Transient ferromagnetic state mediating ultrafast reversal of antiferromagnetically

coupled spins

I. Radu1,2*, K. Vahaplar1, C. Stamm2, T. Kachel2, N. Pontius2, H. A. Dürr2,5, T. A. Ostler3, J.Barker3, R. F. L. Evans3, R. W. Chantrell3, A. Tsukamoto4,6, A. Itoh4, A. Kirilyuk1, Th. Rasing1

and A. V. Kimel1*

1Radboud University Nijmegen,Institute for Molecules and Materials, Heyendaalseweg 135,6525 AJ Nijmegen,The Netherlands

2 Helmholtz-Zentrum Berlin fϋr Materialien und Energie, BESSY II, Albert-Einstein-Strasse 15,12489 Berlin, Germany

3 Department of Physics, University of York, York YO10 5DD, United Kingdom4College of Science and Technology, Nihon University, 7-24-1 Funabashi, Chiba, Japan

5SLAC National Accelerator Laboratory, Menlo Park, CA 94025, USA6PRESTO, Japan Science and Technology Agency, 4-1-8 Honcho Kawaguchi, Saitama, Japan

OVERVIEW

• Study GdFeCo samples– Amorphous– Form two sublattices antiferromagnetically

coupled favouring anti-parallel alignment– Gd=RE, FeCo=TM

• Using ultrafast laser pulses show– Different timescales for dynamics– Induce a transient spin-flip state, against exchange

interaction (strongest force in magnetism)

EXPERIMENT• Samples reset after each run• 60fs laser pulse applied to sample in 0.5T field resets sample• X-ray Magnetic Circular Dichroism (XMCD) technique used to measure

magnetization at a particular instant• Equipment adjusted to measure samples at different times and experiment

repeated• Tuning XMCD to different absorption edges allows for measurement of Gd

and Fe edges (different photon energies)

TIME RESOLVED DYNAMICS

•(A) shows clearly that TM reverses before RE. Sublattices aligned for around 1ps•Alignment against exchange interaction!!!

NUMERICAL MODEL

• The localized atomistic spin model uses a Heisenberg exchange, the Hamiltonian is given by

nn i i

zizijiiji SBKSSSJE

• Exchange, anisotropy, zeeman• Dynamics of spins governed by LLG equation

iiiii

ii

ii HSHSt

S

)1( 2

NUMERICAL MODEL• Thermal fluctuations augments field and allows for transfer of energy and

angular momentum, from bath to spin system• White noise correlator:

t

Tktttt

ii

Biabij

bj

ai

)(2)()(

• To model amorphous nature use crystal graphically disordered fcc lattice• Exchange parameters are

• JTM-TM >0 (Ferromagnetic)

• JRE-RE >0 (Ferromagnetic)

• JTM-RE <0 (antiferromagnetic• Result is two sublattices aligned antiparallel

NUMERICAL RESULTS

•As we can see agreement with exp is excellent with spin-flip for around 1ps.

DEMAGNETISATION TIMES

• Why does the TM sublattice demagnetise faster than the RE sublattice?

• Numerical model shows that initial (short timescale) demagnetisation is proportional the correlator.

t

Tktttt

ii

Biabij

bj

ai

)(2)()(

• Note on-site magnetic moment μi.

• μTM~2μB

• μRE~ 7μB

NUMERICAL TEST• To test the hypothesis we change the moment on RE site and look at

exponential decay. Fit to:/t

z em • Now relaxation time is like

/• Plot λτ as a function of μRE

INCREASING RE-RE EXCHANGE

• Even making the RE-RE exchange as strong as the TM-TM exchange (which is the strongest) does not lead to different dynamics

SUMMARY• Time evolution of the sublattice magnetization agrees very well

with the experiments• Qualitatively reproduces the timescales for the demagnetization of

each sublattice• Ferromagnetic “spin-flip” state is also reproduced, in a time window

close to that observed experimentally• Indicates that the reversal of the antiferromagnetically coupled TM

and RE spins indeed occurs via a transient ferromagnet-like state• Reversal of the sublattice magnetizations is found to occur via the

mechanism of linear reversal• even making the Gd-Gd exchange interaction in the simulations as

strong as the Fe-Fe interaction does not lead to qualitative changes

CONCLUSIONS• Such agreement between the simulations and the experiment is clear

evidence of the fact that the novel magnetization dynamics reported here is an intrinsic property of the spins in a non-equilibrium ferrimagnet.

• Different timescales for the collapse of the magnetizations, can be explained in terms of the characteristic time of longitudinal relaxation of the magnetization

• In spite of the exchange coupling between the RE and TM sublattices, they apparently lose their net magnetizations independently as would be the case for two decoupled TM and RE ferromagnets, so appear decoupled.

• It is reasonable to hypothesize that the much weaker interaction of the spins with an external magnetic field hardly influences the spin dynamics in this ultrafast regime, leading to novel switching scenarios.