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Spinwaves Symposium, June 2013

T . Ostler , S. Wallace, J. Barker and R. W. Chantrell Dept. of Physics, The University of York, York, United Kingdom . Calculations of Spin-Spin Correlation Functions Out of Equilibrium for Classical Heisenberg Ferromagnets and Ferrimagnets. Spinwaves Symposium, June 2013.

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Spinwaves Symposium, June 2013

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  1. T. Ostler, S. Wallace, J. Barker and R. W. Chantrell Dept. of Physics, The University of York, York, United Kingdom. Calculations of Spin-Spin Correlation Functions Out of Equilibrium for Classical Heisenberg Ferromagnets and Ferrimagnets Spinwaves Symposium, June 2013

  2. Motivation: Ultrafast Demagnetization • Currently a lot of interest in the physics behind femtosecond demagnetisation and magnetization process on the fs time-scale. • Collapse of order seen in the magnetization depends on a number of features (fluence, material etc). Figure from Raduet al., Nature, 472, 205-208 (2011).

  3. Spin-Spin Correlation Graves et al., Nature Materials, 12, 293-298 (2013).

  4. Correlation Function • We can study the correlations at different length scales by calculating the correlation function. • By this definition the ordered state (T=0K) has the correlation function equal to 1 for all length scales. +ve Correlation -ve Correlation zi-zj zi-zj • For the TM and RE sublattices we can calculate how correlations vary within each sublattice.

  5. Our Approach: Atomistic LLG • We use a model based on the Landau-Lifshitz-Gilbert (LLG) equation for atomistic spins. • Demagnetisation interpreted as thermal disorder due to thermal excitation. • Temporal variations in temperature mean the strength of our stochastic term changes. • For the ferrimagnetic calculations we create a super cell to give TM3RE1 (allows use of FFT).

  6. Two-Temperature Model of Laser Heating • We use theTwo-temperature[1]model which defines an electron and phonon temperature (Te and Tl) as a function of time. • We couple the electron temperature to the spin system. Laser input P(t) Electrons Lattice Gel e- e- e- e- • The change in temperature gives changes in size of the random thermal field. [1] Chen et al. International Journal of Heat and Mass Transfer.49, 307-316 (2006)

  7. Demagnetization • Correlation function for ferromagnet reaches equilibrium very quickly, same rate as the magnetization. RE • Correlation function decreases quite uniformly over the system. • Similar in ferrimagnets except the rate of each sublattice is different due to different magnetic moments. TM

  8. Transient Ferromagnetic-like State • At the start of the transient ferromagnetic-like state long range correlation dissapears. • Localized regions of switching of TM against exchange field of RE. Atomistic level Correlated regions with different orientations • Build up of order in TM sublattice drives switching of RE. • Collapse and re-emergence of order in TM much faster than RE. More information found on arXiv:1207.4092

  9. Transient Ferromagnetic-like State • For higher fluence case we do not see the large precession induced over the macrospin as the increased temperature means correlations are not built up as readily. • But the correlation function suggests that it occurs on a small length-scale. Low Fluence High Fluence

  10. Remagnetization in a ferromagnet • It has been demonstrated that when ferromagnets are completely demagnetized, recovery of magnetization is very long. • Multi-domain states form on cooling. These domains must also re-order. [1] – Kazantsevaet al. EPL 81, 27004 (2008).

  11. Remagnetization continued • Competition between domains means magnetization can take a long time to recover. • Initial results show that ferrimagnetic materials do not get stuck in this state . • High frequency excitations associated with AFM interactions drives any competing domains out?

  12. Summary & Conclusions Outlook • We have compared how correlations change in ferromagnetic and ferrimagnetic materials. • Demagnetisation shows similar behaviour and the correlations decay in a time-scale that scales with time-scale of the magnetization. • We have observed how the different sublattices in a ferrimagnet change during heat induced switching. • These results could give us insight into the size limitations of a system undergoing thermally induced switching. • Initial calculations show that remagnetisation in ferrimagnets is faster than ferromagnets due AFM exchange interaction. • Requires further investigation into • Further study into the limitations of system size and the key parameters. • Analysis of remagnetisation rates in ferro- and ferri-magnets.

  13. Acknowledgements • The Nuffield Foundation for funding studentships. • European Community’s Seventh Framework Programme (FP7/2007-2013) Grant No. NNP3-SL-20120281043 (FEMTOSPIN). • Thank you for listening.

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