Balance of angular momentum and magnetization switching Andrei !Kirilyuk Radboud University, Institute for Molecules and Materials, Nijmegen
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Andrei Kirilyuk, Belem – November 2014
Radboud University Nijmegen
Acknowledgments Nijmegen K. Vahaplar, I. Radu, S. Khorsand, M. Savoini, J. Mentink,
C.D. Stanciu, F. Hansteen, A.V. Kimel, M.I. Katsnelson, Th. Rasing Chiba A. Tsukamoto, A. Itoh BESSY, Berlin C. Stamm, T. Kachel, N. Pontius LCLS, Stanford C. Graves, A.H. Reid, J. Stöhr, A.O. Scherz, H.A. Dürr SLS, Villingen S.El Moussaoui, L. Le Guyader, F. Nolting York T.A. Ostler, J. Barker, R.F.L. Evans, R.W. Chantrell Madrid U. Atxitia, O. Chubykalo-Fesenko St.-Petersburg A.M. Kalashnikova, R.V. Pisarev Uppsala J. Hellsvik, O. Eriksson, Kiev D. Afanasiev, B.A. Ivanov 2
Andrei Kirilyuk, Belem – November 2014
Radboud University Nijmegen
Magnetic recording – searching for options
Other options: - Bit Patterned Media - Microwave-Assist - Two-Dimensional - .....
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Andrei Kirilyuk, Belem – November 2014
Radboud University Nijmegen
Time-scales and stimuli in magnetism
Time (s)
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Andrei Kirilyuk, Belem – November 2014
Radboud University Nijmegen
Magnetization dynamics N
B
energy gain: ! torque equation:
S Landau & Lifshitz, 1935
with damping:
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Andrei Kirilyuk, Belem – November 2014
Radboud University Nijmegen
Consequence: conservation of angular momentum
Einstein – de Haas & Barnett effects A. Einstein & W.J. de Haas, Experimenteller Nachweis der Amperèschen
Molekülströme, Verhandl. Deut. Phys. Ges. 17, 152 (1915) S.J. Barnett, Magnetization by rotation, Phys. Rev. 6, 239 (1915) 6
Andrei Kirilyuk, Belem – November 2014
Radboud University Nijmegen
What laser does to a magnet?
Beaurepaire et al. PRL 76, 4250 (1996)
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Andrei Kirilyuk, Belem – November 2014
Radboud University Nijmegen
Samples: ferrimagnetic alloys GdFeCo and similar
hysteresis domains
Magnetization
0.3
'up' 0.0
'down' -0.3 -3
0
3
Field (kOe)
‹#›
Andrei Kirilyuk, M-SNOWS – February 2012
Radboud University Nijmegen
Samples: ferrimagnetic alloys GdFeCo and similar TM TA RE (Gd)
MRE ATM
TC~500 K
M A ARE MTM
TM (FeCo) Temperature
gGd < gFeCo ‹#›
Andrei Kirilyuk, M-SNOWS – February 2012
Radboud University Nijmegen
Helicity dependence? Switching with a single
40 fs laser pulse, circularly polarized is this Stanciu et al., PRL 99, 047601 (2007).
Faraday effect (refraction)? or magnetic circular dichroism
(absorption)?
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Andrei Kirilyuk, Belem – November 2014
Radboud University Nijmegen
Helicity-dependent switching revised S. Khorsand et al, PRL 108, 127205 (2012)
beam-size determination, see J. M. Liu, Optics Letters 7, 196 (1982)
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Andrei Kirilyuk, Belem – November 2014
Radboud University Nijmegen
MCD vs Faraday effect
effective field from inverse Faraday effect
amount of energy absorbed in the sample per pulse stays constant
S. Khorsand et al, PRL 108, 127205 (2012)
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Andrei Kirilyuk, Belem – November 2014
Radboud University Nijmegen
Absorbed amount of energy ⇒ demagnetization? Simple question: what happens if we demagnetize a ferrimagnetic structure with two inequivalent sublattices? Answer 1: they demagnetize at different rates o wrong answer, what about exchange?? Answer 2: because of the exchange, they demagnetize in exactly the same way
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Andrei Kirilyuk, Belem – November 2014
Radboud University Nijmegen
X-ray Magnetic Circular Dichroism below Tcomp
above Tcomp
Gd Mtot Fe
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Andrei Kirilyuk, Belem – November 2014
Radboud University Nijmegen
Dynamics of sublattices Fe: 100±23 fs Radu et al., Nature 472, 205 (2011)
Gd: 427±102 fs
ferri-magnet turns ferro! 15
Andrei Kirilyuk, Belem – November 2014
Radboud University Nijmegen
Atomistic simulations localized atomistic spin model with a Heisenberg exchange for two sublattices exchange parameters (Fe-Fe, Gd-Gd, and Fe-Gd) obtained by fitting static MFe,Gd(T) dependencies. the usual stochastic term added to the effective field
! ! ! ! magnetic field can be present during the process Scubic et al, JPCM 20, 315203 (2008); Ostler et al, PRB 84, 024407 (2011)
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Andrei Kirilyuk, Belem – November 2014
Radboud University Nijmegen
Simulation results
Radu et al., Nature 472, 205 (2011)
ferromagnetic state reproduced, as well as the reversal! 17
Andrei Kirilyuk, Belem – November 2014
Radboud University Nijmegen
The role of the compensation point Intensity threshold
x(Gd)=24%
Coercive field Hc
Intensity threshold of
helicity-dependent
all-optical switching
x(Gd)=26%
x(Gd)=22%
It works in the broad vicinity
of the compensation
temperature
x(Gd)=20%
0
50
100
150
200
250
300
350
Temperature, K 18
Andrei Kirilyuk, Belem – November 2014
Radboud University Nijmegen
Longitudinal relaxation in multi-sublattice magnets from eqs. of motion based on Onsager relations, see V. G. Baryakhtar, JETP 87, 1501 (1984); 94, 196 (1988); Low Temp. Phys. 11, 1198 (1985).
dS1 dS 2
dt dt
= λe (H1 − H 2 )+ λ1 H1 = −λe (H1 − H 2 )+ λ2 H 2 exchange
where and
relativistic (usual damping)
Mentink et al., PRL 108, 057202 (2012)
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Andrei Kirilyuk, Belem – November 2014
Radboud University Nijmegen
Temperature-dominated regime
λi >> λe
interaction with the environment dS1
dt
= λe (H1 − H 2 )+ λ1 H1
dt
= −λe (H1 − H 2 )+ λ2 H 2
dS 2
2α iγk BT λi ∝ µi
Bloch relaxation
Dynamics scales with magnetic moment Brown 1963, Kubo 1970
small magnetic moments change faster → less angular momentum to be transferred 20
Andrei Kirilyuk, Belem – November 2014
Radboud University Nijmegen
Exchange-dominated regime
λi