1. Atomistic Modelling of Ultrafast Magnetization Switching Ultrafast Conference on Magnetism J. Barker 1, T. Ostler 1, O. Hovorka 1, U. Atxitia 1,2, O. Chubykalo-Fesenko 2 and R. W. Chantrell 1 1 Dept. of Physics, The University of York, York, United Kingdom. 2 Instituto de Ciencia de Materiales de Madrid, CSIC, Madrid, Spain.

2. Overview Thermal switching observed No good explanation. Can we develop a theory/framework? Can we predict something? Better/new materials. Is it predictive? Can it explain all observed behaviour? Verification.

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

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

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

6. The atomistic model of GdFeCo Amorphous nature Random lattice model Exchange Interactions: Heisenberg Hamiltonian Dynamics T. Ostler et 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? Large demagnetization. Deterministic switching. Suggests something is occurring on microscopic level

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

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

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

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

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

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]. Key ingredients Two bands arising from two (or more) species AFM coupled Stimulus with sufficient energy to excite both bands Stimulus must be faster than the timescale of the decay of the modes The species that reverses first must form stable sublattice [1] R. Evans et al., arXiv: (2013)

20. Acknowledgements/references ReferencesDemagnetization times: Atxitia et al. arXiv:1308.0993 (2013).Transient ferromagnetic-like state: Radu et al. Nature 472, 205-208 (2011).Atomistic model of GdFeCo: T. Ostler et al., Phys. Rev. B 84, 024407 (2011).Thermally induced switching: Nat. Commun. 3, 666 (2012).Switching in heterostructures: R. Evans et al. arXiv:1308.1314 (2013).Switching mechanism: J. Barker et al. Nat. Sci. Rep. (in press) arXiv:1308.1314. Thank you for your attention

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

22. Linear Spin Wave Theory Virtual Crystal Approximation Bogolioubov Transform

23. Linear Spin Wave Theory Virtual Crystal Approximation Bogolioubov Transform

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

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

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