1. Femtosecond Heating as a Sufficient Stimulus for Magnetization Reversal HGST, San Jose, August 2012 Theoretical/Modelling Contributions T. Ostler, J. Barker, R. F. L. Evans and R. W. Chantrell Dept. of Physics, The University of York, York, United Kingdom. U. Atxitia and O. Chubykalo-Fesenko Instituto de Ciencia de Materiales de Madrid, CSIC, Cantoblanco, Madrid, Spain. D. Afansiev and B. A. Ivanov Institute of Magnetism, NASU Kiev, Ukraine.

2. Femtosecond Heating as a Sufficient Stimulus for Magnetization Reversal HGST, San Jose, August 2012 Experimental Contributions S. El Moussaoui, L. Le Guyader, E. Mengotti, L. J. Heyderman and F. Nolting Paul Scherrer Institut, Villigen, Switzerland A. Tsukamoto and A. Itoh College of Science and Technology, Nihon University, Funabashi, Chiba, Japan. A. M. Kalashnikova, K. Vahaplar, J. Mentink, A. Kirilyuk, Th. Rasing and A. V. Kimel Radboud University Nijmegen, Institute for Molecules and Materials, Nijmegen, The Netherlands.

3. Ostler et al., Nature Communications, 3, 666 (2012).

4. Outline Model outline: atomistic LLG of GdFeCo and laser heating Static properties of GdFeCo and comparison to experiment Transient dynamics under laser heating Deterministic switching using heat and experimental verification Mechanism of reversal

5. Background Inverse Faraday[1,2] effect relates E-field of light to generation of magnetization. Can be treated as an effective field with the chirality determining the sign of the field. [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, 047601 (2007). σ-σ- σ+σ+ Inverse Faraday effect M(0) 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?

6.  Recall for circularly polarised light, magnetization induced is given by:  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.  Heat capacity of electrons is smaller than phonons so see rapid increase in electron temperature (ultrafast heating). A model of laser heating Electrons e-e- e-e- e-e- two temperature model energy transfers Lattice e-e- G el Laser input P(t) Two temperature model [1] Chen et al. International Journal of Heat and Mass Transfer. 49, 307-316 (2006)

7. Model: Atomistic LLG For more details on this model see Ostler et al. Phys. Rev. B. 84, 024407 (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.

8. Sub-lattice magnetization Fe Gd Atomic Level Model: Exchange interactions/Structure For more details on this model see Ostler et al. Phys. Rev. B. 84, 024407 (2011) Fe-Fe and Gd-Gd interactions are ferromagnetic (J>0) Fe-Gd interactions are anti-ferromagnetic (J<0)  GdFeCo is an amorphous ferrimagnet.  Assume regular lattice (fcc).  In the model we allocate Gd and FeCo spins randomly.

9. 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. Figure from Ostler et al. Phys. Rev. B. 84, 024407 (2011) compensation point

10. 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, 024407 (2011)

11. Summary so far A way of describing heating effect of fs laser Atomic level model of a ferrimagnet with time  We investigate dynamics of GdFeCo 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.

12. Transient Dynamics in GdFeCo by XMCD & Model Figures from Radu et al. Nature 472, 205-208 (2011). ExperimentModel results  Femtosecond heating in a magnetic field.  Gd and Fe sublattices exhibit different dynamics.  Even though they are strongly exchange coupled.

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

14. Demagnetisation in ferrimagnetic GdFeCo Experiments performed by I. Radu Model results  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

15.  Characteristic demagnetisation time can be estimated as[1]:  GdFeCo has 2 sublattices with different moment (µ).  Even though they are strongly exchange coupled the sublattices demagnetise at different rates (with µ). Timescale of Demagnetisation Figures from Radu et al. Nature 472, 205-208 (2011).[1] Kazantseva et al. EPL, 81, 27004 (2008). Experiment Model results

16. Transient Ferromagnetic-like State Figure from Radu et al. Nature 472, 205-208 (2011). 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. 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  Very unexpected result that the field plays no role.  Is this determinisitic? GdFeCo No magnetic field

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

19. Experimental Verification: GdFeCo Microstructures XMCD 2m2m Experimental observation of magnetisation after each pulse. Initial state - two microstructures with opposite magnetisation - Seperated by distance larger than radius (no coupling)

20. Experimental Verification: GdFeCo Thin Films Initially film magnetised “up” Gd Fe 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. After action of each pulse the magnetization switches, independently of initial state.

21. What about the Inverse Faraday Effect? Stanciu et al. PRL, 99, 047601 (2007) Orientation of magnetization governed by light polarisation. Does not depend on chirality (high fluence) Depends on chirality (lower fluence)

22. What about the Inverse Faraday Effect?

23. 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.

24. 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? 10 T 40 T 50 T Suggests probable exchange origin of effect (more later). GdFeCo B z =10,40,50 T

25. 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. FMRExchange Exchange mode is excited when sublattices are not exactly anti-parallel.

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

27. μ TM =μ RE 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.

28. 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.

29. 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 (FP7/2007-2013) Grants No. NMP3- SL-2008-214469 (UltraMagnetron) and No. 214810 (FANTOMAS), Spanish MICINN project FIS2010-20979-C02-02 European Research Council under the European Union’s Seventh Framework Programme (FP7/2007- 2013)/ ERC Grant agreement No 257280 (Femtomagnetism). NASU grant numbers 228-11 and 227-11. Thank you for listening.

30. 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. FMRExchange Exchange mode is excited when sublattices are not exactly anti-parallel.

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

32. 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 1206.6672

33. Relaxation Rates  Temperature dependent relaxation rates are important for ultrafast switching.  Sign in highlighted area below changes sign. (submitted) Full details of model from Atxitia el al. Arxiv 1206.6672  However, this change in sign alone cannot result in switching!  Different longitudinal relaxation is very important but does not produce switching.

34. Experimental Prediction  Could we see reversal via this dynamical path experimentally?  Effect is averaged out over large systems. LLG

35. 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

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

37. 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. LLBLLG T t Different pulse heights lead to different state before pulse turned off.

38. Transient Ferromagnetic-like State Figure from Radu et al. Nature 472, 205-208 (2011). 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

39. Importance of moments μ TM =μ RE

40. 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].

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

42. Inverse Faraday Effect http://en.wikipedia.org/wiki/Circular_polarization  Magnetization direction governed by E-field of polarized light.  Opposite helicities lead to induced magnetization in opposite direction.  Acts as “effective field” depending on helicity (±). σ+σ+ σ-σ- z z Hertel, JMMM, 303, L1-L4 (2006)

43. 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?

44. Differential Demagnetization Atomistic model agrees qualitatively with experiments Fe and Gd demagnetise in thermal field (scales with μ via correlator) Fe fast, loses magnetisation in around 300fs Gd slow, ~1ps Radu et al. Nature 472, 205-208 (2011). Kazantseva et al. EPL, 81, 27004 (2008).

45. What’s going on? 0 ps time - Ground state 0.5 ps 1.2 ps -T>T C Fe disorders more quickly (μ) 10’s ps -T<T C precessional switching (on atomic level) -Exchange mode between TM and RE - Transient state

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

48. Differential demagnetization times

49. How Can Magnetization Be Reversed? Magnetic FieldCircularly PolarisedSpin Injection E BzBz E BzBz M+M-M+M-

50. The Effect of Heat E 50% EE ? E M+M-M+M- M+M-M+M- M+M-

51. Macrospin Fe Gd Atomic Level Atomic Level Model of GdFeCo For more details on this model see Ostler et al. Phys. Rev. B. 84, 024407 (2011) 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): TM-TM and RE-RE interactions are ferromagnetic TM-RE interactions are anti-ferromagnetic Hamiltonian includes only exchange and anisotropy

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

53. 1500 1000 500 0123 TeTe TlTl Time [ps] Temp [K] θ θ M TM M RE θ TM θ RE M TM M RE Fe disorders faster than Gd. Once temperature is below T C, we have a distribution of angles between TM and RE spins. Locally mode associated with AFM exchange (optical). Fe Gd BzBz Laser heating Magnetic field Applied to system to prevent reversal of Fe