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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

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

Motivation ultrafast demagnetization
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).

Spin spin correlation
Spin-Spin Correlation

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

Correlation function
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



  • For the TM and RE sublattices we can calculate how correlations vary within each sublattice.

Our approach atomistic llg
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).

Two temperature model of laser heating
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









  • 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)


  • Correlation function for ferromagnet reaches equilibrium very quickly, same rate as the magnetization.


  • Correlation function decreases quite uniformly over the system.

  • Similar in ferrimagnets except the rate of each sublattice is different due to different magnetic moments.


Transient ferromagnetic like state
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

Transient ferromagnetic like state1
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

Remagnetization in a ferromagnet
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).

Remagnetization continued
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?

Summary conclusions
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.


  • 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.