Atomistic Modelling of Ultrafast Magnetization Switching

1. Atomistic Modelling of Ultrafast Magnetization Switching J. Barker1, T. Ostler1, O. Hovorka1, U. Atxitia1,2, O. Chubykalo-Fesenko2 and R. W. Chantrell1 1Dept. of Physics, The University of York, York, United Kingdom. 2Instituto de Ciencia de Materiales de Madrid, CSIC, Madrid, Spain. Ultrafast Conference on Magnetism

2. Overview

3. Deterministic all-thermal switching Predicted using atomistic spin dynamics. Single shot. No applied field required. Linear polarised light. No IFE. Verified experimentally. Ostler et al. Nat. Commun., 3, 666 (2012).

4. Important features of thedynamics Element-resolved dynamics. Transient ferromagnetic-like state Reversal of the sublattices Different demagnetization times Initial State Raduet al. Nature, 472, 205-208 (2011).

5. What we know/unanswered questions ? Transient ferromagnetic like state I. Raduet al., Nature 472, 205 (2011) Deterministic reversal without field T.A. Ostleret al., Nat. Commun. 3, 666 (2012) Different demagnetisation times I. Raduet al., Nature 472, 205 (2011)U. Atxitiaet al, arXiv:1308.0993. ? Difference in magnetic moment (mostly, see talk by O. Chubykalo-Fesenko) Understanding the mechanism driving this process is crucial for finding new materials.

6. The atomistic modelof GdFeCo Random lattice model Amorphous nature Exchange Interactions: Heisenberg Hamiltonian Dynamics T. Ostleret al., Phys. Rev. B 84, 024407 (2011)

7. Femtosecond heating Chen et al. Int. Journ. Heat and Mass Transfer.49, 307-316 (2006)

8. Beyond magnetization How can we explain the observed effects in GdFeCo? Suggests something is occurring on microscopic level Large demagnetization. Deterministic switching.

9. Intermediate structure factor (ISF) ISF  distribution of modes even out of equilibrium. 975K Above switching threshold Below switching threshold X/2 FeCo 1090K Gd M/2 X/2 M/2 No significant change in the ISF Excited region during switching 2 bands excited • J. Barker, T. Ostler et al. Nature Scientific Reports, in press. arXiv:1308.1314

10. Dynamic structure factor (DSF) To calculate the spinwave dispersion from the atomistic model we calculate the DSF. Relative Band Amplitude FeCo 1090K Gd X/2 M/2 The point (in k-space) at which both bands are excited corresponds to the spinwave excitation (ISF).

11. Frequency gap By knowing at which point in k-space the excitation occurs, we can determine a frequency (energy) gap. Overlapping bands allows for efficient transfer of energy. This can help us understand why we do not get switching at certain concentrations of Gd. Large band gap precludes efficient energy transfer.

12. What is the significance of the excitation of both bands? Excitation of only one band leads to demagnetization. Excitation of both bands simultaneously leads to the transient ferromagnetic-like state. Can we predict where in k-space both bands will be excited?

13. Effects of clustering Clustering Randomly populating lattice Recall overlap in spectrum. Length-scale corresponds to physical clusters. The point at which we have band overlap in the spinwave spectrum and the cluster size are correlated.

14. Linear Spin Wave Theory Virtual Crystal Approximation Bogolioubov Transform

15. Spinwave dispersion From linear spinwave theory (LSWT) we can derive the magnon dispersion relation. Use cluster analysis to determine which part of spectrum to consider gap.

16. Predicting the switching window VCA LSWT MFA Clustering By combining the analytic treatments: We can predict the energy gap required to excite modes in both bands at significant |k|. Theoretical Prediction Simulation Result Laser Fluence High Switching Low No Switching

17. Can we now explain the observed effects? Transient ferromagnetic like state I. Raduet al., Nature 472, 205 (2011) Deterministic reversal without field T.A. Ostleret al., Nat. Commun. 3, 666 (2012) Different demagnetisation times I. Raduet al., Nature 472, 205 (2011)U. Atxitiaet al, arXiv:1308.0993. • transient state arising from two magnon excitation • cooling ~ps means excitation decays Difference in magnetic moment (mostly, see talk by O. Chubykalo-Fesenko)

18. Summary Our aim was to explain observed dynamics. Distribution of modes showed excitation at finite k-vector. Transient state arises from two-magnon excitation. Energy of two-magnon excitation predicts composition dependent switching.

19. Conclusions/outlook Understanding this mechanism we can engineer other anti-ferromagnetically coupled materials/structures[1]. [1] R. Evans et al., arXiv: (2013)

20. Acknowledgements/references Thank you for your attention

21. Clustering effects Hoshen-Kopelmanmethod to calculate typical correlation length for a given Gd concentration. Only A is fitted to account for finite size lattice, pc and ν are universal exponents. The spin wave spectrum and physical clustering are correlated.

22. Linear Spin Wave Theory Virtual Crystal Approximation Bogolioubov Transform

23. Linear Spin Wave Theory Virtual Crystal Approximation Bogolioubov Transform

24. Predicting switching VCA LSWT MFA Percolation Prediction Switching observed in simulations Laser Fluence High Switching Low No Switching

25. The transfer of energy between sublattices Only a single band in the excited region. Non-linear energy transfer between bands. Large band gap precludes efficient energy transfer.

26. Important features of thedynamics Element-resolved dynamics. Transient ferromagnetic-like state Reversal of the sublattices Different demagnetization times Initial State Raduet al. Nature, 472, 205-208 (2011).