### Calculations of Spin-Spin Correlation Functions Out of Equilibrium

```Calculations of Spin-Spin Correlation Functions Out of
Equilibrium for Classical Heisenberg Ferromagnets and
Ferrimagnets
T. Ostler, S. Wallace, J. Barker and R. W. Chantrell
Dept. of Physics, The University of York, York, United Kingdom.
Spinwaves Symposium, June 2013
Motivation: Ultrafast Demagnetization
 Currently a lot of interest in the physics
behind femtosecond demagnetisation and
magnetization process on the fs timescale.
 Collapse of order seen in the
magnetization depends on a
number of features (fluence,
material etc).
Figure from Radu et al., Nature, 472, 205-208 (2011).
Spin-Spin Correlation
Graves et al., Nature Materials, 12, 293-298 (2013).
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
zi-zj
-ve Correlation
zi-zj
 For the TM and RE sublattices we can calculate
how correlations vary within each sublattice.
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
 We use theTwo-temperature[1] model
which defines an electron and phonon
temperature (Te and Tl) as a function of time.
Laser
input
P(t)
 We couple the electron temperature to the
spin system.
Electrons
Gel
ee- 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)
Lattice
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
Transient Ferromagnetic-like State
 At the start of the transient ferromagneticlike 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. found on arXiv:1207.4092
More
information
 Collapse and re-emergence of order in TM
much faster than RE.
Transient Ferromagnetic-like State
High Fluence
Low Fluence
 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.
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] – Kazantseva et al. EPL 81, 27004 (2008).
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
 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
Outlook
 Further study into the limitations of system size and the key parameters.
 Analysis of remagnetisation rates in ferro- and ferri-magnets.
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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