arXiv:1112.2428v1 [cond-mat.mes-hall] 12 Dec 2011
Theory of laser-induced demagnetization at high temperatures
A. Manchon1,2, Q. Li1, L. Xu1, and S. Zhang1
1Department of Physics, University of Arizona, Tucson, AZ 85721, USA;
2Materials Science and Engineering, Physical Science and Engineering Division, KAUST, Saudi Arabia
(Dated: December 13, 2011)
Laser-induced demagnetization is theoretically studied by explicitly taking into account interac-
tions among electrons, spins and lattice. Assuming that the demagnetization processes take place
during the thermalization of the sub-systems, the temperature dynamics is given by the energy
transfer between the thermalized interacting baths. These energy transfers are accounted for explic-
itly through electron-magnons and electron-phonons interaction, which govern the demagnetization
time scale. By properly treating the spin system in a self-consistent random phase approximation,
we derive magnetization dynamic equations for a broad range of temperature. The dependence of
demagnetization on the temperature and pumping laser intensity is calculated in detail. In par-
ticular, we show several salient features for understanding magnetization dynamics near the Curie
temperature. While the critical slowdown in dynamics occurs, we find that an external magnetic
field can restore the fast dynamics. We discuss the implication of the fast dynamics in the application
of heat assisted magnetic recording.
PACS numbers: 75.78.Jp,75.40Gb,75.70.-i
Laser-induced Demagnetization1,2(LID) and Heat As-
sisted Magnetization Reversal3(HAMR) constitute a
promising way to manipulate the magnetization direc-
tion by optical means. While both LID and HAMR in-
volve laser-induced magnetization dynamics of magnetic
materials, there are several important differences. LID
is usually considered as an ultrafast process where the
hot electrons excited by the laser field transfer their en-
ergy to the spin system, causing demagnization. The
demagnetization time scale ranges from 100 femtosecond
to a few picoseconds. For HAMR, the laser field is to
heat the magnetic material up to the Curie temperature
so that the large room-temperature magnetic anisotropy
is reduced to a much smaller value and consequently, a
moderate magnetic field is able to reverse the magneti-
zation. The time scale for the HAMR process is about
sub-nanosecond, three orders of magnitude larger com-
pared to LID.
LID observationshave beencarried out ina
number of magnetic materials including transition
metals1,4–6, insulators7, half-metals8–10and dilute mag-
netic semiconductors11. A general consensus of the laser-
induced demagnetization process is that the high energy
non-thermal electrons generated by a laser field relax
their energy to various low excitation states of the elec-
tron, spin and lattice12. The phenomenological model for
this physical picture is referred to as three-temperature
model1,5,9where the three interacting sub-systems (elec-
trons, spins, lattice) are assumed thermalized individ-
ually at different temperatures which are equilibrated
according to a set of energy rate equations. By fitting
experimental data to the model, reasonable relaxation
times of the order of several hundred femtosecond to a
few picoseconds have been determined.
Various microscopic theories4,13–16have been proposed
to interpret these ultrafast time scales of electron-spin
and electron-lattice relaxations.
proposed that the laser field can directly excite the spin-
polarized ground states to spin-unpolarized excited states
in the presence of spin-orbit coupling, i.e., the spin-flip
transition leads to the demagnetization during the laser
pulse.In this picture, the demagnetization is instan-
show that due to a few active ”hot spots”, the instan-
taneous demagnetization is expected for at most a few
percent of the magnetization, consistently with experi-
mental arguments18. Koopmans et al.4,5suggested that
the excited electrons lose their spins in the presence of
spin-orbit coupling and impurities or phonons, through
an ”Elliot-Yafet”-type (EY) spin-flip scattering. Recent
numerical evaluations of the EY mechanism in transition
metals14tend to support this point of view. Alterna-
tively, Battiato et al.19recently modelled such ultrafast
demagnetization in terms of superdiffusive currents. Fi-
nally, numerical simulations of the ultrafast demagneti-
zation based on the phenomenological Landau-Lifshitz-
Bloch equation have been achieved successfully20.
While these demagnetization mechanisms provide rea-
sonable estimation for the demagnetization time scales,
the theories are usually limited to the temperature much
lower than the Curie temperature and/or make no di-
rect connection to the highly successful phenomenologi-
cal three-temperature model1,5,9. As it has been recently
shown experimentally7,8, most interesting magnetization
dynamics occur near the Curie temperature.
In this paper, we propose a microscopic theory of the
laser-induced magnetization dynamics under the three-
temperature framework and derive the equations that
govern the demagnetization at arbitrary temperatures.
More specifically we predict magnetization dynamics in
the critical region.
Zhang and H¨ ubner13
Recent numerical simulations17
The paper is organized as follows. In Sec. II, we pro-
pose a model for LID processes. In Sec. III, we describe
the spin system by the Heisenberg model which is solved
by using a self-consistent random phase approximation.
In Sec. IV, the central dynamic equations for the magne-
tization are derived. In Sec. V, the numerical solutions of
the equations are carried out and the connection of our
results with the experimental data of LID and HAMR is
made in Sec. VI. We conclude our paper in Sec. VII.
II.MODEL OF LID
A.Spin loss mechanisms
One of the keys to understand ultrafast demagneti-
zation is to identify the mechanisms responsible for the
spin memory loss. In the case of transition metal ferro-
magnets for example, the spin relaxation processes lead
to complex spin dynamics due to the itinerant character
of the magnetization. Elliott21first proposed that delo-
calized electrons in spin-orbit coupled bands may lose
their spin under spin-independent momentum scatter-
ing events (such as electron-electron or electron-impurity
interaction). This mechanism was later extended to
electron-phonon scattering by Yafet and Overhauser22.
Consequently, the spin relaxation time τsis directly pro-
portional to the momentum relaxation time τp. Whereas
the electron-electron relaxation time is on the order of
a few femtoseconds23(fs), the electron-impurity and
electron-phonon relaxation time is on the picoseconds
(ps) scale. In semiconductors, bulk and structural inver-
sion symmetry breaking as well as electron-hole interac-
tions lead to supplementary spin relaxation mechanisms
such as D’yakonov-Perel24and Bir-Aronov-Pikus25that
are beyond the scope of the present study.
Relaxation processes also apply to collective spin exci-
tations such as magnons. Whereas the electron-magnon
interaction conserves the angular momentum, magnon-
magnon interactions and magnon-lattice interactions in
the presence of spin-orbit coupling contribute to the total
spin relaxation. While the former occurs on the magnon
thermalization time scale26(100fs), the latter is however
at the second order in spin-orbit coupling and is con-
sidered to occur on the 100ps time scale. Therefore, in
a laser-induced demagnetization experiment, it is most
probable that all the processes mentioned above take
place during the thermalization time scale of the excited
electrons and excited magnons.
B. Demagnetization scenario
To establish our model, we first separate the LID pro-
cesses into four steps: (i) generation of non-thermal hot
electrons by laser pumping; (ii) relaxation of these hot
electrons into thermalized electrons characterized by an
electron temperature Te; (iii) energy transfer from the
thermalized hot electrons to the spin and lattice sub-
systems; (iv) heat diffusion to the environment.
In our model, to be given below, we will take steps
(i) and (ii) infinitely fast. In the step (i), a laser pump
excites a fraction of electrons below the Fermi sea to ≈1.5
eV above the Fermi level. This excitation process is of the
order of a few fs. The photo-induced electron transition is
considered spin conserving and thus does not significantly
contribute to the demagnetization although the spin-flip
electron transition could occur in the presence of the spin-
In step (ii), the strong Coulomb interaction among
electrons relaxes these non-thermal high-energy electrons
to form a hot electron bath which may be described by
a thermalized hot electron temperature Te. During this
electron thermalization process, strong electron-electron
interaction-induced momentum scattering in the pres-
ence of spin-orbit coupling leads to the ultrafast transfer
of the spin degree of freedom to the orbital one27. In our
model, the electron thermalization is considered instan-
taneous and any possible femtosecond coherent processes
are disregarded28. Therefore, due to ultrafast (fs) mo-
mentum scattering, the thermalized hot electrons act as
a spin sink. Under this approximation, the demagnetiza-
tion itself, defined as the loss of spin angular momentum,
takes place during the thermalization of the electron bath
in the presence of (either intrinsic or extrinsic) spin-orbit
Following the definition of the three-temperature
model, we assume that the system can be described
in term of three interacting baths composed of laser-
induced hot electrons, spin excitations of the ground
state (magnons) and lattice excitations (phonons). The
applicability of this assumption is discussed in Sec. IID.
Therefore, the magnetic signal essentially comes from the
collective spin excitation and it is assumed that the laser-
induced hot electron only contribute weakly to the mag-
netization. Consequently, under the assumption that the
spin loss occurs during the thermalization time of the
electron and spin systems, the demagnetization problem
reduces to tracking the energy transfer between the spin
bath and the electron and phonon bathd.
Our main objective is then to understand step (iii),
where the electrons at a higher temperature transfer
their energy to the spin and lattice sub-systems. Un-
der the electron-magnon interaction, the magnons spin is
transferred to the electron system, and is eventually lost
through thermalization of the electron bath. Through
interactions among electrons, spins and lattice, the en-
tire system will ultimately reach a common temperature.
Finally, a heat diffusion, step (iv), will expel the heat to
the environment; this last step will be considered via a
simple phenomenological heat diffusion equation.
To quantitatively determine the energy transfer among
electrons, spins and lattice in the step (iii), one not only
needs to know the explicit interaction, but also the distri-
bution of the densities of excitations (electrons, magnons
and phonons). Within the spirit of the three tempera-
32N. W. Ashcroft and N. D. Mermin, Solid State Physics,
(Holt, Rinehart and Winston, New York), 1976.
33S. V. Tyablikov, Methods in the quantum theory of mag-
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34G. V. Vasyutinskii and A. A. Kazakov, Theor. Math. Phys.
95, 450 (1993).
35C. Kittel, Introduction to Solid State Physics, 4th Ed.
(John Wiley & Sons, New York) (1971).
36D. L.Connelly, J. S. Loomis, and D. E. Mapother, Phys.
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