, MOKE refers to the change of the polarization state of light which is reflected from the sample in the external magnetic field. If s- or p-linearly polarized light is reflected from a magnetic sample, the outgoing light will be elliptically polarized, see Fig For thin iron films the magnitude of the Kerr effect is of the order of deg. For more details about the description of the polarization state of light see Appendix B. Magnetooptical effects result from the interaction of the electromagnetic wave with the magnetization of the studied medium. In the macroscopic theory, all the material properties are included in a dielectric permittivity tensor ~ i j. The magnetooptical properties depend on the magnetization of the sample. Therefore, the dielectric tensor can be written as [97] It has been shown by Wettling et al. [97], that the magnetization of the sample

64 CHAPTER 3. EXPERIMENTAL APPARATUS 46 creates a small perturbation of the permittivity tensor. Therefore, the permittivity tensor may be written as [97] where EO is the permittivity of the material, Sij is the Kronecker symbol, and Kijk represents components of the linear magnetooptical effect. It can be shown [98, 991 that the permittivity tensor has to satisfy ~ i(m) j = E~~ (- M). (3.22) Eq is in agreement with the well-known Onsager reciprocity relation [loo, The permittivity tensor for the longitudinal Kerr effect of the magnetic layer (the surface normal parallel to the z-axis) can be written where EZ corresponds to the off-diagonal element of the permittivity tensor. Some authors [102, 1031 introduce the Voigt constant Q = E ~ / E ~. The complex magnetooptical parameters QKs and QKp, for the s- and ppolarization of the incident wave, are defined by Figure 3.16: A graphical representation of the Kerr effect. A linearly polarized light in the s-direction is reflected from the sample. The reflected beam is elliptically polarized. The polarization is characterized by the Kerr rotation OK and Kerr ellipticity angle EK, see Appendix B.

65 CHAPTER 3. EXPERIMENTAL APPARATUS where OK and EK represent Kerr rotation and ellipticity, respectively. r,, and rpp represent the Fresnel reflection coefficients. The parameters rsp and rps are defined by where Ei and E, is the electric field amplitude of the incident and reflected electro- magnetic wave, respectively. The magnetooptical response can be calculated using Yeh's matrix formalism [I041 extended by ViSiiovskf for the magnetic response [98]. Analytical expressions can be derived for simple magnetic multilayers [105, It can be shown that mag- netooptical response is proportional to the off-diagonal elements of the permittivity tensor &ij(m), i + j. It follows, that in linear response, the magnetooptical effect is proportional to the magnetization of the sample. The MOKE signal can be measured in different dc and modulation configurations, see e.g. [99]. Generally, two polarizing elements (polarizer and analyzer) are required. The sample in the magnetic field is placed between the polarizer and the analyzer, see Fig In our set up, a laser diode is used as a stable monochromatic light source (A = 640 nm). A focused laser beam is polarized by a calcite Glan-Thompson polar- izing cube (typically the beam is s-polarized due to the higher reflection coefficient when approaching Brewster's angle). The light beam is reflected from the sample mounted on a 5-axis rotational stage and analyzed by a Wollaston prism1. The prin- ciple direction of the analyzer is fixed and rotated by 45" away from the s-polarization. In this configuration the intensities of the two mutually orthogonal, linearly polarized beams are equal. To measure the Kerr ellipticity a quarter wave-plate is used between the sample and the analyzer, see Fig The two orthogonally polarized beams are detected by a differential detector. It uses two identical photodiodes which are connected back-to-back. The voltage difference is amplified by a low noise operational amplifier. This configuration provides high sensitivity, independent from source in- stabilities, and linearity around the zero signal (zero signal corresponds to no Kerr signal from the sample). A quadruple magnet (B,,, FZ I koe) allows one to rotate the magnetic field independently with respect to the plane of the incidence. In this way one can measure both in-plane components of the magnetization, see Fig 'two calcite prisms cemented together splitting the beam into two mutually orthogonal, linearly polarized beams which are deflected from the original direction by well defined angle typically 7 or 10 degrees

66 i laser diode h = 640 nm Figure 3.17: Experimental set up for measuring longitudinal and transversal component of MOKE signal. The sample is mounted on the 5-axis rotational stage in the special quadruple electromagnet. Wollaston prism splits the reflected beam which is detected by the differential photodiode detector.

67 CHAPTER 3. EXPERIMENTAL APPARATUS Figure 3.18: Two orientations of the sample (Fe whisker), the optical plane of incidence, and the external magnetic field. It allows one to measure both in-plane components of the magnetization vector M; (a) longitudinal (along the whisker axis) and (b) transversal (perpendicular to the whisker axis). 3.7 Kerr microscopy Using an optical microscope with polarization sensitive detection allows one to image the magnetic state of samples, see e.g. [53]. The high resolution, lower Kerr sensitivity microscope can have a lateral resolution of about 200 nm, while the high Kerr sensitivity version using a wide angle objective can reach a resolution of about 1-2 pm. A block diagram of a high resolution microscope is shown in Fig The depth sensitivity (imaging magnetic layers in different depths) is achieved using a rotatable compensator (in our case X/8 wave-plate was used, see Fig. 3.19) [53]. The phase of the Kerr signal can be adjusted relative to the regularly reflected light. CCD camera Slit Filters Analyzer aperture (optional) I Compensator (k18 wave-plate) I Hg arc lamp W Adjustable lens sample Objective lens Figure 3.19: A sketch of a common high lateral resolution Kerr microscope.

68 CHAPTER 3. EXPERIMENTAL APPARATUS 50 In this way, the Kerr signal from the selected depth region can be made "invisible". The depth-sensitive Kerr microscopy was first demonstrated for Fe/Cr/Fe multilayers in [107]. The total Kerr signal is given by the superposition of the signals from different depths of the sample. The phase of light contributing to the Kerr signal from a thin slice of magnetic medium, located in the depth z from the interface, is given by the complex penetration function 4(z). The complex penetration function for bulk materials [102, 108, 531 as well as for ultrathin films including multiple reflections at interfaces [106] can be written as 4(z) = exp -47riN-, [ ;I where N = n - i~ is the complex index of refraction and X is the wavelength of light. The function +(z) describes the phase lag experienced by a beam on the way to the layer at depth z and back to the surface. The phase difference between the contributions from different depths limits the range of the Kerr signal to a higher degree than the absorption [102]. A typical dependance of the complex penetration function is shown in Fig. 3.20a. Let us first follow the real part of the penetration function. In this case one is most sensitive to the magnetization at the surface. The magnetization at a certain depth where the penetration function crosses the zero will be "invisible"; the contributions from deeper layers will decrease the overall signal. The first zero of the real part determines the information depth parameter [I021 which is specific for the given material. From Eq. 3.26, the depth of the first zero crossing is found to be zo = X/8n. Choosing the right phase by adjusting the compensator, one can select any linear combination of the real and imaginary parts of the complex penetration function, see Fig. 3.20a. This allows one to put the the zero crossing z; in the middle of the magnetic layer making it "invisible" since the total signal can be found by integrating the penetration function +(z) where t represents the thickness of the magnetic layer, see Fig. 3.20b. The magnetooptical contrast is in general very weak. Contrast enhancement is achieved by storing a reference image of the saturated state in memory [log, 1101.

69 CHAPTER 3. EXPERIMENTAL APPARATUS Depth z [nm] Depth z [nm] Figure 3.20: (a) The complex penetration function as a function of the depth for complex index of refraction N = 3-3i and wavelength X = 580 nm. (b) The complex amplitude adjusted such a way to compensate the signal from the region between z,* f t/2. t represents the thickness of the layer. The reference image is then subtracted from the image containing the magnetic contrast [53]. This allows one to remove any other optical contrast such as structural defects and surface imperfections. The reference image can be used as long as the settings of the microscope remain unchanged. This requires a high mechanical, optical, and electrical stability of the microscope. The advantage of this method is that the magnetization processes can be observed and recorded in real-time.

70 Chapter 4 Fe/MgO/Fe whisker (001) tunnel structures In the following Chapter the growth, structural, magnetic, and electron transport properties of crystalline Au/Fe/MgO/Fe-whisker(001) magnetic tunnel junctions (MTJs) are presented. The local tunneling properties are investigated by in-situ STM spectroscopy on MgO/Fe-whisker and Au/Fe/MgO/Fe-whisker samples. The magnetic properties were studied by means of FMR, Brillouin light scattering (BLS), vectorial MOKE, and MOKE microscopy. An AFM system operating in an external dc magnetic field was employed to measure the tunneling magnetoresistance (TMR) effect. 4.1 Theoretical considerations It has been shown by Butler and coworkers [I], that the free-electron model presented in Section 2.4 is not sufficient to describe all TMR features of crystalline tunnel junctions. They have shown that the electronic states of the electrodes and the tunneling barrier are extremely important to understand the tunneling process. Butler et a1 [I] have used a layered Korringa-Kohn-Rostoker (LKKR) approximation and Mathon and Umerski [2] have used a real-space Kubo formula approach to investigate crystalline Fe/MgO/Fe(OO 1) tunnel junctions and to explore the TMR effect. The tunneling conductance was calculated using Landauer's approach [72]. It relates the TMR conductance to the electron transmission T+ through the MgO

71 CHAPTER 4. FE/MGO/FE WHISKER(001) TUNNEL STRUCTURES 53 barrier [I]. The tunneling current IT can be written as where p1,2 are the chemical potentials of the left and right electrodes, respectively and kll is the component of the wave-vector parallel to the interface. The summation is carried out over all Bloch states (kll, j) contributing to the tunneling current. Eq. 4.1 yields the Landauer conductance formula In fully crystalline tunnel junctions the symmetry of the Bloch states is crucial for the understanding of the tunneling conductance. For an Fe/MgO/Fe(OO 1) tunnel junction, both the majority and minority channels have four Bloch states for kll = 0. In the majority channel there are Al, A21, and the doubly degenerate A5 states. For the minority channel there are A2, A21, and the doubly degenerate A5 states [I]. The attenuation across the MgO barrier for the different Bloch states strongly depends on the band structure of the tunneling barrier. Detailed studies have shown, that only the majority channel has the Al state which decays slowly across the MgO barrier. Therefore, its conductance is much higher than that for the minority channels. The detailed discussion of the band calculations can be found in [I]. The Al state dominates the conductance for the parallel configuration, which is about lox larger than that for the anti-parallel configuration for a 4 ML MgO barrier. For 12 ML, the conductance in the parallel configuration is nearly looox larger than that in the anti-parallel configuration [I, 21. Butler and coworkers pointed out, that interface resonance states are very sensitive to interface structure. Therefore, high quality crystalline Fe/MgO/Fe(001) samples are required to test theoretical predictions. The crystalline Fe/MgO/Fe(001) structures grown on a bulk MgO(001) substrate have shown Ohmic characteristics due to pinholes inside the MgO barrier [Ill]. This poor behavior is due to the initial rough 3D growth of Fe on the MgO substrate. Significantly better results are obtained by growing the MgO barriers on Fe-whisker(001) templates [112, 113, 114, 631.

72 CHAPTER 4. FE/MGO/FE WHISKER(001) TUNNEL STRUCTURES Growth and structure of Fe/MgO/Fe-whisker tunnel junctions The Fe-whisker was held on a Mo sample holder by a single soft tantalum clip. This prevented the whisker from bending during the annealing process when the sample was heated to 650 C. The surface contaminants were removed in four main steps: (a) room temperature (RT) Ar+ sputtering (2 kev), (b) Ar+ sputtering at elevated temperature (= 300 "C), (c) annealing at 600 "C and (d) fast cooling to RT. The initial ion sputtering was used to clean the surface of contaminants. Interstitial carbon is a common impurity in Fe whiskers. The interstitial C atoms are relatively mobile at RT with a pronounced energy minimum at the whisker surface. Auger spectroscopy (AES) has shown that even for very low bulk concentrations of carbon (parts per billion) one can observe up to 10% of carbon at the surface of Fe-whiskers. The sputtering at elevated temperatures (T x 300 C) increases the mobility of interstitial carbon atoms creating a C depleted region close to the whisker surface [115]. The subsequent annealing at 650 C and rapid cooling to RT prevent the surface segregation of carbon. The AES ratio of C to Fe can be brought readily below 2%. The surface quality of annealed Fe-whiskers was monitored by the means of RHEED, LEED, and STM, see Fig The RHEED and LEED diffraction patterns showed sharp diffraction spots with a low intensity of diffuse background, see Fig. 4.la,b. This indicates a long-range coherence with low density lattice defects. The STM images revealed atomically flat terraces exceeding 1 pm in lateral dimensions, see Fig. 4.1~. Figure 4.1: Clean Fe-whisker(001) surface. (a) The RHEED pattern at Vbe- = 10 kev along the [loo] direction, (b) The LEED pattern at Vb- = 147 ev, and (c) 2 x 2 pm2 STM image recorded at a bias voltage VB = +0.6 V and a feedback current IT = 0.6 na. Vertical corrugations correspond to the one atomic step (1.4 A).

73 CHAPTER 4. FE/MGO/FE WHISKER(001) TUNNEL STRUCTURES Growth of MgO on an Fe-whisker(001) template Magnesium oxide (MgO) has a rock-salt crystalline structure with the lattice parameter a~,o = A, see e.g. [117]. The crystal lattice of Fe and MgO are 3.8% mismatched when the Fe (100) directions are aligned with the MgO (110) directions,. - 3 Meyerheim and coworkers [116, 1171 have determined the atomic configuration at the -:, I +- - ti - ' " *i,-,! MgO/Fe(001) interface using surface X-ray diffraction (SXRD), see Fig At the ' interface, the 0 atoms occupy the hollow sites of the Fe bcc lattice creating one atomic : - layer of FeO. This is not surprising since the MgO and FeO have identical crystalline L:S-7% ' I structures; the Fe and Mg atoms are interchanged. Iron oxide is an insulator with a band gap of 2.4 ev. FeO is paramagnetic at RT and has an anti-ferromagnetic ordering below the N6el temperature TN = K [118]. The MgO films were deposited on Fe-whiskers at room temperature using a modified electron beam source, see Section 3.2. During the MgO deposition, the pressure in the growth chamber increased from the base pressure of 1 x 10-lo Torr to 2-5 x Torr. The surface energy of MgO is smaller compared to that of the Fe(001) surface, hence MgO "wets" the Fe surface resulting in a nearly perfect layer-by-layer growth. The MgO growth was monitored by RHEED intensity oscillations; the intensity of the specular and the first diffracted spot were recorded as a function of time, see Fig. A2.? - - MgO layer "FeO" layer Figure 4.2: The reconstruction of the Fe/MgO interface from the surface X-ray diffraction (SXRD) experiments [116]. Blue spheres represent the bcc structure of the Fe substrate. Red and white spheres represent the 0 and Mg atoms of the MgO film, respectively

74 CHAPTER 4. FE/MGO/FE WHISKER(001) TUNNEL STRUCTURES specula SPO 2% 8ooFs:~ 11 - ~iffracted spot Shutter closed fl primar bean I. I. I. I I. I Time [s] Figure 4.3: (a) The RHEED pattern of the Fe-whisker(001) surface prior to the MgO growth. Distance between the primary beam and specular spot corresponds to the first anti-bragg condition. The azimuth of the electron beam is adjusted in such a way, that the through beam, specular spot, and first diffracted spot create a rightangle triangle. (b) The RHEED intensity oscillations of a 6 ML MgO film deposited on the clean Fe-whisker(001) surface at RT. (c) RHEED diffraction pattern of 6 ML of I MgO deposited onto clean Fe-whisker(001) at RT. The clear splitting (fan-out) of the.. specular spot indicates surface corrugations due to the formation of misfit dislocations., 4.3b. The intensity of the specular and the diffracted spots oscillated out-of-phase with respect to each other. The RHEED intensity oscillations persist up to 10 ML of MgO; one period of oscillations corresponds to 1 ML. The RHEED diffraction pattern of up to 6 ML of MgO remains sharp with the well-defined specular and diffracted spots, see Fig. 4.3~. The MgO growth rate is approximately 4 ML/min. For a MgO growth rate of 1-2 ML/min, the RHEED intensity oscillations are less pronounced and disappear earlier. The rate of growth is limited by a substantial increase of the base pressure due to an increased temperature of the MgO rod. The STM images have shown [I131 that the best filling of the MgO atomic layers occurred when the growth was terminated at a maximum of the RHEED diffracted spot. The lattice mismatch between the bulk Fe and the MgO film creates a compressional stress on the MgO layer. MgO grows pseudomorphically with the Fe lattice constant up to approximately 5 ML. After 5 ML the compressional stress is partially released and, g,wamzkpf misfit dislocations is created at the MgO/Fe-whisker inter- l--, < : - i>.

75 CHAPTER 4. FE/MGO/FE WHISKER(001) TUNNEL STRUCTURES 57 Figure 4.4: STM topographic images of 6 ML MgO grown on Fe-whisker(001) at RT; VB = +4 V and IT = 0.14 na. Arrows indicate the misfit dislocations lines which are parallel to the (100) crystallographic directions of MgO. face 1119, This transition can be observed in distinct features which occur in the RHEED and LEED patterns and STM images, see Figs In Fig. 4.4, STM topographic images of a 6 ML MgO layer are shown. There are three distinct features : (i) large areas corresponding to the atomically flat terraces of the Fe-whisker(001) surface which are separated vertically by a single Fe atomic step height of 1.4 A, (ii) three exposed layers of MgO (black : filled 5th layer, grey: partially filled 6th layer, and white: small islands of the 7th layer), (iii) the network of misfit dislocation lines (see arrows) which are oriented along the (001) direction of the MgO lattice; this corresponds to the (011) direction of the Fe-whisker. In LEED patterns, the network of misfit dislocations results in additional satellite spots around the main diffraction peaks, see Fig. 4.5a. The additional spots maintain the 4-fold symmetry of the MgO lattice. The separation between the principal and additional spots increases with increasing energy of the electron beam. This behav- ior can be explained by atomic corrugations of the MgO surface [119, These corrugations lead to additional reciprocal rods which are inclined with respect to the reciprocal rods of the average MgO surface plane. From the separation of the main and inclined diffracted spots one can evaluate a tilt angle associated with the network of misfit dislocations, see Fig Let's define Ax as a distance on the LEED screen between the main LEED and satellite spot and xll as a distance between the two main diffraction spots, see Fig. 4.6b. In the Ewald sphere construction xll is directly proportional to the in-plane

76 CHAPTER 4. FE/MGO/FE W'KER(001) TUNNEL STRUCTURES 58 9 ML MgO 12 ML MgO I Figure 4.5: The LEED patterns for MgO layers grown on a Fe-whisker template. The labels show the thickness of MgO and the energy of the primary electron beam. Up to 5 ML MgO grows with the lattice spacing of Fe, see the sharp diffraction pattern for 5 ML of MgO. For larger thicknesses of MgO the lattice stress is gradually released by formation of a rectangular network of misfit dislocations; the additional LEED spots around main diffractions satisfy the 4-fold symmetry of MgO. reciprocal wave-vector kii = 4n/aM,o = 2.98 x 1010 m-', corresponding to the inplane reciprocal vector along the [loo] direction of the MgO lattice. The radius of the Ewald sphere, ke, is determined by the energy E (in ev) of the primary electron beam where me is the electron mass, e is the electron charge, and K = 2.63 x 1019 m-2ev-1. From the reciprocal space geometry, see Fig. 4.6, one can evaluate the tilt angle < where Ak is the reciprocal space counterpart to Ax, see Fig Eq. 4.4 can be

77 CHAPTER 4. FE/MGO/FE WHISKER(001) TUNNEL STRUCTURES projection plane T action pattern I Ewald sphere - m LEED screen i * , L+n - Axax;....,..... : ; Figure 4.6: (a) A schematic diagram of the MgO LEED pattern with the additional diffraction spots due to incline reciprocal rods. The red plane indicates the projections of the Ewald sphere. (b) A cross-section of the Ewald sphere dong the [loo] direction. The cross-section plane is shifted with respect to the center of the Ewald sphere, see (a). The radius kb is smaller than /Q and therefore the cross-section appears above the origin of the reciprocal space. The upper part represents the LEED screen with diffraction pattern.

78 CHAPTER 4. FE/MGO/FE WHISKER(001) TUNNEL STRUCTURES 60 MgO thickness [ML] Figure 4.7: The tilt angle J evaluated from Eq. 4.4 as a function of the MgO thickness d~go. rewritten as where s is found to be The tilt angle J decreases from 3.6" for the MgO thickness dmgo = 8 ML to 1.5" at dmgo = 15 ML, see Fig Notice, a sharp decrease of the tilt angle 5 with increasing MgO thickness indicating, that the misfit dislocations are buried at the MgO/Fe interface. This is in good agreement with the studies of Dynna and coworkers [119]. They have shown that the inclined reciprocal rods are caused by the lattice displacement fields created by interface. (011) (011) misfit dislocations at the Fe/MgO Growth of Au/Fe on MgO/Fe-whisker(001) template The top Fe layer (20 ML in thickness) was deposited at RT and the growth was monitored by means of RHEED intensity oscillations. The difference in the surface

79 CHAPTER 4. FE/MGO/FE WHISKER(001) TUNNEL STRUCTURES 6 1 Figure 4.8: The RHEED patterns of 20 ML Fe grown on MgO/Fe-whisker(001). (a) RT growth. (b) Cryogenic growth : The first 10 ML of Fe were grown at cryogenic temperature (T z 100 K) and the additional 10 ML of Fe were deposited at T = 350 K. energy, which promotes almost ideal layer-by-layer growth of MgO on Fe, leads to a 3D growth of Fe on MgO. The RHEED intensity of the specular spot drops to zero and a typical 3D diffraction pattern is formed after deposition of a few monolayers of Fe, see Fig. 4.8a. A high mobility of Fe atoms at RT and a low surface energy of the MgO surface are the driving forces behind the 3D growth of Fe on MgO. The Fe islands eventually coalesce creating a continuous layer with a high surface roughness. In order to suppress this kind of growth, the MgO/Fe-whisker template was cooled to 100 K to minimize the surface mobility of the Fe adatoms. This resulted in a crystalline Fe layer with short atomic terraces and no signs of 3D growth. After deposition of 10 ML of Fe, the sample was heated to 350 K and an additional 10 ML were deposited at an elevated substrate temperature. This procedure resulted in a flat Fe layer with narrow RHEED diffraction streaks, see Fig. 4.8b. A 20 ML cap layer of Au(001) was deposited on the top of the Fe film for protection of the sample under ambient conditions. Au(001) grows epitaxially with a typical (5 x 1) surface reconstruction. The crystallinity was maintained throughout the whole growth. The peak-to-peak roughness of the top Au/Fe metallic electrode for the samples exposed to ambient conditions was measured using AFM and found to be 1.7 nm [112].

80 CHAPTER 4. FE/MGO/FE WHISKER(001) TUNNEL STRUCTURES 62 UPS signal 7 Figure 4.9: A schematic diagram of the electronic band structure of the FelMgO interface. UPS was used to determine the separation between the Fe Fermi level and the top edge of the MgO valence band. The MgO band gap was assumed to be 7.8 ev. 4.3 In situ transport properties The electron band alignment between the Fe Fermi level and the MgO valence band was determined by means of UPS. The difference between the Fe Fermi level and the top edge of the MgO valence band (Mg 1s and 0 2p levels) was found to be 4.2 ev. Assuming 7.8 ev for the MgO band gap [121, 1221 one can conclude that the energy difference between the Fe Fermi level and the bottom of the MgO conduction band is 3.6 ev, see Fig STM spectroscopy of the MgO/Fe-whisker system The electron tunneling properties of a MgOIFe-whisker(001) were studied using an in-situ Omicron STM system. The local I-V curves and current maps were recorded and analyzed using a simple electron band model. Fig. 4.10a shows a topological image of 3.5 ML of MgO grown on Fe(001). Three contrast levels correspond to the

81 CHAPTER 4. FE/MGO/FE WHISKER(001) TUNNEL STRUCTURES 63 U) 1.1 (d) 1. at % ao{ # 4.4- : 4.8- *. ZZ) , - -, Figure 4.10: The STM morphology of 3.8 ML MgO on Fe(001); 100 x 100 nm2, VB = +4.1 V, IT = 0.7 na. The inset shows the RHEED pattern along the [I101 crystallographic direction of MgO. (b) The tunneling I-V curves for different MgO thicknesses (3rd, 4th, and 5th layer). (c) The spectroscopic current image of the local MgO defects recorded at VB = -4 V. (d) The tunneling I-V characteristics of the MgO barrier : the solid line corresponds to the grey area in (c) of a perfect MgO barrier, and the dashed and dotted lines correspond to dark grey and black spots of the localized defects. The dark and black spots show an appreciable increase of the tunneling current at negative VB.

82 CHAPTER 4. FE/MGO/FE WHISKER(001) TUNNEL STRUCTURES 64 Fe MgO vac Ptlr tip Fe MgO vac Ptlr tip Fe MgO vac Ptlr tip Figure 4.11: A schematic electronic band diagram of Fe-whisker/MgO/vacuum/PtIr- tip junction for different values of VB. (a) and (b) correspond to VB = +4 V and VB = -4 V, respectively. In (a), electrons tunnel from the tip into the conduction band of MgO, and in (b) electrons tunnel from the valance band of MgO into the tip. This results in asymmetric I-V characteristics due to the different vacuum barrier height for these two cases. In fig. (c), there are localized states included in the middle of the band gap of MgO allowing electrons to tunnel through these states. The vacuum barrier decreases resulting in symmetric I-V characteristics. 3rd, 4th, and 5th atomic layers, indicating a nearly perfect layer-by-layer growth [113]. The tunneling I-V spectra for each exposed layer are displayed in Fig. 4.10b. The I-V characteristics of the MgO/Fe-whisker structure appear to be very asymmetric with an abruptly increasing tunneling current for a bias voltage VB > +3 V and with a negligible tunneling current for VB between +2.5 to -4.5 V. The increase of the tunneling current for VB > +3 V occurs when electrons from the STM tip tunnel into the conduction band of MgO, see Fig. 4.11a. On the other hand, the barrier height of the vacuum gap increases with decreasing bias voltage resulting in negligible tunneling current, see Fig. 4.11b. The tunneling current images and the I-V characteristics have shown that most of the scanned surface area has an ideal tunneling properties corresponding to a perfect MgO barrier, see the solid line in Fig. 4.10d. However, the spectroscopic current

83 CHAPTER 4. FE/MGO/FE WHISKER(001) TUNNEL STRUCTURES 65 image at VB = -4 V, see Fig. 4.10c, has also shown localized regions (black spots) of increased tunneling current. The tunneling spectra of the black spots correspond to the dotted line in Fig. 4.10d. The tunneling current shows a dramatic increase for VB < -2.5 V. Notice, that the I-V spectra of the localized defects became symmetric, see dotted line in Fig. 4.10d. This behavior can be explained, in principle, by the presence of pinholes in the MgO barrier. It has been demonstrated by Keavney et al. [Ill] that pinholes in the MgO layer lead to strong ferromagnetic coupling between the Fe layers. It will be shown in Section 4.5, that in our structures, there is no evidence of ferromagnetic coupling between the Fe thin film and the Fe- whisker substrate. Therefore, the observed "defects" are not related to pinholes in the MgO barrier, but originate in the MgO interband states which are created by local crystalline defects. The increase in the tunneling current in the defects at VB = -2.5 V suggests, that the additional tunneling states are located close to the middle of the MgO band gap, see Fig. 4.11~. The STM images of these local defects produce contrast on the order of several nm across, see Fig. 4.10~. Similar behavior was observed by Da Costa et al. [123] using AFM on amorphous A1203 barriers grown on a Co film. The above results have shown, that both STM and AFM techniques allow one to investigate local properties of tunneling barriers. The sharp current onset in the I-V characteristics for a positive bias voltage, see Fig. 4.10b, corresponding to tunneling from the PtIr tip into the conduction band of MgO was used to determine the MgO barrier height. The barrier height was taken as the voltage for which the tunneling current reached 0.01 na [113]. The barrier height as a function of the MgO layer thickness is plotted in Fig The barrier height increases from 2.5 ev for 2 ML of MgO to the full MgO barrier height of 3.6 ev for films thicker than 8 ML. Therefore, the MgO band gap changes from 6.7 V to 7.8 V assuming a constant difference of 4.2 V between the MgO valence band and the Fermi level of Fe. The variations of the barrier band gap can be related to the formation of the FeO layer at the MgO/Fe interface [117]. A network of misfit dislocations is created in MgO layers thicker than 6 ML, see Fig The STM topology and current maps around the dislocations lines are shown in Fig Surprisingly, the electronic defects in the MgO barrier (black spots in Fig. 4.13~) are not correlated with the misfit dislocation lines shown in Fig. 4.13a. This means, that good tunnel junctions are not limited to thin MgO layers (less than 5 ML). The tunneling experiments can be carried out on thicker MgO layers which

84 CHAPTER 4. FE/MGO/FE WHISKER(001) TUNNEL STRUCTURES 66 MgO thickness [ML] Figure 4.12: The experimental values of the MgO tunneling barrier height as a func- tion of the MgO film thickness. The barrier height was determined from the I-V spectra measured by STM. are accompanied by a network of misfit dislocations STM spectroscopy of Au/Fe/MgO/Fe-whisker Tunneling I-V characteristics were also studied for the complete tunnel junction 20 Au/20 Fe/5 MgO/Fe-whisker (001); the integers represent the number of ML. The STM spectroscopic map at negative bias voltage, VB = -4 V and the I-V curves are shown in Fig Most of the sample area exhibited a low tunneling current and asymmetric I-V characteristics corresponding to an ideal MgO tunnel barrier, see Fig The localized black spots in Fig. 4.14b have shown an enhanced tunneling current for large negative bias voltages, see dashed line in Fig. 4.14b. They are caused by localized defects in the MgO barrier. The ability to see locally different I-V spectra through the conducting top Au/Fe electrode grown over an insulating MgO layer is definitely not obvious result. It strongly supports the idea of ballistic electron transport in these structures. If the electron transport in the top electrode was diffuse, then the tunneling current would be determined by the averaged properties of the MgO layer across the whole sample; no local variations in the tunneling current would have been observed. However, in

85 CHAPTER 4. FE/MGO/FE WHISKER(001) TUNNEL STRUCTURES Figure 4.13: (a) The STM morphology of 7 ML MgO grown on Fe(001); 100 x 100 nm2, VB = +4 V, IT = 0.3 na. The misfit dislocation lines are marked by arrows. (b) The tunneling spectra for different thicknesses of MgO layer (6th, 7th, and 8th layer). (c) The spectroscopic current image of the localized defects recorded at VB = -4 V. (d) The tunneling I-V characteristics of a perfect MgO film (solid line corresponding to the grey area in (c)) and the localized defects (dash line corresponding to the black spots in (c)).

86 CHAPTER 4. FE/MGO/FE WHISKER(001) TUNNEL STRUCTURES 68 Figure 4.14: (a) The tunneling spectra and (b) the spectroscopic current image at VB = -4 V observed in the 20 A420 Fe/5 MgO/Fe-wbisker(001) sample using STM. The asymmetric I-V characteristics (solid line in (a)) was observed over most of the scanned area (grey region in (b)). The localized defects (black spots in (b)) exhibited a symmetric I-V characteristic (dashed line in (a)). the ballistic limit, eiectrons emitted from the tip can cross the top metallic layers without scattering and the tunneling current is determined by the locd height and thickness of the MgO barrier. When the Fermi energy of the tip reaches the conduction band of MgO (VB w 3 V), the transmission probability and the tunneling current - abruptly increases. This leads to an important conclusion : STM spectroscopy in high quality crystalline MTJs allows one to investigate the local tunneling properties of buried tunneling barriers [I 14, = Magnetic properties The magnetic properties of Fe layers grown on MgO(001) wafers were studied using FMR. The effective demagnetizing field perpendicular to the film surface 4rMeE and the in-plane four-fold (cubic) K1l I and uniaxial KuI I anisotropies were determined for the 20 Au/lO, 20, 30 Fe/Mg0(001) structures. 4rMeE and KIII were inversely proportional to the Fe film thickness dfe, see Fig The constant and linear terms represent the bulk and interface magnetic contributions, respectively, see Appendix A. The strength of the bulk and interface contributions to the in-plane 4-fold anisotropy were found to be (5.0 f 0.1) x lo5 erg/cm3 and -(0.36 f 0.03) erg/cm2, respectively. The bulk contribution is close to the value found in bulk Fe crystals, Kc = 4.7 x lo5

87 CHAPTER 4. FE/MGO/FE WHISKER(001) TUNNEL STRUCTURES 69 K" U~ (1.64 * 0.01) erglcm 1 31 K,,, = (5.0 k 0.1) erglcm Figure 4.15: The effective demagnetizing field perpendicular to the film surface 47rMeE and the in-plane four-fold (cubic) Kill and uniaxial KuII anisotropies are plotted as a function of l/dfe for the single Fe films grown on MgO(001) wafers; dfe is the Fe film thickness. The solid lines represent linear fit to the data. erg/cm3. The surface uniaxial perpendicular anisotropy K:, = (l.64f 0.01) erg/cm2. The surface uniaxial perpendicular anisotropy for the Fe/Au interface is 0.47 erg/cm2 [3]; it follows that the strength of the surface anisotropy for the Fe/MgO interface is (1.17 f 0.03) erg/cm2 [113], which is one of the largest reported values of K:, for 3d transition metals, see Tab Brillouin light scattering (BLS) technique [I241 was used to investigate the in- terlayer exchange coupling J [125, 6, 31 in Fe/MgO/Fe-whisker(001) samples [113]. Knowing the magnetic properties of the Fe layers grown on MgO(001) and the bulk

88 CHAPTER 4. FE/MGO/FE WHISKER(001) TUNNEL STRUCTURES 70 Table 4.1: The values of the interface uniaxial perpendicular anisotropy K:, for thin Fe layers in contact with different materials. The values of K:, for metallic interfaces were taken from 131. Fe-whisker, the measured BLS data allowed one to estimate the strength of the in- terlayer exchange coupling constant J. Within the resolution of BLS (about 100 Oe) no exchange coupling was detectable for the MgO spacer with dmgo 2 5 ML (10 A). MOKE magnetometery measurements have also not shown any evidence of exchange interaction or orange peel coupling between the thin Fe layer and the Fe-whisker. 4.5 Magnetic studies using MOKE microscopy MOKE studies were carried out with the external dc field applied along the whisker length. The sample and the external field were rotated with respect to the optical plane of incidence in order to record the longitudinal (along the whisker axis) and transversal (perpendicular to the whisker axis) components of the magnetization vector. The static hysteresis loops obtained on the 20 Au/20 Fe/5 MgO/Fe-whisker sample using the vectorial Kerr effect (see Section 3.6) revealed that there is some transversal component of the magnetization in the thin Fe film, see Fig In the longitudinal configuration, the Fe-whisker (Fig. 4.16a) saturated at 20 Oe, while the MOKE signal for the 20 Au/20 Fe/MgO/Fe-whisker(001) sample saturated at about 70 Oe, see Fig. 4.16b-c. The middle region of the hysteresis loop (between f 70 Gauss) was complex and not reproducible. This behavior indicated, that the magnetization reversal of the thin Fe film was not, in a simple manner, related to the remagnetization of the Fe whisker. The non-zero signal for the transversal configuration suggests, that the magnetization of the thin Fe film is at least partly oriented perpendicular to the

89 1 CHAPTER 4. FE/MGO/FE WHISKER(OO1) TUNNEL STRUCTURES 7 1 Figure 4.16: MOKE measurements on the Au/Fe/hlgO/Fe-whisker sample in the longitudinal configuration (H parallel to the whisker axis). (a) A longitudinal magnetization component of a bare whisker. A longitudinal (b) and a transversal (c: magnetization component of the Au/Fe/MgO/Fe-whisker sample. Notice, that the saturation field of a bare Fe-whisker (a) is much lower than that of a thin Fe film, (b: and (c). Blue and red lines correspond to increasing and decreasing an external dc field, respectively., whisker axis. It was difficult to make any firrn conclusion based on the MOKE stud- ies only. An additional imaging technique was required for a better understanding of the magnetization reversal of the Fe film in the 20 Au/20 Fe/MgO/Fe-whisker(001) structures. A depth-selective MOKE microscopy, see Section 3.7, was employed to image the Fe-whisker and the thin Fe film separately. A pair of Helmholtz coils was used to apply an external dc field which was oriented along the whisker axis. The reference image of a fully saturated sample was always subtracted from the actual image in or- der to enhance the domain contrast. The sample and the external field were rotated with respect to the optical plane of incidence in order to record the magnetization components in the direction parallel or perpendicular to the whisker axis, which cor- respond to the easy crystallographic directions. According to crystal anisotropy only three levels of gray are expected: black and white for domains magnetized along the sensitivity axis! and gray for both kinds of transverse domains, see Fig The depth sensitive MOKE images of the cornplete Au/Fe/MgO/Fe-whisker(001) system showing domain patterns in the Fe thin film and Fe-whisker separately are presented in Fig The domain state was obtained after demagnetizing the sample in an alternating magnetic field of decreasing amplitude along the whisker axis. As compared to the simple diamond domain present in the whisker (Fig. 4.17, 1

90 CHAPTER 4. FE/MGO/FE WHISKER(001) TUNNEL STRUCTURES 72 Figure 4.17: The depth-selective MOKE image of the Au/Fe/MgO/Fe-whisker structure. The phase of the reflected signal was selected in such a way that one observed magnetic domains in either the Fe film (left) or the Fe-whisker (right). right), the film domains (Fig. 4.17, left) appear highly complex with no clear relation between the film and the whisker magnetization directions. This is a clear indication of the absence of a significant interlayer exchange or orange peel coupling between the Fe film and the whisker. However, strong ferromagnetic coupling has been observed by Keavney et al. [I1 1 due to the pinholes in the MgO layer. This indicates, that our MgO layers grown on Fe-whiskers(001) are of a very high quality with no pinholes Magnetization reversal in the Fe/MgO/Fe-whisker MOKE images have shown, that the Fe film is coupled to the Fe-whisker by the stray field of the Fe-whisker domain walls (DWs) [63]. The magnetic coupling between the Fe-whisker and the Fe thin film can be demonstrated by following the motion of a 180" whisker wall, see Fig The whisker and the Fe film were initially saturated in a longitudinal external field towards the right. The external field was then gradually decreased until a 180" DW appeared in the lower part of the Fe whisker, see blue arrow in Fig. 4.18a. In images (a) to (c), the external field was gradually decreased. The area of the film, which had been passed by the whisker DW remained magnetized in the perpendicular direction with respect to the whisker magnetization, either up or down (white and black domains, respectively). There was a narrow zone of transverse magnetization where the whisker DW has not passed yet. The magnetization of this front zone was opposite to that of the passed zone. It follows, that the head-on wag is formed in the Fe film right above the whisker DW. When the whisker wall was

91 Whisker axis - Figure 418: MOKE image8 of the Au/Fe/MgO/Fe-whisker structure for different dua of the external dc field. The MOKE microscope is sensitive to the vertical component of the thin film magnetization. Originally, the whole sample was saturated and the magnetization vector pointed to the right (B ~ e &). (a) The external field atas grkh-dually d ~ r until d a 180" domain wall (marked by blue arrow) appeared in the whisker (B w +10 Oe). By moving the whisker DW across the sample, the Fe film is magnetized in the tmuverd diredim. Fip. b-c shows the further decrease of the external field, B w O Oe and -10 Oe, r~pectively. Note, that this switching process is irreversible. The retracting DW (d) switches the orientation of the magnetization right above the wall; in other areas of thin film the magnetization is unchanged.

92 CHAPTER 4. FE/rwCO/FE WHISKER(001) TUNNEL SmUCTURES 74 E - I u Whisker axis Figure 4.19: A low magnification image of the domain pattern of the 20 Au/20 Fe/20 MgOjFe-whisker(001) structure. Image (a) shows the domains of the thin film and (b).,.;?>: the corresponding domain pattern of the Fe-whisker substrate. The contrast within',. -", r the whisker DW corresponds to the different in-plane surface rotation of the N&l'~~++,. cap. The changes of the internal rotation of the magnetization inside the whisker wall- ' (Bloch line, BL) are labelled by white arrows. Notice, that BL changes the transverse {. magnetization direction of the thin film (a) going from black to white and via versa. - moving back (Fig. 4.18d), the wall boundary that separated the front zone from the non-switched area in the film was kept in the same position as in Fig. 4.18~; a retracting whisker wall left the transversely magnetized film domains in the same direction as those in front of DW. This is a remarkable effect. In this-manner, one is able to orient the direction of the magnetization in the Fe film perpendicular with respect to the magnetization direction of the Fe-whisker. Fig indicates what features of the whisker DW affect the direction of the transversal domains of the Fe film. The whisker wall in Fig. 4.19b has two explicit features: (a) Narrow black and white regions corresponding to the surface Ned cap and (b) Bloch lines (BL), accompanied by kinks, see Section 2.3. Fig shows that the orientation of the transversal domains does not depend on the surface orientation of the NBel cap. The direction of the transversal film domains changes at every BL and therefore it has to be related to the internal rotation in the whisker Bloch wall. The internal Bloch rotation changes sign across BL. Note, that Bloch lines may aldo be shifted along the wall when a 180" wall moves across the whisker. Therefore, A

93 CHAPTER 4. FE/MGO/FE WHISKER(001) TUNNEL STRUCTURES 75 the direction of the checkerboard pattern in the film may deviate from the vertical directions, depending on the position of the BL during the wall motion, see Fig. 4.19a Magnetic stray field interaction The physical mechanism of the remagnetization process can be understood from Fig The perpendicular component of the residual stray field of the 180" domain wall of the Fe whisker acts like a magnetization "source" or "sink" depending on the internal rotation of magnetization in the wall, see Fig. 4.20b-e. The stray field of the whisker DW remagnetizes the Fe film in the direction perpendicular to the whisker axis, see Fig The lateral distance in which the DW stray field is effective is shown by the zones of the transversally oriented domains where the whisker DW have not passed yet. Figs. 4.20b-c and 4.20d-e explicitly demonstrate why a retracting whisker DW does not change the magnetization direction of these zones. Strength of the stray field of 180" domain walls of Fe-whiskers was estimated by Scheinfein et al. [126]. The perpendicular component of the magnetization was found to be 300 Oe at distance of 16 nm above the whisker surface. In our case, separation between the Fe-whisker and the Fe film ranges from I to 3 nm and therefore the strength of the domain wall stray field is expected to be larger. This interaction does not require any electron transport and therefore it is present in any material. The domain wall stray field interaction in magnetic multilayers has been observed by McCartney et al. [I271 in MTJs and by Thomas et al. [128, 1291 in GMR sensors. They have shown that the magnetic moment of the hard (pinned) layer is eventually decreased by repeated remagnetization of the soft magnetic layer. Magnetotrasport studies using AFM Understanding of the magnetization processes is important for measuring tunneling magnetoresistance (TMR). In TMR studies, one can proceed in the following way: (a) saturate the sample in one direction and measure the tunneling current for the parallel orientation of the magnetic moments (Ill) and (b) decrease the external field and sweep it up and down in the region, where the 180" domain wall remains within the whisker; in this state one can measure the tunneling current for the perpendicular orientation of the two magnetizations (I*).

94 I Fe film MgO barrier Figure 4.20: A schematic diagram of the interaction of the domain wall stray field with the magnetization of the Fe film. The whisker axis is going out of the page and the sample is saturated along this direction (Fig. a). Sequence (b)-(c) shows the part of the 180" Bloch wall where the internal direction of the magnetization points downwards. The stray field of the whisker DW (blue arrows) is coupled to the Fe film magnetizing the Fe layer before and after the Bloch wall in mutually antiparallel directions. Series (d)-(e) represents the part of the 180" Bloch wall where the internal direction of magnetization points upwards. Notice, that retracting DW does not change the orientation of the transversal direction of the magnetization in the Fe film, see (c) and (e).

95 CHAPTER 4. FE/MGO/FE WHISKER(001) TUNNEL STRUCTURES 77 Our previous experiments have shown that a macroscopic contact (thin In wire or 10 pm thick Au wire with a 20 pm sphere at the end) damages the structure to the point that only ohmic I-V characteristics are observed. An AFM system with a conducting tip operating in the external dc magnetic field was employed to measure the TMR effect at RT. The AFM tip "lands" on the sample surface in a controllable manner; the feedback is controlled by the sample-tip force allowing one to obtain a good ohmic contact between the tip and the sample surface. The AFM imaging can be done using the same tip operating in the non-contact mode. The sample was glued to a thin A1 plate using Ag epoxy and attached to the x - y stage between the pole pieces of an electromagnet with a maximum dc field of = 400 Gauss. The AFM set up was operated in vacuum chamber (base pressure about noise of the cantilever. Torr) to reduce thermal I-V measurement in external magnetic field The I-V characteristics were measured in the contact mode using a Au coated Si cantilever. Our previous AFM studies using Au/Fe-whisker(001) samples have shown, that good a ohmic contact can be established using Au coated tips. This is in agreement with the detailed studies by Ishizaka et al. [130]. The force between the tip and the sample did not exceed 100 nn. In order to achieve a low contact resistance the applied force varied between 20 to 50 nn. The I-V characteristics measured for the saturated sample (120 and 200 Oe) and at zero applied field are presented in Fig All curves appear to be non-linear with negligible current between &3 V. This behavior is expected for electron transport due to tunneling through the MgO barrier. The TMR effect would be proportional to where Ill and I1 represent the tunneling current in the saturated state (H = 120 Oe) and in the remanent state, respectively. The remanent state is considered to have the magnetization of the whisker substrate perpendicular with respect to the magnetization of the thin film. Remarkably, the TMR reaches nearly 100 % at RT for a bias voltage above 3 V. However, this is not a typical result. Most of the I-V characteristics taken on our samples were not reproducible. AFM imaging using the non-contact mode has revealed significant topological corrugations in the area where

96 Figure 4.21: The AFM I-V characteristics of Au/Fe/MgO/Fe-whisker for different - values of the external dc field. This is not a typical result., the I-V curves were measured. Unfortunately, even in AFM the direct contact results in a significant damage to the crystalline MTJ Charging effects The vertical topological variations measured using AFM were of the order of nm. This is not likely; one can expect that they have a different origin. The fact that the measured I-V curves were not reproducible can be related to the additional charge which was deposited and stored in the area where the AFM tip was in contact with the top Au electrode, see Fig In AFM imaging, the stored charge creates a large electrostatic force resulting in a large vertical displacement of the cantilever. This assertion can be tested by reversing the polarity of the bias voltage. Indeed, the image becomes the "negative" of the previous one, see Fig. 4.22b. This indicates, that a localized charge can be stored in the Au/Fe/MgO/Fe-whisker tunnel junction. The charge can be stored in this way for at least one day. More detailed studies of this effect shows, that one is able to "write" either a white or a black spot depending on the applied bias voltage when in the contact mode. The AFM studies have shown, that the charge is confined to an area smaller then 100 nm in diameter, see Fig During AFM imaging, the AFM tip is relatively far from the sample (N 10 nm or more) and therefore the charged part of the sample can be

97 CHAPTER 4. FE/MGO/FE WHISKER(001) TUNNEL STRUCTURES 79 Figure 4.22: The AFM images of Au/Fe/MgO/Fe-whisker taken at (a) positive and (b) negative sample bias voltage. The series of dots in the left part of the image were made by applying a negative voltage to the tip (-3 and -6 V) in the contact mode. as small as the tip contact area which might be a few nm in diameter. At the present time it is not clear if the charge is held within the insulating barrier or at a thin layer of surface contamination. Since the charge can be stored for a long time one expects that it is most likely localized within the MgO layer. Additional studies are required to investigate this point.

98 CHAPTER 4. FE/MGO/FE WHISKER(001) TUNNEL STRUCTURES 80 (3 x 3) um2 Distance [pm] Distance [pm] Figure 4.23: (a) AFM image (3 x 3 pm2) of a Au/Fe/MgO/Fe-whisker structure taken at positive sample bias voltage. Two bright and dark spots were previously created using positive and negative tip voltage, respectively. (b)-(c) Line profiles were taken to estimate the size of the dots and the effective hight and depth, respectively.

99 Chapter 5 Fe/Cr and Fe/Au multilayers This Chapter is devoted to studies of the static and the dynamic magnetic properties of ultrathin magnetic layers of Fe grown directly on GaAs(001) substrates. The understanding of spin dynamics plays an important role for the magnetization reversal process in thin magnetic films. It will be demonstrated that non-magnetic overlayers (Au and Cr) can affect strongly the magnetic relaxation process. In the case of Fe/Au multilayers, a novel non-local relaxation mechanism has been observed. It will be shown that this additional relaxation process can be described by spin-pump [I311 and spin-sink [I321 models. 5.1 Growth and structure of M/Fe/GaAs(OOl); M = Au and Cr All samples were prepared using MBE on GaAs(001) templates. An epi-ready GaAs wafer (10 x 10 mm2) was inserted into the UHV chamber and outgassed at 500 C for 1 hour. A low energy Arf etching (E x 500 ev) was used to remove residual contaminants. To minimize structural damage grazing incidence was used and the GaAs wafer was rotated around its normal during sputtering. After all contaminants were removed, the sample was annealed under RHEED observation until a well ordered 4 x 6 reconstruction was observed [112, The final GaAs reconstruction is very much dependent on the annealing cycle used for a clean GaAs wafer. A detailed study of GaAs(001) substrates using STM in combination with RHEED and LEED was carried out by Xue et al. [134]. They have

100 CHAPTER 5. FE/CR AND FE/A U MULTILAYERS Deposition time [s] Figure 5.1: The RHEED intensity oscillations of a 16 ML Fe film deposited on 4 x 6- GaAs(001) at RT. The polar angle of the incident electron beam was set to the first anti-bragg condition for Fe. The azimuth angle is set close to the [I 101 crystalographic direction of Fe. also proposed the surface atom arrangements for different reconstructions. They have shown that there is no genuine 4 x 6 reconstruction for a clean GaAs(001) substrate except when Ga droplets are formed at the surface [134]. There are two possible reconstructions which occur after Arf sputtering and annealing at 600 "C : (a) a Ga rich 1 x 6 phase and (b) an As rich 4 x 2 phase. Our recent STM studies have shown that a 4 x 6 reconstruction of GaAs(001), as observed by means of RHEED, indeed consists of two domains, 4 x 2 and 1 x 6. In RHEED, one sees a combination of these two domains yielding a 4 x 6 diffraction pattern [135, 136, The ultrathin Fe layers were deposited at RT at rate of 1 ML/min from a thermal source. RHEED intensity oscillations were observed for up to 30 monolayers (ML), see Fig In the early stage of the growth the intensity of the specular spot shows weak monolayer oscillations. After approximately 5 ML the Fe layer forms a continuous film [137]; the RHEED intensity increases and shows strong monolayer oscillations. The magnetic studies were carried out for Fe layer thickness dfe 2 5 ML to avoid the complex structure obtained during the initial stages of the growth. Two series of samples covered by either a Au or Cr cap layer (20 ML in the thickness) were prepared. Both materials were deposited at RT from thermal evaporation

101 CHAPTER 5. FE/CR AND FE/AU MULTILAYERS 83 sources at the rate of 1 ML/min. The growth of Au and Cr has also shown RHEED intensity oscillations. XPS and Auger spectroscopy revealed the presence of As which is segregated on the top of metallic layers [135, 112, From the XPS intensity ratio between the Fe 2p312 and As 2p312 signals, one can estimate that about 0.6 ML of As floats on the top of Fe. The same amount of As was observed on the top of Au or Cr cap layers; no As stays either within the metallic layers or at the Fe/Au or Fe/Cr interfaces. 5.2 Magnetic properties of Fe/GaAs(001) The magnetic properties of thin Fe layers grown directly onto (4 x 6)-GaAs(001) substrates were investigated by FMR. Two sets of samples were prepared: (a) 20 Au/8, 11, 16, 31 Fe/GaAs(001), and (b) 20 Cr/5, 10, 15, 20 Fe/GaAs(001). The integers represent the number of ML. The measured FMR absorption lines showed symmetric Lorentzian profiles with well defined HFMR and AH for both in-plane and out-of-plane configurations, see Fig. 5.2a. The FMR field and the FMR linewidth were measured as a function of the in-plane angle c p between ~ the direction of the external dc field and a cubic axis. A typical angular dependance of the FMR field is shown in Fig. 5.2b. The angular dependance of the FMR field was fitted using Eq to determine the strength of the in-plane four-fold and uniaxial magnetic anisotropies, External dc field [koe] Figure 5.2: (a) FMR lines for two different in-plane angles c p between ~ the direction of the external dc field and a cubic axis at f = 36 GHz. (b) FMR field HFMR as a function of the azimuthal angle c p for ~ 20 Au/16 Fe/GaAs(001) sample at f = 36 GHz.

102 CHAPTER 5. FE/CR AND FE/AU MULTILAYERS Figure 5.3: The effective demagnetizing field perpendicular to the film surface 47-rMeE and the in-plane four-fold (cubic) Kill and uniaxial KuII anisotropies plotted as a function of l/dfe for the single Fe films; dfe is the Fe film thickness. The Fe films were grown on GaAs(001) and covered by (a) 20 ML of Au(001) and (b) 20 ML of Cr(001). The solid lines represent linear fit to the data.

103 CHAPTER 5. FE/CR AND FE/AU MULTILAYERS 85 Table 5.1: The measured values of the anisotropy constants for Au/Fe and Cr/Fe grown on GaAs(001). Superscripts and tributions to the magnetic anisotropies. represent the bulk and the interface con- Kill and KuIl, and the effective demagnetizing field perpendicular to the film surface, 47rMeff. The results are shown in Fig The magnetic anisotropies were well described by a linear dependance on l/dfe. The constant and linear terms represent the bulk and interface magnetic contributions, respectively, see Appendix A. Ultrathin Fe films grown on GaAs(001) have magnetic properties nearly equal to those found in bulk Fe (K$ = 4.7 x lo5 erg/cmp3 [138]), modified only by sharply defined interface anisotropies, see Tab. 5.1, indicating that the Fe layers are of a high crystalline quality with well defined interfaces. The in-plane 4-fold interface anisotropy K,SII was found to be larger than the value 0.02 erg/~m-~ found by Brockmann et al. [139]. The in-plane uniaxial interface anisotropy K:Il is very sensitive to the GaAs substrate preparation resulting in a large scatter of the experimental results [140, 141, In has been shown by Krebs et al. [140], that the in-plane interface uniaxial anisotropy is caused by hybridization of the valence band electrons of Fe with the dangling bonds of GaAs(001). The overall magnetic anisotropies were found to be the same for both Cr(001) and Au(001) cap layer materials. They are in agreement with the results of the measurements of Monchesky et al. [I351 on Cu/Fe/GaAs(001) structures. The values of Ki, and 47rMs, see Tab. 5.1, deserve some comments. It has been shown by Gordon et al. [142], that Fe films grown on GaAs(001) substrates are tetragonally distorted relative to bulk bcc iron. The distortion involves an in-plane contraction and an expansion in the direction perpendicular to the sample plane. The c/a ratio for a 10 ML thick Fe film was found to be (1.03 f 0.02). The strain of the Fe layer affects the effectivve magnetization perpendicular to the sample plane [3, 143, 1421 where B1 is the magnetoelastic coupling coefficient (B1 = x lo7 erg/cm3 for

104 CHAPTER 5. FE/CR AND FE/AU MULTILAYERS 86 Fe [143]) and el and ell are the strains perpendicular and parallel to the Fe film plane. It has been shown by Thomas et al. [I441 that for our thickness range, the strain in the Fe films remain constant. Therefore, the magnetoelastic contribution will renormalize the value of 47rMs. If we take the values of el = (0.022 f 0.010) and ell = ( f 0.004) from [142], the effective field due to magnetostriction -2Bl (el - ell)/ms = (1.1 f 0.5) koe. This will decrease the value of 47rMs listed in Tab It has been shown in Section that the FMR linewidth in ferromagnetic metals for microwave frequencies greater than 10 GHz can be described by where AH(0) was shown to be of an extrinsic origin. Geff was used to express the fact that the slope of the FMR linewidth can include both intrinsic, Gint, and extrinsic, GeXt, contributions. The frequency dependence of the FMR linewidth of the 15 ML thick Fe layer covered by Au or Cr is shown in Fig In both cases, the FMR linewidth is linearly proportional to the microwave frequency f. The effective Gilbert damping parameter for Fe/Cr and Fe/Au was found to be (2.26 f 0.34) x lo8 s-' and (l.3i'f 0.06) x lo8 s-', respectively. In addition, the FMR linewidth in the Fe/Cr(001) structure possesses an appreciable zero-frequency offset (see Eq. 5.2) AH(0) 2 80 Oe. f [GHz] f [GHz] Figure 5.4: The FMR linewidth AH as a function of microwave frequency f for (a) 20 Cr/15 Fe/GaAs(001) and (b) 20 Au/16 Fe/GaAs(001). The integers represent the number of ML.

105 CHAPTER 5. FE/CR AND FE/AU MULTILAYERS 5.3 Two-magnon scattering in Cr/Fe/GaAs To study the extrinsic contribution to the FMR linewidth in Cr/Fe/GaAs(001) structures, a series of samples with different Fe thicknesses, dfe = 5, 10, 15, and 20 ML were prepared. The in-plane and the out-of-plane measurements of the FMR linewidth were investigated as a function of the Fe layer thickness and the microwave frequency f. The in-plane FMR measurements were performed at f = 9.5, 24, and 36 GHz. The out-of-plane FMR measurements were performed only at 9.5 and 24 GHz because we were not able to reach the FMR field at 36 GHz for the perpendicular configuration. It is important to realize that for the 2D spin-wave manifold there are no degen- erate magnons with the FMR mode in the perpendicular configuration. Therefore, in the presence of two-magnon scattering the FMR linewidth, AHl, should be smaller than that in the parallel configuration, AHIl. The crystalline Cr/Fe/GaAs(001) sam- ples satisfied this conditions for dfe = 15 and 20 ML. These samples allowed us to interpret the FMR linewidths in terms of intrinsic damping and the two-magnon scattering mechanism Out-of-plane FMR linewidth The FMR field and the FMR linewidth for the 20 Cr/15 Fe/GaAs(001) sample as a function of the polar angle OH between the direction of the external dc field and the sample plane are shown in Fig For f = 24 GHz, the FMR field increases monotonically from 3.3 koe for the in-plane configuration to 25.4 koe for the perpendicular FMR configuration, see Fig. 5.5a. The solid line represents the theoretical calculation including the magnetocrystalline anisotropies and dragging effect [6]. The FMR linewidth increases with increasing angle, reaches a maximum around OH = 72" away from the sample plane, and then abruptly decreases to AHl = 45 Oe in the perpendicular configuration. A significant increase of the FMR linewidth for the intermediate angles is related to the dragging effect. For intermediate polar angles OH the direction of the magnetization vector M is not parallel to the direction of the external field H due to the strong demagnetizing field, 4n-MeR. As the external dc field is swept, the direction of the magnetization vector is changing and therefore the internal field changes during FMR measurements. This results in a broadening of the FMR line. The FMR linewidth in the perpendicular configuration AHl = 45 Oe is substantially lower than the one in the parallel configuration, AHlI = 150 Oe.

106 CHAPTER 5. FE/CR AND FE/AU MULTILAYERS 88 Figure 5.5: (a) FMR field (0) and (b) FMR linewidth (A) at f = 24 GHz as a function of the polar angle OH for the 20 Cr/15 Fe/GaAs(001) sample. The in-plane and perpendicular FMR configuration corresponds to OH = OM = 0" and OH = OM = 90, respectively. The solid line in (a) represents the calculated HFMR(OH) using the following magnetic parameters: 47rMeE = 16.4 kg, Kill = 3 x lo5 erg/cm3, KuII = 3.5 x lo5 erg/cm3, and g = The solid line in (b) shows the calculated dependence of the FMR linewidth as a function of the angle OH using the above magnetic parameters with the Gilbert damping equal to 1.5 x lo8 s-'. The substantial drop of the FMR linewidth in the perpendicular configuration was observed for dfe = 15 and 20 ML. Perpendicular FMR measurements at 9.5 and 24 GHz, see Fig. 5.6, showed no measurable AH(O), and one can assume that the measured slope led to the intrinsic Gilbert damping parameter Gin, = (1.51 f 0.02) x lo8 s-', see Tab One should point out, that for Fe-whiskers and thin Fe layers grown on Ag(001) substrates, the direction AH(0) [Oe] Geff [lo8 s-'1 hard uniax. axis [lio] 95 f f 0.01 easy uniax. plane [I f f 0.26 cubic axes (100) 127 f f 0.34 perpendicular [001] f 0.02 Table 5.2: The AH(0) and effective Gilbert damping Geff for the three principal inplane and perpendicular orientations of the 20 Cr/15 Fe/GaAs(001) structure. The error bars represent uncertainties in the linear fits. The accuracy of the measured FMR linewidth is a few Oe.

107 CHAPTER 5. FE/CR AND FE/AU MULTILAYERS Figure 5.6: The FMR linewidth for the parallel FMR configuration for the 20 Cr/15 Fe/GaAs(001) sample as a function of microwave frequency, f, measured along: (v) cubic axes {100), (A) hard uniaxial axis [I~o], and (m) direction corresponding to the easy uniaxial plane [110]. (0) represents the perpendicular FMR linewidth AHL as a function of f. Solid lines are linear fits using Eq Note, that AH(0) = 0 Oe for the perpendicular FMR measurements; the slope of the solid line determines the intrinsic Gilbert damping Gint, see Eq Gilbert damping parameter was was found to be 0.6 x lo8 s-i [I451 and 0.7 x lo8 s-' [37], respectively. The increased damping parameter in Fe grown on GaAs(001) templates can be caused by the lattice mismatch between Fe and GaAs and therefore related to the stress. In the following text, intrinsic damping Gint refers to the small- est Gilbert parameter found in Au/Fe/GaAs(001) and Cr/Fe/GaAs(001) multilayers respectively with no zero frequency offset. The absence of defect scattering in the perpendicular configuration, see Fig. 5.6, provides strong evidence for the presence of two-magnon scattering in the 20 Cr/15,20 Fe/GaAs(001) structures. The values of AH(0) and the Gilbert damping parameter GeR for the principal in-plane and perpendicular orientations are summarized in Tab Note, that the in-plane effective Gilbert damping parameters are always larger than the intrinsic Gilbert damping Gint.

108 CHAPTER 5.; FlY/;I[=iR AND YERS Two-magnon contribution to the FMR linewidth It has been shown in Section that the magnon energies are given by the Darnon Eshbach modes see Eq For the in-plane orientation the energy of magnons with k( 1 M, initially decreases with increasing k, and eventually, at k = h, crosses the frequency of the homogeneous mode, see Fig. 5.7a. This means that magnons with ko are degenerate with the homogeneous mode and can be involved in the two-magnon scattering process. The value of k = k,-, decreases with increasing angle $k (angle between the spin-wave wave-vector k and the direction of the saturation magnetization M,), see Fig No degenerate modes are available for $k > >ma( f, OH); sin2 ($ma) = H/(H + 4rMeff) = H/Beff. The difference between the measured FMR linewidth and that expected for the intrinsic damping (the solid line in Fig. 5.5b), AH&, can be caused by two-magnon scattering. Arias and Mills have derived an analytical " expression for the additional FMR linewidth, which includes the ellipticity factor 32 AH@) Ktl b 2 ~ = rdm,z be^ + + H )~ (~eff + (( C >- 1) +.zf ((f)- I)] where a and c are the lateral dimensions of the defects, and b is the defect depth. Parameter p represents the fraction of the surface covered by defects. For more details, Figure 5.7: (a) The 2D spin-wave manifold for OH = 50, OM = 13", and $k = 0". k, corresponds to the spin-wave which is degenerate in the energy with the homogeneo& mode. (b) The dependance of ko on the out-of-plane angle OH and $k.

109 CHAPTER 5. FE/CR AND FE/AU MULTILAYERS f [GHz] Figure 5.8: The extrinsic FMR linewidth AHext as a function of the microwave fre- quency f. The points represent the experimental data along the [loo] direction. The solid blue was calculated using Eq see Section The frequency dependance is dominated by sin-' J~lB,ft. ; =,, $I other terms showed only weak dependance on the microwave frequency. The exper- imental data showed, that AHext is the same along the cubic axes. Therefore, it is reasonable to assume that (c/a) = (a/c). The best fit to experimental data is shown in Fig Clearly, Arias-Mills's theory does not describe the experimental data well. In our frequency range, this theory somewhat overestimates the strength of the ex- trinsic Gilbert damping Gext (= Geff - Gint). In this respect Arias and Mills correctly pointed out, that the slope obtained by using Eq. 5.2 does not necessarily represent intrinsic properties. The slope in AH(w) for the parallel FMR configuration includes both, the intrinsic and extrinsic contributions to the Gilbert damping [146]. The expression by Arias and Mills (Eq. 5.3) is only valid for a particular type of defect. One can go back and use a general expression for the two-magnon contribution (including ellipticity) where N(0, k;i) was defined in Eq One can simplify this equation using

110 CHAPTER 5. FE/CR AND FE/AU MULTILAYERS f [GHz] Figure 5.9: The additional FMR linewidth AHext as a function of microwave frequency f for dfe = 15 ML along the cubic axis. Blue lines correspond to the calculated values using Eq The solid line corresponds to a Lorentzian distribution of laki2, see Eq. 5.8, with SA = 3 x lo4 cm-'. The dashed line corresponds to (AkI2 = const. where Ak couples the uniform precession and spin-wave modes. To evaluate the S- function in Eq. 5.4 one needs to expand w(kll) given by Eq around k = ko using Taylor's expansion The frequency dependance of the additional FMR linewidth AHext along the cubic axis is shown in Fig Notice, that the AH,",": is strongly dependant on the coupling constant \Ak 1 2. In order to reproduce experimental results, the enhancement of (AkI2 for small k-vectors is required. In this calculations, IAkI2 was approximated by a Lorentzian distribution with maximum at k = 0 where SA represents the width of the distribution. The dependance of the measured FMR linewidth AHext as a function of the polar angle OH is shown in Fig The extrinsic contribution to the additional

111 CHAPTER 5. FE/CR AND FE/A U MULTILAYERS Figure 5.10: The additional FMR linewidth as a function of the out-of-plane angle OH. FMR linewidth AHext is nearly independent of OH < 40, increases gradually for intermediate angles and reaches maximum at OH = 72" and decreases abruptly when the magnetization is pulled towards the sample normal by the external dc field H, see Fig The extrinsic FMR linewidth is zero for OH > 80". This corresponds to the critical polar angle, for which the spin-wave manifold only increases from kll = 0, see Fig. 5.7b. The calculation of the extrinsic contribution to the FMR linewidth for arbitrary out-of-plane orientation of the magnetization is rather complex. One would have to account for the ellipticity factor which changes with the polar angle OM. 5.4 Non-local damping in Au/Fe/GaAs and Au/Fe/Au/Fe/GaAs Magnetic multilayers provide a special case where the dynamic interaction between the itinerant electrons and the magnetic moments in ultrathin films offers new exciting possibilities. This is currently one of the main topics of the basic research on magnetic nanostructures and has much promise for spintronics applications. It has been shown in a number of experiments using either pillar shape nanoscopic samples [147], or point contact geometries [148], that the magnetization reversal can be driven by a

112 CHAPTER 5. FE/CR AND FE/AU MULTILAYERS 94 spin polarized current flowing perpendicular to the magnetic layers. Slonczewski has shown [I491 that a transfer of vectorial spin accompanying an electric current flowing through the interfaces of two magnetic films separated by a non-magnetic metallic spacer (magnetic double layer) can result in a "negative Landau-Lifshitz-like" relaxation torque. This leads, for sufficiently high current densities, to spontaneous magnetization precession and switching phenomena [150]. Berger has evaluated the role of the s-d exchange interaction in systems consisting of two magnetic layers separated by a non-magnetic spacer (N) using a somewhat different approach [151]. One magnetic layer was assumed to be static (F2), and the direction of its magnetic moment determined the axis of the static equilibrium. Magnons were introduced by allowing the magnetic moment of the second (thinner) layer (Fl) to precess around the equilibrium direction. The itinerant electrons entering the thin ferromagnetic layer through a sharp interface cannot immediately accommodate the direction of the precessing magnetization. Berger has shown that this leads to an additional exchange torque which is directed towards the equilibrium axis, and represents an additional relaxation term. This relaxation torque is confined to the vicinity of the N/F1 interface. The additional relaxation term was calculated using the conservation of the total angular momentum; this means that the electrons in N have to flip from up to down as a magnon is annihilated in F1, and vice versa. The relaxation equations for spin up and spin down electrons in the spacer layer were obtained using Fermi's golden rule which has to include the change in energy of an electron when emitting or absorbing a magnon, and the spin up and spin down Fermi level shifts. The resulting relaxation torque in a magnetic double layer structure, Hgd, can be written as [151, 121 where represent the magnetization unit vectors in F1 and F2, respectively and Ap = Apr - Apl is the difference in the spin up and spin down Fermi level shifts. The sign of Ap depends on the direction of the dc current passing through the film interfaces. This term involves the spin transfer by conduction processes resulting in a net exchange relaxation torque which depends on the density of the perpendicular current and upon the spin-up and spin-down mean free paths. This part corresponds to Slonczewski's prediction of the current-induced precession. The second term in Eq. 5.9 is not present in Slonczewski's model. This term can be obtained using the full dynamic treatment of the s-d exchange interaction where magnons are included

113 CHAPTER 5. FE/CR AND FE/AU MULTILAYERS 95 explicitly in the relaxation equations for occupation numbers. The second part of Eq. 5.9 is always positive and proportional to the microwave frequency and does not require a dc current crossing the interfaces. It represents a non-local interface damping Experimental evidence for non-local damping The thin Fe films (Fl) which were studied in the single layer structures (see Section 5.2) were regrown as a part of double layer structures. The thin Fe film was separated from the second thick Fe layer (F2) of 40 ML thickness by a 40 ML thick Au spacer. The double layers were covered by a 20 ML Au(001) layer for protection under ambient conditions. The complete structure was 20 Au/40 Fe/40 Au/8, 11, 16, 21, 31 Fe/GaAs(001). The thickness of the Au spacer layer was much smaller than the spin-diffusion length and mean free path (ballistic limit) [152, 1531, and therefore the scattering in the Au spacer did not effect the spin transport between the magnetic layers. The FMR absorption lines in magnetic double layers maintained symmetric Lorenztian profiles with well defined FMR fields and FMR linewidths, see Fig. 5.11a-b. The interface magnetic anisotropies separated the FMR field of F1 from F2 by a big margin, see Fig. 5.11a-c. That allowed us to carry out the FMR measurements of F1 in the double layer structures with F2 possessing a negligible angle of precession. The FMR linewidths in single and double layer structures were only weakly dependent on the azimuthal angle (PH, see Figs. 5.11b and 5.12b. The thin Fe film in the single and double layer structures had the same FMR fields, see Fig. 5.12a1 showing that the interlayer exchange coupling through the 40 ML thick Au spacer was negligible 131, and the magnetic properties of the Fe films grown by MBE on well prepared GaAs substrates were fully reproducible. The FMR linewidth in F1 always increased in the presence of the second Fe layer, F2, see Fig. 5.12b. The additional FMR linewidth, AHadd, followed an inverse dependence on the thin film thickness dfe, see Fig. 5.13a. The l/dfe dependence of AHadd shows that the non-local contribution to the FMR linewidth originates at the film interface. AHadd deviates from the straight line mainly for the thinnest Fe layer, dfe = 8 ML. This can be expected. According to Berger [151], the l/dfe dependence

114 CHAPTER 5. FE/CR AND FE/AU MULTILAYERS Figure 5.11: The measured FMR signal for (a) c p = ~ 0" (cubic axis) and (b) 9~ = 45" (hard uniaxial axis) in the the 20 Au/40 Fe/40 Au/16 Fe/GaAs(001) sample measured at f = 36 GHz. (c) The FMR field, HFMR, and (d) FMR linewidth, AH, as a function of the azimuthal angle c p for ~ the 20 Au/40 Fe/40 Au/16 Fe/GaAs(001) structure at f = 36 GHz. The in-plane hard uniaxial axis corresponds to c p = ~ 45". (a) correspond to the 16 ML Fe film and (A) correspond to the 40 ML Fe film.

115 CHAPTER 5. FE/CR AND FE/AU MULTILAYERS 97 Figure 5.12: (a) The FMR field, HFMR, and (b) FMR linewidth, AH, for the 16 ML Fe film as a function of the azimuthal angle c p at ~ f = 36 GHz. The solid lines corresponds to the 20 Au/16 Fe/GaAs(001) structure, and (H) corresponds to the 20 Au/40 Fe/40 Au/16 Fe/GaAs(001) structure. fails when the film thickness is comparable to the spin coherence length where kti are the spin-up and spin-down Fermi surface wave-numbers. A gradual deviation of AHadd from the l/dfe dependence indicates that the thickness of F1 approaches that limit. The frequency dependance of the FMR linewidth of the single Fe film (16 ML) is shown in Fig. 5.13b. The FMR linewidth is linearly dependent on the microwave frequency, see Eq The corresponding Gilbert damping parameter G and zero frequency offset AH(0) were found to be (1.37 i 0.06) x lo8 s-' and (4 f 2) Oe, respectively. Within the accuracy of our measurements (a few Oe) the zero frequency offset AH(0) can be considered to be zero. This means lattice imperfections do not contribute to the FMR linewidth and therefore the measured G represents the intrinsic Gilbert damping, Gint. This is a unique result not commonly reported for ultrathin films [154]. The linear dependence of AHadd on the microwave frequency with no zero-frequency offset (AHadd(0) = (1 i 2) Oe), see Fig. 5.13b1 is a vital result of our studies. It means that the additional contribution to the FMR linewidth is described by the interface Gilbert damping, G,,. The interface Gilbert damping for the 16 ML thick film was found to be weakly dependent on the crystallographic direction; GSp =

116 CHAPTER 5. FE/CR AND FE/AU MULTILAYERS Figure 5.13: (a) The dependence of the additional FMR linewidth, AHadd, along the Fe cubic axis on l/dfe at f = 36 GHz. (b) The FMR linewidth, AH, as a function of the microwave frequency f. (0) corresponds to the 16 ML Fe film in the single layer structure. (0) shows the additional FMR linewidth, AHadd, for the 16 ML Fe film. The solid lines are linear fits to the data. The dashed line corresponds to Berger's additional linewidth A ~ zi~~~, see Eq (1.11& 0.03) x lo8 s-' along the cubic axis. Note, that its strength is comparable to the intrinsic Gilbert damping in the single Fe film (Gint = (1.37 f 0.06) x lo8 s-i). Berger's expression in Eq. 5.9 was derived for circular polarization of the rf precession. This would be nearly correct for the perpendicular FMR configuration. However, for the parallel configuration, where the ellipticity of the precession has to be taken into account, Berger's expression leads to a Bloch-Blombergen-like damping with the relaxation parameter proportional to the microwave frequency [12]. For the in-plane configuration, the FMR linewidth would be given by The frequency dependance of the FMR linewidth AH^:^^' is shown by the dashed line in Fig. 5.13b. Clearly, Berger's prediction does not reproduce the measured AHadd for low frequencies. The non-local FMR linewidth was found to be strictly proportional to the microwave frequency.

117 CHAPTER 5. FE/CR AND FE/AU MULTILAYERS Spin-pump model of the non-local damping Tserkovnyak et al. [131] have shown that the interface damping can be generated by a spin current from a ferromagnet (Fl) into adjacent normal metal reservoirs (N). The spin flow is generated by a precessing magnetic moment in F1. A precessing magnetization at the Fl/N interface acts as a "peristaltic spin-pump"; there is no charge transfer across the Fl/N interface. The direction of the spin flow is perpen- dicular to the Fl/N interface and points away from the interface towards N. The spin momentum carried away by the spin flow is time dependant and can be written as where m^ is a unit vector in the direction of M in F1. The spin current causes an additional magnetic damping. Not ice, that the additional damping has the form of the Gilbert damping field, see Eq In contrast to Berger's predictions, the spin-pump theory results in Gilbert damping, AH oc w, independent of the ellipticity of precession [155, A, is the interface scattering parameter, which is given by where rgn and tg, are the electron reflection and transmission matrix elements at the Fl/N interface for the spin up and down electrons, respectively. For interfaces with some degree of diffuse scattering, the sum in A, is close to the number of the transverse channels at the Fermi level in N [I571 and can be simply written as where S is the area of the interface, kf is the Fermi wave-vector and n is the density of electrons per spin in N [157]. Brataas et al. [158, 1571 have shown that A, can be evaluated from the interface mixing conductance Gtl [159] where gtl represents a "dimensionless interface mixing conductivity". Xia et al. [I591 have evaluated GTL from first principle calculations for various interfaces. They have shown that for the Cu/Co interface the dimensionless mixing conductivity gtl = 1.05 x 1015 cm-2 which is in agreement with Eq

118 CHAPTER 5. FE/CR AND FE/AU MULTILAYERS 100 The generated spin flow propagates through N, and is deposited at the N/F2 interface. It has been shown by Brataas et al. [I581 and Stiles and Zangwill [132, 1601 that the transverse component of the spin flow is entirely absorbed at the N/F2 interface, see Fig. 5.14a; spin momentum is neither reflected nor transmitted. For small precessional angles the spin flow is almost entirely transverse. This means that the N/F2 interface acts as an ideal spin sink, and provides an effective spin brake for the precessing magnetic moment in F1. The resulting Gilbert damping parameter Gsp can be evaluated from the conservation of the total spin momentum Figure 5.14: A cartoon representing the dynamic coupling between two magnetic layers F1 and F2, which are separated by a non-magnetic spacer N. (a) represents two magnetic layers with different FMR fields. F1 is at resonance, and F2 is nearly stationary. A large grey arrow in the normal spacer describes the direction of the spin current. The dashed lines represent the instantaneous direction of the spin momentum. For a small angle of precession it is nearly parallel to the transverse rf magnetization component shown in short dotted arrows. F1 acts as a spin-pump, F2 acts as a spin-sink. (b) represents a situation when Fl and F2 resonate at the same field. Both layers act as spin-pumps and spin-sinks. In this case, the net spin momentum transfer across each interface is zero. No additional damping is present.

119 CHAPTER 5. FE/CR AND FE/AU MULTILAYERS 101 where MtOt is the total magnetic moment in Fl. After simple algebraic steps one obtains an expression for the additional Gilbert damping where dl is the thickness of Fl and g is the electron g-factor. The inverse dependence of G,, on the film thickness clearly testifies to its interfacial origin. For a quantitative comparison between experiment and the spin-pump theory, one needs to include the additional relaxation term into the LLG equation of motion [161, 162, In the ballistic limit, the layers Fl and F2 act as mutual spin pumps and spin sinks. For small precessional angles the equation of motion for F1 can be written as where are the unit vectors along The exchange of spin currents is a symmetric concept and the equation of motion for layer F2 is obtained by interchang- ing the indices 1 F' 2. The third and fourth terms in Eq represent the spin pump and spin sink of F1. The fourth term is generated by the spin pump from F2. For clarity it is worthwhile to point out that the signs (+) and (-) in the third and fourth terms in Eq represent the spin current directions (F1 t F2) and (F2 -+ Fl), respectively. Eq was used to calculate the FMR line including all magnetic anisotropies and the results were compared to the measured signal for 20 Au/40 Fe/40 Au/16 Fe/GaAs(001), see Fig The agreement for different in-plane angles is remarkable. Eq is valid for any difference HkMR - [161, Non-local damping plays an important role in Fe/Cu/Fe(001) double layers, where the Fe films are coupled by an interlayer exchange coupling [164]. In this case, the magnetizations of the two ferromagnetic layers precesses in-phase (acoustic) and out- of-phase (optical mode). The interlayer exchange interaction can be included in Eq and the FMR response can be calculated for a 5 Fe/12 Cu/lO Fe structure [164].

120 CHAPTER 5. FE/CR AND FE/AU MULTILAYERS 102 Figure 5.15: The measured field dependance of the FMR signal for 20 Au/40 Fe/40 Au/16 Fe/GaAs(001) at 24 GHz for two different in-plane angles (blue circles). The red lines represent the calculated FMR signal using Eq including all magnetic anisotropies for this structure. The black vertical lines mark the FMR fields for each layer. Calculations were carried out at 36 GHz using the spin-pump and spin-sink theory. For zero interlayer exchange coupling, the spin pumping contribution to the FMR linewidth for the 5 Fe layer is 150 Oe. For a moderate value of antiferromagnetic exchange coupling, J = -0.2 ergs/cm2, the optical peak was broadened by 200 Oe while the acoustic peak was only broadened by 36 Oe compared to the intrinsic FMR linewidth; the optical peak mostly arises from the 5 ML thick Fe layer. This should be expected considering that the optical peak corresponds to an out-of-phase precession of the magnetic moments in the 5 ML Fe and 10 ML Fe layers, and therefore the spin-pump effect is more efficient than for the acoustic peak. In the experiment, the FMR optical peaks were always observed to be wider than the acoustic peaks. In a 5 Fell2 Cull0 Fe sample grown on a Ag(001) substrate the measured optical peak was broadened by 500 Oe [164]. The above calculation indicates that approximately 50% of the broadening was due to spin pumping and only 50% was caused by an inhomogeneous exchange coupling as discussed by Heinrich et a1 [164].

121 Chapter 6 Semiclassical theory of the spin transport A semi-classical model of the spin momentum transfer in ferromagnetic (FM)/normal metal (NM) structures will be presented in this Chapter. It is based on the LLG equation of motion and the exchange interaction in the FM, and the spin diffusion equation in the NM spacer. The internal rf magnetic field is treated by employing Maxwell's equations. A precessing magnetization in the FM creates a spin current which is described by the spin pump model proposed by Tserkovnyak et al. [131]. The back flow of spins from the NM into the FM is assumed to be proportional to the spin accumulation in the NM as proposed by Silsbee et al. [165, The theoretical calculations are tested against the experimental results. 6.1 Landau-Lifshitz-Gilbert equation of motion for FM and NM The LLG equation of motion for an ultrathin ferromagnetic film was discussed in detail in Section For thick layers the internal rf electromagnetic fields have to be treated using Maxwell's equations. The coordinate system was chosen in such a way that the sample normal was parallel to the z-axis. The external dc field, H, and the saturation magnetization Ms lie in the sample plane and are parallel to the y-axis, see Fig The internal electromagnetic rf fields, h and e are written as h = (h, O,O), e = (0, e, 0). (6.1)

122 CHAPTER 6. SEMICLASSICAL THEORY OF THE SPIN TRANSPORT 104 Figure 6.1: A schematic coordinate system. The time and spatial variations of the rf components were assumed to vary like exp (iwt- kz), where k is the z-component of the wave-vector and w is the rf angular frequency. In this configuration, Maxwell's equations in Gaussian units neglecting the displacement current can be written as [7] where a is the conductivity, c is the velocity of light in free space, and ki = (4xaw)/c2. The skin depth 6 is usually defined as [30, 311 Ferromagnetic layer : The LLG equations of motion in FM can be written as where y is the absolute value of the electron gyromagnetic ratio, M, is the saturation magnetization, and ac is the dimensionless Gilbert damping parameter (= GIyM,). The effective field H:~ contains the external fields and exchange interaction [3]; mangetocrystalline anisotropies will be excluded for simplicity. Eq. 6.5 was solved in the small angle approximation using

123 CHAPTER 6. SEMICLASSICAL THEORY OF THE SPIN TRANSPORT 105 To find appropriate wave-vectors, we have to solve the LLG equation of motion and Maxwell's equations self-consistently. Inserting MF and H$ into the LLG equation of motion (Eq. 6.5) and using Maxwell's equation (Eq. 6.2 and 6.3) we get a set of linear equations in the form [3] i" - (47rM, + H) + ;ii;k 2A 2 - ifac 0 Y = 0. (6.7) [ H - gk2 + ifac ] iw Y M 47rik: 0 k2 - ik: Normal metal layer : The equations of motion including the spin diffusion and relaxation terms in the NM was solved in the form [I651 where Tsf is the spin-flip relaxation time and 6~~ = M" - xph is the excess magnetization in the NM; xp is the Pauli susceptibility, see Eq in Section or [20, 211 for more details. The diffusion constant D is defined as where v~ is the Fermi velocity and ~~l is the electron momentum relaxation time. The effective field HZ in NM contains only the external dc, internal rf field h, and the demagnetizing field perpendicular to the sample plane. In the small angle approximation the total magnetization vector MN and the excess magnetization vector 6MN in NM can be written as Inserting MN and H$ into LLG equation of motion (Eq. 6.8) and using Maxwell's equation (Eq. 6.2 and 6.3) we get a set of equations in the form Eqs. 6.7 and 6.12 provide secular equations for k for FM and NM, respectively. In both cases, the secular equation results in a cubic equation in k2 which leads to six k-wave vectors with corresponding 6 modes of propagation. The rf magnetization and electromagnetic field components are given by a linear superposition of 6 waves. The coefficients are evaluated by matching the boundary conditions at the film interfaces.

124 CHAPTER 6. SEMICLASSICAL THEORY OF THE SPIN TRANSPORT Boundary conditions We assume no direct exchange interaction between the FM and NM layers. The coupling between FM and NM is caused by spin currents across the FM/NM interface. We consider three contributions to the net spin flow : IFM-~~ is described by the spin pumping model proposed by Tserkovnyak et al. [131, The gfl is the number of conducting channels per unit area [167] which is directly related to the interface mixing conductance Gfl by, see Section 5.4.2, where e is the electron charge and n is the density of electrons per spin in NM. INM-~~ was proposed by Silsbee et al. [I651 and Sparks et al. [I661 from a simple kinematic argument. tnm is the transmission coefficient for conduction electrons from NM into FM. Tserkovnyak et al. used for INM-~~ a similar term (I:"~ in their notation). A direct comparison determines the transmission coefficient tnm where kf is the Fermi wave vector in the NM. Note, that the coefficient in Eq and tnm are proportional to the number of conducting channels, which reduces the number of free fitting parameters. Since gfl x k;/4 7r [157], the transmission coefficient is = ID is present only in the NM. It represents the flux of non-equilibrium spins away from the FM/NM interface into the NM bulk. 6MN relaxes back to equilibrium with the rate of l/rsfi Since we have six unknown wave amplitudes in each layer we require six boundary conditions at each interface between two adjacent layers. Two boundary conditions arise from the continuity of the h- and e-field at the interface and another four equations come from the interface torque equation for magnetic moment m, and m,

125 CHAPTER 6. SEMICLASSICAL THEORY OF THE SPIN TRANSPORT 107 Figure 6.2: Spin currents at the interface between FM and NM. The torque equation is written for the full circles. Figure (a) corresponds to the net spin flow for the FM layer and (b) corresponds to the net spin flow for the NM spacer. at each side of the interface. The interface torque equations include the spin currents defined in Eqs , see Fig The complete set of boundary conditions for the first FM/NM interface is where superscripts and " label quantities in the ferromagnetic and non-magnetic layer, respectively. Eqs and 6.19 represent the continuity of the internal electromagnetic fields. Eqs and 6.21 correspond to the magnetic boundary conditions at the side of the FM and Eqs and 6.23 represent the magnetic boundary con-

126 CHAPTER 6. SEMICLASSICAL THEORY OF THE SPIN TRANSPORT 108 ditions at the side of the NM, see Fig The boundary conditions for the second interface are rather similar. The microwave absorption is calculated using Pointing vectors of the incident and reflected waves. 6.3 Results and discussion The theoretical model presented above enables one to investigate magnetic properties of ferromagnetic layers of arbitrary thicknesses. There are no limitations to the ultrathin limit since the exchange interaction and Maxwell's equations are taken fully into account. The equations of motion for the FM layer includes the spin pumping term which accounts for the additional damping mechanism in FM/NM multilayers. The spin transport inside the NM spacer is considered to be diffusive. The qualitative comparison between the experimental results and theory are presented Single magnetic layer In Section we have derived the resonance condition for an ultrathin magnetic medium. It has been shown, that the effective magnetization 47rMeff is written as where KiI represents the strength of the interface perpendicular uniaxial anisotropy. In our model, K:I enters the magnetic boundary conditions, see Eq For a given strength of K:I, one can evaluate the effective demagnetizing field 47rMf;" using where HFMR represents the FMR field calculated from the complete theory. The values of 47rMi;" as a function of dfm evaluated for Kz, = 0.75 erg/cm2 are shown in Fig. 6.3a. The sold line represents the strict l/dfm dependance, see Eq Clearly, there is no significant difference up to the thickness of 300 ML. From the experimental point of view, the strength of Ki, is evaluated from the measured values of 47rMeff by the least-square-fit using Eq One can proceed in

127 CHAPTER 6. SEMICLASSICAL THEORY OF THE SPIN TRANSPORT Figure 6.3: (a) The effective demagnetizing field perpendicular to the sample plane 47rMeff as a function of l/dfe. The circles represent the values evaluated from the complete theory, see Eq. 6.25, for Ki, = 0.75 erg/cm2. The blue solid line corresponds to the Eq calculated for the same strength of the interface perpendicular uniaxial anisotropy. (b) The relative difference in the effective uniaxial perpendicular field 6Hu1, see Eq as a function of the Fe thickness evaluated at f = 24 GHz. the same way using the values of 47rMefi evaluated from the complete theory. Using the thickness range from ML, the value of Ki, is found to be ( f ) erg/cm2, which represents less that 2 % error. However, if one analyzes the data from the thickness range between 100 and 200 ML, the value of Ki, is found to be (0.805 f 0.001) erg/cm2, which represents an error of about 7 %. as The relative difference in the effective uniaxial perpendicular field bhul is defined is plotted in Fig. 6.3b. For dfm -+ 0, the full theory and a simple l/dfm dependance give identical results. The simple l/dfm dependance underestimates the strength of the uniaxial perpendicular interface anisotropy. The relative difference is 10 % at dfm = 100 ML and reaches 20 % at dfm = 350 ML. In our thickness range between 5 to 40 ML, the relative error is below 5 %. This is in a agreement with calculations by F'rait and F'raitovk [30]. In the theoretical introduction (Section 2.2.2) we have discussed qualitatively the influence of the finite exchange interaction on the FMR linewidth. Fig. 6.4

128 CHAPTER 6. SEMICLASSICAL THEORY OF THE SPIN TRANSPORT 110 shows the total FMR peak-to-peak linewidth, AHp-,, as a function of the FM layer thickness dfm calculated using the full theory. There are two distinct regions: (i) For dfm < 0.5pm, AHp-p is dominated by the intrinsic damping Gint of a single layer and (ii) for dfm > 0.5 pm, the additional broadening arises from eddy currents. In the thick limit regime dfm > 1 pm the FMR linewidth reaches a constant value, which corresponds to the exchange conductivity limit AHfU", see Tab The sharp maxima of the FMR linewidth for the well-defined thicknesses of the ferromagnetic layer are quite surprising. At larger thicknesses, the spin-waves are generated. They appear at a lower field compared to the FMR field, see t = 0.2 pm in Fig With increasing thickness, the spin-wave approaches the FMR resonance and its amplitude increases. When the spin-wave resonance field appears within the FMR linewidth, the interaction results in a strongly distorted resonance line. A similar effect is observed for higher order spin-waves. However, the effect becomes less pronounced with increasing thickness. Spin-wave resonance in various materials has been studied since the seventies, see e.g To our knowledge, no such effect has been reported so far Spin pumping effect The FMR linewidth can be investigated when spin-pumping is included, see Fig The strength of spin-pumping gt1 is related to the density of conduction electrons per spin in the NM, see Eq. 6.16, and ranges between 1-2 x 1015 ~ m-~. Let us assume that the surrounding of the FM layer acts as a perfect spin sink; the spin momentum which leaves the FM layer is fully absorbed. This situation corresponds to the limit, in which the transmission coefficient tnm = 0, see Eq and It has been shown in Section 5.4.2, that in the ballistic limit this can be realized by the second FM layer which acts as a perfect spin sink. This results in the maximum additional damping. Note, that the additional FMR broadening due to the spin-pumping always scales like l/dfm. For dfm > 50 nm the additional interface damping is negligible; the difference in the FMR linewidth with and without spin pumping is less than 1 Oe. It has been shown in Section that the l/dfm dependance deviates for a thickness less than the spin coherence length, see Fig. 6.5b. However, in our calculation, there is no limit for the FM layer thickness. This is due to the fact, that one uses the classical limit; quantum coherence effects have been neglected. This implies, that the spin pumping and spin absorption occurs right at the inter-

129 CHAPTER 6. SEMICLASSICAL THEORY OF THE SPIN TRANSPORT 111 Fe thickness [prn] External dc field [Oe] Figure 6.4: The FMR linewidth calculated for Fe at 10 GHz as a function of the Fe layer thickness. The Gilbert damping G = 1.4 x lo8 s-'. The maxima correspond to the enhancement of the FMR linewidth due to the presence of spin waves. The amplitude of the spin-wave resonance increases as it approaches the FMR field. The hybridization between the FMR and spin-wave resonances distorts dramatically the absorption lines leading to the increase of the peak-tepeak linewidt h, A Hp-,.

130 CHAPTER 6. SEMICLASSICAL THEORY OF THE SPIN TRANSPORT d,, [nml lld,, [llnm] Figure 6.5: (a) The FMR linewidth AHp-,, as a function of the FM layer thick- ness dfm calculated at 10 GHz. The dashed line represents the intrinsic magnetic relaxation and the solid line includes the additional damping due to spin pumping, gt1 = 1 x 1015 ~ m-~. The magnetic properties correspond to Fe grown by MBE, see Tab The Gilbert damping was set equal to 1.4 x 10' s-'. (b) The additional FMR linewidth as a function of l/dfm. The red symbols correspond to the experimen- tal results obtained from the 20 Au/40 Fe/40 AuldFM Fe/GaAs(001) and 20 AuldFM Fe/GaAs(001) structures. face; no minimum thickness of FM medium is required. However, it has been shown in Section that the l/dfm dependance deviates for the thickness below the spin coherence length, see Fig. 6.5b. The l/dfm dependance has been observed by Mizukami et al. [I681 in permalloy (Py)/Pd and Py/Pt samples prepared on glass substrates by rf sputtering. The Py thickness was varied from 2 to 10 nm. In this thickness range, the additional FMR linewidth was inversely proportional to the Py thickness FM/NM bilayer The NM overlayer on its own can act as a partial spin sink [167, For small NM thicknesses (dnm << Xsd), the spin momentum accumulates in the NM spacer and the back flow INM+~M compensates the spin pumping contribution resulting in no increase of the FMR linewidth. As the thickness of NM becomes comparable to the spin diffusion length, the spin relaxation in the NM spacer acts as a partial spin sink leading to a broadening of the FMR line. However, the additional FMR broadening is

131 CHAPTER 6. SEMICLASSICAL THEORY OF THE SPIN TRANSPORT 113 small compared to the broadening obtained in FM/NM/FM double layers. This can be understood using the resistor model [167, In the limit, in which the thickness of NM is comparable to the spin diffusion length Asd, the strength of the spin pumping is determined by the effective interface mixing resistivity l/geff, which is given by where ~ N M represents the resistivity of the NM overlayer. The maximum value of the spin resistance per unit area of NM is determined by the spin diffusion length Asd. For further discussion it is useful to define a ratio between the spin-flip relaxation time and the electron relaxation time The spin diffusion length Asd is then expressed as where A* is electron mean free path in NM. It has been shown by Yang et a1 [170], that for simple paramagnetic materials such as Ag and Cu, E = 200 and 100, respectively. Elezzabi et a1 [I711 have shown that in polycrystalline gold samples, E = 2000 at RT. The transmission electron spin resonance experiments by Monod et a1 [I721 gave a rough estimate for E in a thin Au foil of w 10. The Au thickness dependance of the FMR linewidth is shown in Fig No appreciable additional FMR linewidth was observed. In our case, for the Au grown on Fe/GaAs(001) templates, the mean free path in Au was determined to be 38 nm [153]. Assuming a Fermi velocity UF = 1.4 x lo8 cm/s, the electron relaxation time rel = 2.7 x 10-l4 s. Assuming E = 20, the spin diffusion length Asd = 70 nm (350 ML). Therefore, the thicknesses of the Au spacer shown in Fig. 6.6 are much smaller than the spin diffusion length. In this case, the rf magnetization accumulates in the NM spacer and the back flow INM+FM compensates the spin pumping contribution resulting in no increase of the FMR linewidth. The strength of the spin pumping g~l was determined from the electron density in Au using Eq. 5.14; it was found to be 1.0 x 1015 crnp2. This leads to the Gilbert damping due to spin pumping

132 CHAPTER 6. SEMICLASSICAL THEORY OF THE SPIN TRANSPORT 114 Au thickness [ML] Figure 6.6: The total FMR linewidth in da, Au/16 Fe/GaAs(001) samples as a func- tion of the gold thickness measured at f = 24 GHz. The solid blue line represents the calculated values assuming the strength of the spin pumping gtl = 1.3 x 1015 ~m-~, the electron relaxation time re, = 2.7 x 10-l4 s, and the spin-flip relaxation time r,f = 50 x 10-l4 S. G,, = 1.3 x 10' s-i which is in an agreement with values found in Fe/Au/Fe double layers [173], see Section The results for the Fe/Pd bilayers are shown in Fig For small Pd thicknesses, the results are identical to those found in the Fe/Au sample. As the thickness of the Pd layer becomes comparable to the spin diffusion length, the spin relaxation in the NM spacer acts as a spin sink leading to a broadening of the FMR line. The calculations were carried out for a Fermi velocity v~ = 1.2 x 10' cm/s [I741 and an electron relaxation time re, = 0.7 x 10-l4 S. The maximum increase of the FMR linewidth for dpd + cm is determined by gt~ and rsf. The experimental thickness dependence in Fig. 6.7 can be explained by using g ~l = 1.6 x 1015 cm-2 and r,f = 0.9 x 10-l4 s, which yields E = 1.3. The value of g ~l seems rather high. Anderson [I751 quoted the number of elec- trons per Pd atom to be Using simple a relation between electron density and g~l, see Eq. 6.16, yields g ~l = 0.8 x 1015 ~ m-~. However, the Fermi surface of Pd is quite complex. Eq is only valid for simple metals like Au or Cu. Earlier stud-

133 CHAPTER 6. SEMICLASSICAL THEORY OF THE SPIN TRANSPORT 115 Pd thickness [ML] Figure 6.7: The total FMR linewidth in Au/dpd Pd/Fe/GaAs(OOl) samples as a function of the palladium thickness measured at f = 24 GHz. The solid blue line represents the calculated values assuming the strength of the spin pumping g~l = 1.6 x 1015 crnp2, the electron relaxation time re, = 0.7 x 10-l4 s, and the spin-flip relaxation time r,f = 0.9 x 10-l4 S. ies of the Au/Pd/Au structures have shown a large exchange (Stoner) enhancement in palladium It has been shown by sim~nek and Heinrich [I771 that Stoner enhancement can increase the spin pumping mechanism. Similar results were found by Mizukami and coworkers [178,179] in dc, Cu/Py/Cu/Glass samples; dc, = nm. Since the spin diffusion length in Cu XSd M 200 nm, they observed an increase in the FMR linewidth for thick Cu layers. The increase is rather small (about 5 Oe) since Cu, like Au, is a poor spin sink due its weak spin-flip scattering and long spin diffusion length. A broadening of the FMR has also been observed by Heinrich et al. 1371, when a thin Fe layer was deposited on a Ag(001) substrate. The Gilbert damping increased from 0.65 x lo8 s-i for 24 ML to 5.7 x lo8 s-' for 4 ML of Fe. Considering the same strength of spin pumping for Ag as for Au gtl = 1.0 x lol5 ern-', T,, = 3.5 x 10-l4 s, and E = 100 results in a 3-fold increase of the Gilbert damping over the same thickness range. However, a zero frequency offset AH(0) was observed which indicated the presence of an extrinsic contribution to the magnetic damping, which can increase the Gilbert parameter as well.

134 Chapter 7 Conclusions High quality crystalline Fe/MgO/Fe-whisker(001) magnetic tunnel junctions (MTJs) were prepared by means of MBE. Thin MgO films were found to grow in an almost perfect layer-by-layer manner. Structural properties were investigated by means of RHEED, LEED, and STM. The MgO films were found to grow pseudomorphically with the lattice constant of Fe for up to 5 ML in thickness. After 5 ML, the compressive stress was gradually released and a network of misfit dislocations was created. The misfit dislocation lines were oriented along the (100) directions of the MgO lattice and were imaged using STM. The network of misfit dislocations resulted in additional LEED satellite spots around the main diffraction peaks. The additional spots maintain the 4-fold symmetry of the MgO lattice. The separation between the principal and additional spots increased with increasing energy of the electron beam. This behavior can be explained by atomic corrugations of the MgO surface resulting in additional reciprocal rods, which are inclined by the angle [ with respect to the reciprocal rods of the averaged MgO plane. The angle [ was found to decrease with increasing MgO thickness. Therefore one can conclude that the misfit dislocations are buried at the MgO/Fe-whisker(001) interface. The electron tunneling characteristics were investigated by in-situ STM and tun- neling spectroscopy. The tunneling I-V characteristics were found to be asymmetric with a sharp increase of the tunneling current for bias voltages VB > 3 V. NO mea- surable tunneling current was observed for negative bias voltages up to -4.5 V. Local I-V curves for MgO layers thicker than 8 ML revealed a barrier height of 3.6 V cor- responding to a perfect MgO barrier. For thinner MgO films, the barrier height was smaller which can be explained by the formation of FeO(001) at the MgO/Fe-whisker

135 CHAPTER 7. CONCLUSIONS 117 interface. For negative bias voltages, localized spikes in the tunneling current were observed on the lateral scale of 2 x 2 nm2. These defects are not caused by pin holes; they can be explained by the presence of interband electronic states which were created by local crystalline defects. The total tunneling current was dominated by areas which exhibit perfect tunneling properties. The observation of localized defects in the MgO/Fe-whisker and Fe/MgO/Fe-whisker structures is a strong indication of ballistic transport in crystalline Au/Fe/MgO/Fe-whisker(001) systems. The STM spectroscopy in high crystalline quality MTJs allows one to investigate the local tunneling properties of buried tunneling barriers. The magnetic properties of thin Fe layers grown on MgO(001) wafers were investigated using FMR. The magnetocrystalline anisotropies were described by bulk and interface contributions. The bulk properties were close to those found in bulk Fe crystals. A strong uniaxial perpendicular interface anisotropy was found for the Fe/MgO interface, KiI = (1.18 f 0.03) erg/cm2, which is one of the largest reported values for 3d transition metals. BLS and MOKE studies were used to determine the strength of the interlayer exchange coupling between a thin Fe film and an Fe-whisker in the Au/Fe/MgO/Fewhisker(001) structures. No measurable coupling was found for MgO thicknesses ranging from 5 to 20 ML. MOKE microscopy has revealed that the residual magnetic stray field of the whisker domain wall magnetizes the Fe film, causing the direction of the magnetization of the thin film to be perpendicular to the magnetization direction in the Fe-whisker substrate. This interaction results in the mutual perpendicular orientation of the magnetic moments in the Fe-whisker and the Fe thin film. This is a necessary step in TMR measurements. An AFM with conducting tip operating in an external dc field was employed to measure TMR in the Au/Fe/MgO/Fe-whisker samples. The AFM feed-back was used to establish a good ohmic contact between the AFM tip and the upper Au electrode. In this configuration, one was able to measure TMR of almost 100% at RT for bias voltages above 2 V. However, this was not a typical result. Structural damage of the crystalline tunnel junction by the AFM tip resulted in charging effects in the MgO layer. Spin dynamics and spin transport have been investigated in Cr/Fe and Au/Fe multilayers grown on GaAs(001) templates. The non-magnetic overlayer did not strongly affect the magnetocrystalline anisotropies. In both cases, the magnetic anisotropies

136 CHAPTER 7. CONCLUSIONS 118 were equal to those found in bulk Fe crystals modified only by the sharply defined interface anisotropies. However, a profound difference was observed in the spin relaxation mechanism. The Au/Fe/GaAs(001) samples have shown strictly Gilbert damping, negligible zero-frequency offset, and the strength of the damping parameter was found to be (1.37 f 0.06) x lo8 s-'. For the in-plane FMR configuration, the Cr/Fe/GaAs(001) samples have shown an appreciable zero-frequency offset, AH(0) 2 80 Oe, which measures the strength of an extrinsic contribution to the magnetic damping. On the other hand, for the perpendicular FMR configuration, no measurable zero-frequency offset was observed in the 20 Cr/15, 20 Fe/GaAs(001) samples, and the Gilbert damping parameter was found to be (1.51 f 0.02) x lo8 s-'. The extrinsic contribution to damping in Fe/Cr multilayers was found to be caused by two-magnon scattering. The absence of extrinsic contributions to the magnetic damping and narrow Lorentzian FMR peaks in the Au/Fe/GaAs(001) magnetic single layers have allowed us to study spin transport in the Au/Fe/Au/Fe/GaAs(OOl) magnetic double layers. The experiments were carried out for a Au spacer much thinner than the electron mean free path, and therefore the spin current, generated by the rf precessing magnetization, propagated ballistically across the Au spacer. We found, that even in the absence of static interlayer exchange coupling, the magnetizations were still coupled through the normal metal (NM) spacer by emitting and absorbing non-equilibrium spin currents. The ultrathin Fe layer in double layer structures acquired an additional interface Gilbert damping compared to the Fe film in the magnetic single layers. For a 16 ML thick Fe layer, the additional Gilbert damping parameter Gsp was found to be (1.11 f 0.03) x lo8 s-l and only weakly dependant on the crystallographic direction. Non-local Gilbert damping can be described by a spin-pump and a spin-sink. The precessing magnetization acts as a spin pump and the second ferromagnetic (FM) layer acts as a spin momentum sink. The electron scattering at the Fe/Au interface is partially diffuse and in this case, the spin pumping theory is simple. The strength of the non-local Gilbert damping can be evaluated by using the electron density in the NM; no other details of the band structure are required. For the Fe/Au/Fe multilayers, the spin pump theory predicts Gsp = 1.2 x lo8 s-l, which is in a very good agreement with the experimental value of (1.11 f 0.03) x lo8 s-l. This agreement provides strong evidence that the spin-pump and spin-sink theory is valid and needed to account for non-local damping in magnetic multilayers.

137 CHAPTER 7. CONCLUSIONS 119 A semi-classical model of the spin momentum transfer in FM/NM structures was formulated. This theory is valid for measurements where the thickness of the NM layer becomes comparable to the spin diffusion length. The model is based on the Landau- Lifshitz-Gilbert equation of motion and the exchange interaction in FM, and the spin diffusion equation in the NM spacer. The internal rf magnetic field is treated by employing Maxwell's equations. The spin pump and spin sink concepts are employed to account for the spin momentum transfer. It has been shown, that a thick NM layer can act also as a spin momentum sink. In the case of a Au overlayer, only a small increase of the FMR linewidth (a 3 Oe at f = 24 GHz) has been observed for a 120 ML thick film. This can be explained by the long spin diffusion length in Au, Ad = 70 nm (350 ML). For Pd, the increase of the FMR linewidth was found to be 30 Oe at f = 24 GHz, and saturated for dpd > 30 ML. This result implies that the spin diffusion length in Pd is short, Asd = 4 nm (20 ML). In this case, the spin-flip relaxation time r,f is only 1.3 x longer than the electron relaxation time r,~.

138 Appendix Magnetic anisot roples This Appendix includes an evaluation of the effective field Heff for the parallel and perpendicular FMR configuration. The magnetocrystalline anisotropy energy and the demagnetizing energy which is associated with the magnetization component perpen- dicular to the film surface will be included. The solution will be found in the small an- gle approximation; the total magnetization vector M can be written as M = M, +m, see Section The Cartesian coordinate system is always chosen in such a way, that the direction of the z-axis is parallel to the sample normal. In the ultrathin limit, the effective field Heff is given by the magnetization deriva- tive of the magnetic Gibbs (free) energy density E (see Section 2.1.1) The Gibbs energy E contains the Zeeman energy of the external dc and rf magnetic field Ez, the demagnetizing energy which is associated with the magnetization component perpendicular to the film surface ED, and the magnetocrystalline anisotropy energy Ea,i. A.l Parallel configuration In the parallel FMR configuration, the external dc field H and the saturation magnetization vector M, lie in the sample plane, see Fig. A.1. The Zeeman, demagnetizing, and magnetocrystalline energy densities can be written as [6]

139 APPENDIX A. MAGNETIC ANISOTROPIES Figure A. 1: Coordinate system Kll1 4 K Kull (M. U)2, 2 2 M: (A.4) &mi = -- (a, + a:) - -a, - Kula, - - where 47rD is the demagnetizing factor perpendicular to the sample surface, a,, a,, and a, are directional cosines with respect to the [loo], [OlO], and [OOl] crystallo- graphic directions (ai = Mi/Ms, i = x, y, z), Kill and KuIl represent the strength of the in-plane four-fold and uniaxial anisotropy, respectively. KUI characterize the strength of the uniaxial perpendicular anisotropy, where u is the unit vector in the direction of the in-plane uniaxial axis where cp, direction. u = (COS cp,, sin cp,, 0), (A-5) is the angle between the uniaxial axis direction and [loo] crystallographic The evaluation of the effective field is usually solved by rotating the original Carte- sian coordinate system which is related to the crystallographic directions by angle c p ~ around [OOl] direction, where PM is the angle between the static magnetization vector M, and the [loo] crystallographic direction, see Fig. A.la. This transformation effects both in-plane components of magnetization. The rotation matrix can be written as ( COS (PM sin c p ~ M= - sincp~ coscp~

140 APPENDIX A. MAGNETIC ANISOTROPIES 122 The anisotropy energy density Eani in the new coordinate system can be written as K,l 1 Ms - 7 [M: (1 + cos 2p) + Mx M, sin 2p + M: (1 - cos 2p) ], (A.7) where p = cp, - c p ~. The saturation magnetization in the new coordinate system is parallel to the x-axis, see Fig. A.la It is easy to derive the magnetization derivatives and the resulting effective fields are given by (A.9) (A. lo) (A. 11) where c p is ~ the angle between the direction of the external dc field H and [loo] crystallographic direction, see Fig. A. la. A.2 Perpendicular configuration In the perpendicular configuration, the external dc field and the saturation magnetization are oriented perpendicular to the sample plane, see Fig. A.lb. We define the external field and magnetization vectors as (A. 12) (A. 13)

141 APPENDIX A. MAGNETIC ANISOTROPIES 123 The energy densities associated with the Zeeman, demagnetizing, and magnetocrys- talline energy densities can be written in the analogy to Eq. A.2 E. = - - Kill 4 an1 K (a, + a:) - -a, 2 - Ku1a, -- Kull (A. 15) M: (M. u)2, (A. 16) where Kll is the perpendicular 4-fold anisotropy. From the symmetry of the problem, we can place x-axis along [loo] direction and y-axis along [OlO], see Fig. A.1b. The effective fields can be expressed keeping only linear terms in small (transversal) components (A. 17) (A. 18) 2KUl l M," - (m, sin p, cos p, + my sin2 p,), - A.3 Effective magnetic anisotropy 2Ku1+=). MS MS (A.19) The effective anisotropy constants (KlI1, Kull, and KuI) can be expressed in terms of bulk and interface magnetic properties [3, 6, 71. Let us assume, that all atomic magnetic moments posses the bulk magnetic properties. The interface atoms have additional magnetic anisotropies which originate in the broken symmetry at the in- terface. The interface anisotropies are usually expressed as energies per unit area [6]. After simple algebraical steps, the effective anisotropy fields can be expressed as (A. 20) where d is the film thickness and subscripts A and B correspond to the film interfaces. Superscripts and " represents the bulk and surface contribution to the appropriate

142 APPENDIX A. MAGNETIC A NISOTROPIES 124 magnetic anisotropy. The effective anisotropy fields in ultrathin magnetic layers are given by the sum of the bulk anisotropy fields and the surface effective fields which scale linearly with l/d. The detailed description and discussion of the surface anisotropy fields can be found elsewhere [180, 181, 1821.