Femtosecond Heating as a Sufficient Stimulus for Magnetization Reversal

Transcription

1 Femtosecond Heating as a Sufficient Stimulus for Magnetization Reversal T. Ostler, J. Barker, R. F. L. Evans and R. W. Chantrell Dept. of Physics, The University of York, York, United Kingdom. Seagate, August 2012

2 Ostler et al., Nature Communications, 3, 666 (2012). Atomistic model prediction & experimental verification (submitted) Atxitia et al., Arxiv: (2012). Analysis of origin of phenomena via ferrimagnetic LLB.

3 Outline Model outline: atomistic LLG of GdFeCo/NiFe and laser heating Static properties of GdFeCo and comparison to experiment Differential demagnetisation Transient dynamics under laser heating Deterministic switching using heat and experimental verification Mechanism of reversal (atomistic and LLB analysis)

4 Background Inverse Faraday[1,2] effect relates E-field of light to generation of magnetization. σ + σ - Can be treated as an effective field with the chirality determining the sign of the field. Inverse Faraday effect Control of magnetization of ferrimagnetic GdFeCo[3] High powered laser systems generate a lot of heat. What is the role of the heat and the effective field from the IFE? M(0) [1] Hertel, JMMM, 303, L1-L4 (2006). [2] Van der Ziel et al., Phys Rev Lett 15, 5 (1965). [3] Stanciu et al. PRL, 99, (2007).

5 A model of laser heating Recall for circularly polarised light, magnetization induced is given by: Laser input P(t) For linearly polarized light cross product is zero. Energy transferred as heat. Two-temperature[1] model defines an electron and phonon temperature (T e and T l ) as a function of time. Electrons e - e - e - e - G el Lattice Heat capacity of electrons is smaller than phonons so see rapid increase in electron temperature (ultrafast heating). Two temperature model [1] Chen et al. International Journal of Heat and Mass Transfer. 49, (2006)

6 Model: Atomistic LLG For more details on this model see Ostler et al. Phys. Rev. B. 84, (2011) We use a model based on the Landau-Lifshitz-Gilbert (LLG) equation for atomistic spins. Time evolution of each spin described by a coupled LLG equation for spin i. Hamiltonian contains only exchange and anisotropy. Field then given by: is a (stochastic) thermal term allowing temperature to be incorporated into the model.

7 Model: Exchange interactions/structure For more details on this model see Ostler et al. Phys. Rev. B. 84, (2011) GdFeCo is an amorphous ferrimagnet. Assume regular lattice (fcc). In the model we allocate Gd and FeCo spins randomly. We do the same for NiFe but all exchange interactions are ferromagnetic. Fe-Fe and Gd-Gd interactions are ferromagnetic (J>0) Fe-Gd interactions are antiferromagnetic (J<0) Fe Fe-Fe, Ni-Ni and Ni-Fe interactions are ferromagnetic (J>0) Gd Ni Fe Atomic Level Sub-lattice magnetizati on Atomic Level Sub-lattice magnetizati on

8 Bulk Properties Exchange values (J s) based on experimental observations of sublattice magnetizations as a function of temperature. Compensation point and T C determined by element resolved XMCD. Variation of J s to get correct temperature dependence. Validation of model by reproducing experimental observations. compensation point Figure from Ostler et al. Phys. Rev. B. 84, (2011)

9 Bulk Properties Experimental hysteresis loops (measured for both Fe and Gd species) show out-of-plane magnetisation (see reference below for sample loops). Experiments of various compositions of GdFeCo (with different compensation points) show diverging coercive field at compensation point. Qualitative agreement with atomistic model. Figure from Ostler et al. Phys. Rev. B. 84, (2011)

10 Summary so far Atomic level model of multi-component alloys A way of describing heating effect of fs laser We investigate dynamics of GdFeCo and NiFe and show differential sublattice dynamics and a transient ferromagnetic state. Then demonstrate heat driven reversal via the transient ferromagnetic state. Outline explanation is given for reversal mechanism.

11 Demagnetisation in ferromagnetic Ni 50 Fe 50 Femtosecond heating shows decoupled behaviour in NiFe. Sublattice magnetizations are measured by element specific XMCD. Each sublattice demagnetises on a different timescale. Experiment Model results Experiments performed by I. Radu

12 Demagnetisation in ferrimagnetic GdFeCo High fluence completely demagnetises GdFeCo as temperature quickly increases over the Curie temperature. Again, dispite strong antiferromagnetic exchange coupling the two sublattices demagnetise at different rates. Experiment Model results Experiments performed by I. Radu

13 Parametric study By fitting the magnetisation dynamics to a double exponential function the time constants can be determined, for each sublattice. The damping parameter greatly effects the relaxation rates as one would expect. For high damping the rate of energy transfer into the system leads to almost identical rates.

14 Parametric study Variations in the composition of Ni x Fe 1-x show that the exchange gives the overall trend in demagnetisation times. The difference in the moments drives the difference in the relaxation time.

15 Timescale of Demagnetisation Characteristic demagnetisation time can be estimated as[1]: Experiment GdFeCo has 2 sublattices with different moment (µ). Model results Even though they are strongly exchange coupled the sublattices demagnetise at different rates (with µ). [1] Kazantseva et al. EPL, 81, (2008). Figures from Radu et al. Nature 472, (2011).

16 Transient Ferromagnetic-like State Laser heating in applied magnetic field of 0.5 T System gets into a transient ferromagnetic state at around 400 fs. Transient state exists for around 1 ps. Figure from Radu et al. Nature 472, (2011). As part of a systematic investigation we found that reversal occured in the absence of an applied field.

17 Numerical Results of Switching Without a Field No magnetic field GdFeCo Very unexpected result that the field plays no role. Is this determinisitic?

18 Sequence of pulses Do we see the same effect experimentally?

19 Experimental Verification: GdFeCo Microstructures - two microstructures with opposite magnetisation - Seperated by distance larger than radius (no coupling) Initial state XMCD 2mm Experimental observation of magnetisation after each pulse.

20 Effect of a stabilising field What happens now if we apply a field to oppose the formation of the transient ferromagnetic state? Is this a fragile effect? B z =10,40,50 T 10 T 40 T GdFeCo 50 T Suggests probable exchange origin of effect (more later).

21 Importance of Moments As previously stated, the short time-scale demagnetisation time is governed by the magnitude of the correlator. If we artificially make the local magnetic moments equal, the correlators are equal and no switching occurs. μ TM =μ RE

22 Landau-Lifshitz-Bloch equation of motion So far we have used a model for each atomic magnetic moment. A macro-spin approach should show the same behaviour. We write a Landau-Lifshitz-Bloch (LLB) equation for the TM and RE sublattices. Usual precession and damping term Longitudinal relaxation of magnetisation (submitted) Full details of model from Atxitia el al. Arxiv

23 Relaxation Rates Temperature dependent relaxation rates are important for ultrafast switching. Sign in highlighted area below changes sign. However, this change in sign alone cannot result in switching! Different longitudinal relaxation is very important but does not produce switching. (submitted) Full details of model from Atxitia el al. Arxiv

24 Linearising the LLB Equation From the atomistic simulations, after the pulse is turned off we assume that. Linearise Note: to simplify the analysis we have assumed a square pulse from 0K->1500K->0K

25 System Close to Reversal Analysis shows that when the temperature is lowered there is a transfer of angular momentum from the (unstable) linear (m z ) component to transverse (ρ). Requires a small initial transverse component. T Different pulse heights lead to different state before pulse turned off. t LLB LLG

26 Mechanism of Reversal After heat pulse TM moments more disordered than RE (different demagnetisation rates). On small (local) length scale TM and RE random angles between them. The effect is averaged out over the system. FMR Exchange Exchange mode is excited when sublattices are not exactly anti-parallel.

27 Perpendicular Component LLB analysis shows that we require a perpendicular component to induce switching. no transverse component, no switching (dashed) LLB simulation small transverse component leads to switching (solid) In LLG simulations, high thermal fluctuations give rise to local perpendicular component. Note: high frequency of oscillations associated with exchange mode.

28 Experimental Prediction Could we see reversal via this dynamical path experimentally? Effect is averaged out over large systems. Plotting transverse component of transition metal for different system sizes. LLG

29 Summary Demonstrated numerically switching can occur using only a heat pulse without the need for magnetic field. Switching is deterministic. Verified the mechanism experimentally in microstructures (and thin films, see paper). Shown that stray fields play no role. The magnetic moments are important for switching. Demonstrated a possible explanation via a local excitation of exchange mode by decreasing system size and observing induced precession.

30 Acknowledgements Experiments performed at the SIM beamline of the Swiss Light Source, PSI. Nederlandse Organisatie voor Wetenschappelijk Onderzoek (NWO), de Stichting voor Fundamenteel Onderzoek der Materie (FOM). The Russian Foundation for Basic Research (RFBR). European Community s Seventh Framework Programme (FP7/ ) Grants No. NMP3- SL (UltraMagnetron) and No (FANTOMAS), Spanish MICINN project FIS C02-02 European Research Council under the European Union s Seventh Framework Programme (FP7/ )/ ERC Grant agreement No (Femtomagnetism). NASU grant numbers and Thank you for listening.

31 Energetics of system described by Hamiltonian: Numerical Model Dynamics of each spin given by Landau-Lifshitz-Gilbert Langevin equation. Effective field given by: Moments defined through the fluctuation dissipation theorem as:

32 Transient Ferromagnetic-like State Laser heating in applied magnetic field of 0.5 T For short time sublattices align against TM-RE exchange interaction State exists for around 1ps Figure from Radu et al. Nature 472, (2011).

33 The Effect of Compensation Previous studies have tried to switch using the changing dynamics at the compensation point[ref]. Simulations show starting temperature not important. Supported by experiments on different compositions of GdFeCo support the numerical observation.

34 Experimental Verification: GdFeCo Thin Films After action of each pulse (σ+) the magnetization switches, independently of initial state. Initially film magnetised up Fe Gd MOKE Similar results for film initially magnetised in down state. Beyond regime of all-optical reversal, i.e. cannot be controlled by laser polarisation. Therefore it must be a heat effect.

35 What about the Inverse Faraday Effect? Orientation of magnetization governed by light polarisation. Stanciu et al. PRL, 99, (2007) Does not depend on chirality (high fluence) Depends on chirality (lower fluence)

36 Importance of moments μ TM =μ RE

37 Linear Reversal Usual reversal mechanism (in a field) below T C via precessional switching At high temperatures, magnetisation responds quickly without perpendicular component (linear route[1]). Laser heating results in linear demagnetisation[2].

38 The Effect of Heat Heat Cool E Ordered ferromagnet Uniaxial anisotropy θ Heat (slowly) through T C Cool below T C E E 50% 50% M+ M- M+ M- System demagnetised M+ M- Equal chance of M+/M-

39 Inverse Faraday Effect σ+ Magnetization direction governed by E-field of polarized light. z Opposite helicities lead to induced magnetization in opposite direction. Acts as effective field depending on helicity (±). σ- z Hertel, JMMM, 303, L1-L4 (2006)

40 Outlook Currently developing a macro-spin model based on the Landau-Lifshitz-Bloch (LLB) formalism to further support reversal mechanism. How can our mechanism be observed experimentally? Time/space/element resolved magnetisation observation spin-spin correlation function/structure factor. Once we understand more about the mechanism, can we find other materials that show the same effect?

41 Differential Demagnetization Atomistic model agrees qualitatively with experiments Fe and Gd demagnetise in thermal field (scales with μ via correlator) Kazantseva et al. EPL, 81, (2008). Gd slow, ~1ps Fe fast, loses magnetisation in around 300fs Radu et al. Nature 472, (2011).

42 What s going on? 0 ps - Ground state 0.5 ps -T>T C Fe disorders more quickly (μ) 1.2 ps -T<T C precessional switching (on atomic level) -Exchange mode between TM and RE - Transient state 10 s ps time

43 Reversal Trivial solution in which transverse component is zero is unstable in regime of reversal. LLB Perturbations from zero lead to generation of perpendicular component in TM. This triggers the same motion of RE via angular momentum transfer. This process occurs on small length scales so effect can be averaged out in atomistic model. LLG By decreasing system size we see this effect.

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45 Differential demagnetization times

46 How Can Magnetization Be Reversed? Magnetic Field Circularly Polarised Spin Injection E B z E B z M+ M- M+ M-

47 The Effect of Heat E E 50% 50% M+ M- M+ M- M+ M- E E? M+ M- M+ M-

48 For more details on this model see Ostler et al. Phys. Rev. B. 84, (2011) Atomic Level Model of GdFeCo TM-TM and RE-RE interactions are ferromagnetic TM-RE interactions are anti-ferromagnetic Hamiltonian includes only exchange and anisotropy Fe Gd Atomic Level Macrospin Each spins motion is described by a Landau-Lifshitz- Gilbert equation Effective field in LLG augmented by thermal term at each time-step (temperature effects, more later):

49 Femtosecond laser induced magnetisation dynamics Atomistic modelling of non-equilibrium dynamic response Exchange interaction ~100 fs Femtosecond stimulation of magnetic materials Two sub-lattice ferrimagnetic material GdFeCo

50 Temp [K] θ M TM θ TM M TM Fe Laser heating M RE θ M RE θ RE M RE Fe disorders faster than Gd. B z Magnetic field Applied to system to prevent reversal of Fe Gd Once temperature is below T C, we have a distribution of angles between TM and RE spins. T e Locally mode associated with AFM exchange (optical). 500 T l

51 Overview Introduction Model Results Mechanism The story so far (motivation) Testing the The model Atomistic and how LLG to incorporate model laser heating model Numerical results Switching in a Experimental verification field Motivation Ferrimagnetic (all-optical exchange reversal) Key features interactions of the reversal process Switching Mechanism of reversal Twotemperature model of laser heating using heat alone Experimental verification AFM exchange driven switching

52 Introduction Model Results Mechanism Atomistic LLG model Testing the model Motivation (all-optical reversal) Ferrimagnetic exchange interactions Switching in a field Switching using heat alone AFM exchange driven switching Twotemperature model of laser heating Experimental verification

53 Introduction Introduction Motivation (all-optical reversal) Inverse Faraday effect Model Atomistic Landau-Lifshitz-Gilbert equation Ferrimagnetic exchange interactions Two temperature model of laser heating Results Testing the model Switching in a field Switching using heat alone Experimental verification Mechanism of reversal Exchange driven switching

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55 Two Temperature Model Equations solved using numerical integration to give electron and phonon temperature as a function of time. Heat capacity of electrons is smaller than phonons so see rapid increase in electron temperature (ultrafast heating). Example of solution of two temperature model equations Now we have changing temperature with time and we can incorporate this into our model. A semi-classical two-temperature model for ultrafast laser heating Chen et al. International Journal of Heat and Mass Transfer 49, (2006).

56 Numerical Results of Switching Without a Field As a result of systematic investigation discovered that no field necessary. Applying a sequence of pulses, starting at room temperature (a). Reversal occurs each time pulse is applied (b). Fe Gd Ground state ~1 ps ~2 ps Ground state

57 Mechanism of Reversal Ferrimagnets have two eigenmodes for the motion of the sublattices; the usual FMR mode and an Exchange mode. FMR Exchange Exchange mode is high frequency associated with TM-RE exchange. We see this on a local level. TM more disordered because of faster demagnetisation (smaller moment). Locally TM and RE are misaligned. Effect is averaged out because of random phase.

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59 Femtosecond Heating Experimental observations of femtosecond heating in Nickel shows rapid demagnetisation. Experiments on Ni Chance of magnetization reversal by thermal activation (not deterministic) but generally magnetization recovers to initial direction. Our goal was to develop a model to provide more insight into such processes. Figure from Beaurepaire et al. PRL 76, 4250 (1996).

60 Model: Thermal Term More Details The stochastic process has the properties (via FDT): Example of a single spin in a field augmented by thermal term. Each time-step Laser a Gaussian random number is generated heating (for x,y and z component of field) and multiplied by Magnetic square root of variance. Fe field applied to prevent Point to note: noise scales with T reversal of Fe and µ. If T changes then so Gd sublattice does size of noise. For more details on this model see Ostler et al. Phys. Rev. B. 84, (2011) Image from thesis of U. Nowak.

61 Mechanism of Reversal end of pulse If we decrease the system size then we still see reversal via transient state. RE For small systems a lot of precession is induced. Frequency of precession associated with exchange mode. TM TM For systems larger than 20nm 3 there is no obvious precession induced (averaged out over system). end of pulse Further evidence of exchange driven effect. TM sublattice