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Ultrafast optical manipulation of magnetic order
Andrei Kirilyuk,
*
Alexey V. Kimel, and Theo Rasing
Radboud University Nijmegen, Institute for Molecules and Materials, Heyendaalseweg
135, 6525 AJ Nijmegen, The Netherlands
共Published 22 September 2010兲
The interaction of subpicosecond laser pulses with magnetically ordered materials has developed into
a fascinating research topic in modern magnetism. From the discovery of subpicosecond
demagnetization over a decade ago to the recent demonstration of magnetization reversal by a single
40 fs laser pulse, the manipulation of magnetic order by ultrashort laser pulses has become a
fundamentally challenging topic with a potentially high impact for future spintronics, data storage and
manipulation, and quantum computation. Understanding the underlying mechanisms implies
understanding the interaction of photons with charges, spins, and lattice, and the angular momentum
transfer between them. This paper will review the progress in this field of laser manipulation of
magnetic order in a systematic way. Starting with a historical introduction, the interaction of light with
magnetically ordered matter is discussed. By investigating metals, semiconductors, and dielectrics, the
roles of 共nearly兲 free electrons, charge redistributions, and spin-orbit and spin-lattice interactions can
partly be separated, and effects due to heating can be distinguished from those that are not. It will be
shown that there is a fundamental distinction between processes that involve the actual absorption of
photons and those that do not. It turns out that for the latter, the polarization of light plays an essential
role in the manipulation of the magnetic moments at the femtosecond time scale. Thus, circularly and
linearly polarized pulses are shown to act as strong transient magnetic field pulses originating from the
nonabsorptive inverse Faraday and inverse Cotton-Mouton effects, respectively. The recent progress
in the understanding of magneto-optical effects on the femtosecond time scale together with the
mentioned inverse, optomagnetic effects promises a bright future for this field of ultrafast optical
manipulation of magnetic order or femtomagnetism.
DOI: 10.1103/RevModPhys.82.2731 PACS number共s兲: 75.78.Jp, 85.75.⫺d, 78.47.jh, 75.60.⫺d
CONTENTS
I. Introduction 2732
A. Issues and challenges in magnetization dynamics 2732
B. The problem of ultrafast laser control of magnetic
order 2733
II. Theoretical Considerations 2734
A. Dynamics of magnetic moments:
Landau-Lifshitz-Gilbert equation 2734
B. Finite temperature: Landau-Lifshitz-Bloch equation 2735
C. Interaction of photons and spins 2735
III. Experimental Techniques 2737
A. Pump-and-probe method 2737
B. Optical probe 2737
C. Ultraviolet probe and spin-polarized electrons 2738
D. Far-infrared probe 2739
E. X-ray probe 2739
IV. Thermal Effects of Laser Excitation 2739
A. Ultrafast demagnetization of metallic ferromagnets 2739
1. Experimental observation of ultrafast
demagnetization 2740
2. Phenomenological three-temperature model 2742
3. Spin-flip and angular momentum transfer in
metals 2743
4. Interaction among charge, lattice, and spin
subsystems 2744
a. Time-resolved electron photoemission
experiments 2744
b. Time-resolved x-ray experiments 2745
5. Microscopic models of ultrafast
demagnetization 2746
B. Demagnetization of magnetic semiconductors 2747
C. Demagnetization of magnetic dielectrics 2748
D. Demagnetization of magnetic half metals 2749
E. Laser-induced coherent magnetic precession 2750
1. Precession in exchange-biased bilayers 2750
2. Precession in nanostructures 2751
3. Precession in 共III,Mn兲As ferromagnetic
semiconductors 2752
4. Precession in ferrimagnetic materials 2753
F. Laser-induced phase transitions between two
magnetic states 2755
1. Spin reorientation in TmFeO
3
2755
2. Spin reorientation in 共Ga,Mn兲As 2756
3. AM-to-FM phase transition in FeRh 2756
G. Magnetization reversal 2757
V. Nonthermal Photomagnetic Effects 2758
A. Photomagnetic modification of magnetocrystalline
anisotropy 2758
1. Laser-induced precession in magnetic garnet
films 2758
a. Experimental observations 2758
b. Phenomenological model 2759
c. Microscopic mechanism 2760
2. Laser-induced magnetic anisotropy in
antiferromagnetic NiO 2761
*
a.kirilyuk@science.ru.nl
REVIEWS OF MODERN PHYSICS, VOLUME 82, JULY–SEPTEMBER 2010
0034-6861/2010/82共3兲/2731共54兲 ©2010 The American Physical Society2731
3. Photomagnetic excitation of spin precession
in 共Ga,Mn兲As 2761
B. Light-enhanced magnetization in 共III,Mn兲As
semiconductors 2762
VI. Nonthermal Optomagnetic Effects 2763
A. Inverse magneto-optical excitation of magnetization
dynamics: Theory 2763
1. Formal theory of inverse optomagnetic
effects 2763
2. Example I: Cubic ferromagnet 2765
3. Example II: Two-sublattice antiferromagnet 2766
B. Excitation of precessional magnetization dynamics
with circularly polarized light 2766
1. Optical excitation of magnetic precession in
garnets 2766
2. Optical excitation of antiferromagnetic
resonance in DyFeO
3
2767
3. Optical excitation of precession in GdFeCo 2768
C. All-optical control and switching 2769
1. Double-pump coherent control of magnetic
precession 2769
2. Femtosecond switching in magnetic garnets 2771
3. Inertia-driven switching in antiferromagnets 2771
4. All-optical magnetization reversal 2772
5. Reversal mechanism via a nonequilibrium
state 2773
D. Excitation of the magnetization dynamics with
linearly polarized light 2774
1. Detection of the FMR mode via magnetic
linear birefringence in FeBO
3
2775
2. Excitation of coherent magnons by linearly
and circularly polarized pump pulses 2776
3. ISRS as the mechanism of coherent
magnon excitation 2776
4. Effective light-induced field approach 2778
VII. Conclusions and Outlook 2778
Acknowledgments 2779
References 2779
I. INTRODUCTION
A. Issues and challenges in magnetization dynamics
The time scale for magnetization dynamics is ex-
tremely long and varies from the billions of years con-
nected to geological events such as the reversal of the
magnetic poles down to the femtosecond regime con-
nected with the exchange interaction between spins.
From a more practical point of view, the demands for
the ever-increasing speed of storage of information in
magnetic media plus the intrinsic limitations that are
connected with the generation of magnetic field pulses
by current have triggered intense searches for ways to
control magnetization by means other than magnetic
fields. Since the demonstration of subpicosecond demag-
netization by a 60 fs laser pulse by Beaurepaire et al.
共1996兲, manipulating and controlling magnetization
with ultrashort laser pulses has become a challenge.
Femtosecond laser pulses offer the intriguing possi-
bility to probe a magnetic system on a time scale that
corresponds to the 共equilibrium兲 exchange interaction,
responsible for the existence of magnetic order, while
being much faster than the time scale of spin-orbit inter-
action 共1–10 ps兲 or magnetic precession 共100–1000 ps兲;
see Fig. 1. Because the latter is considered to set the
limiting time scale for magnetization reversal, the option
of femtosecond optical excitation immediately leads to
the question whether it would be possible to reverse
magnetization faster than within half a precessional pe-
riod. As magnetism is intimately connected to angular
momentum, this question can be rephrased in terms of
the more fundamental issues of conservation and trans-
fer of angular momentum: How fast and between which
reservoirs can angular momentum be exchanged and is
this even possible on time scales shorter than that of the
spin-orbit interaction?
While such questions are not relevant at longer times
and for equilibrium states, they become increasingly im-
portant as times become shorter and, one by one, the
various reservoirs of a magnetic system, such as the
magnetically ordered spins, the electron system, and the
lattice, become dynamically isolated. The field of ul-
trafast magnetization dynamics is therefore concerned
with the investigation of the changes in a magnetic sys-
tem as energy and angular momentum are exchanged
between the thermodynamic reservoirs of the system
共Stöhr and Siegmann, 2006兲.
Although deeply fundamental in nature, such studies
are also highly relevant for technological applications.
Indeed, whereas electronic industry is successfully enter-
ing the nanoworld following Moore’s law, the speed
of manipulating and storing data lags behind, creating
a so-called ultrafast technology gap. This is also evident
in modern PCs that already have a clock speed of a
few gigahertz while the storage on a magnetic hard disk
requires a few nanoseconds. A similar problem is expe-
rienced by the emerging field of spintronics as in, for
example, magnetic random access memory devices.
Therefore, the study of the fundamental and practical
limits on the speed of manipulation of the magnetiza-
tion direction is obviously also of great importance for
Laser
1ns
1ps
1fs
100 ps
10 ps
100 fs
10 fs
Magnetic
field
~ 0.01 ps – 0.1 ps
Exchange
interaction
Spin-orbit (LS)
interaction
L
S
Spin
precession
~1ps-1ns
~ 0.1 ps-1 ps
FIG. 1. 共Color online兲 Time scales in magnetism as compared
to magnetic field and laser pulses. The short duration of the
laser pulses makes them an attractive alternative to manipulate
the magnetization.
2732
Kirilyuk, Kimel, and Rasing: Ultrafast optical manipulation of magnetic order
Rev. Mod. Phys., Vol. 82, No. 3, July–September 2010
magnetic recording and information processing tech-
nologies.
In magnetic memory devices, logical bits 共“ones” and
“zeros”兲 are stored by setting the magnetization vector
of individual magnetic domains either “up” or “down.”
The conventional way to record a magnetic bit is to re-
verse the magnetization by applying a magnetic field
共Landau and Lifshitz, 1984; Hillebrands and Ounadjela,
2002兲. Intuitively, one would expect that switching could
be infinitely fast, limited only by the attainable strength
and shortness of the magnetic field pulse. However, re-
cent experiments on magnetization reversal using
uniquely short and strong magnetic field pulses gener-
ated by relativistic electrons from the Stanford Linear
Accelerator 共Tudosa et al., 2004兲 suggest that there is a
speed limit on such a switching. It was shown that deter-
ministic magnetization reversal does not take place if
the magnetic field pulse is shorter than 2 ps. Could
optical pulses be an alternative?
B. The problem of ultrafast laser control of magnetic order
The discovery of ultrafast demagnetization of a Ni
film by a 60 fs optical laser pulse 共Beaurepaire et al.,
1996兲 triggered the new and booming field of ultrafast
laser manipulation of magnetization. Subsequent experi-
ments not only confirmed these findings 共Hohlfeld et al.,
1997; Scholl et al., 1997; Güdde et al., 1999; Ju et al.,
1999; Koopmans et al., 2000; Bigot, 2001; Hicken, 2003;
Rhie et al., 2003; Bigot et al., 2004; Ogasawara et al.,
2005兲 but also demonstrated the possibility to optically
generate coherent magnetic precession 共Ju, Nurmikko,
et al., 1998; van Kampen et al., 2002兲, laser-induced spin
reorientation 共Kimel, Kirilyuk, et al., 2004; Bigot et al.,
2005兲, or even modification of the magnetic structure 共Ju
et al., 2004; Thiele et al., 2004兲 and this all on a time scale
of 1 ps or less. However, despite all these exciting ex-
perimental results, the physics of ultrafast optical ma-
nipulation of magnetism is still poorly understood.
A closer look at this problem reveals that excitation
with a femtosecond laser pulse puts a magnetic medium
in a highly nonequilibrium state, where the conventional
macrospin approximation fails and a description of mag-
netic phenomena in terms of thermodynamics is no
longer valid. In the subpicosecond time domain, typical
times are comparable to or shorter than the characteris-
tic time of spin-orbit interaction, and the magnetic an-
isotropy becomes a time-dependent parameter. Note
that, although the spin-orbit coupling is an important
ingredient of the magnetic anisotropy mechanism, the
latter is the result of a balance between different crystal-
field-split states. Therefore, the typical anisotropy en-
ergy is considerably lower than that of spin-orbit cou-
pling, which is also translated into the corresponding
response times. At shorter time scales even the ex-
change interaction should be considered as time depen-
dent. All these issues seriously complicate a theoretical
analysis of this problem. In addition, experimental stud-
ies of ultrafast magnetization dynamics are often ham-
pered by artifacts, and interpretations of the same data
are often the subject of heated debates.
What are the roles of spin-orbit, spin-lattice, and
electron-lattice interactions in the ultrafast optical con-
trol of magnetism? How does the electronic band struc-
ture affect the speed of the laser-induced magnetic
changes? A systematic study of the laser-induced phe-
nomena in a broad class of materials may answer these
questions, as optical control of magnetic order has been
demonstrated in metals, semiconductors, and dielectrics.
So far several attempts to summarize and systematize
these studies have been dedicated to metals 共Bigot,
2001; Zhang, Hübner, et al., 2002; Hicken, 2003
; Benne-
mann, 2004; Bovensiepen, 2007兲, ferromagnetic semi-
conductors 共Wang et al., 2006兲, or dielectrics 共Kirilyuk et
al., 2006; Kimel et al., 2007兲.
This review aims to introduce and summarize the ex-
perimental and theoretical studies of ultrafast optical
manipulation of spins in all the classes of both ferromag-
netically and antiferromagnetically ordered solids stud-
ied so far, including metals, semiconductors, and di-
electrics. We present an overview of the different experi-
mental and theoretical approaches to the problem and
distinguish effects of light on the net magnetization,
magnetic anisotropy, and magnetic structure. As a result,
important conclusions can be drawn about the role of
different reservoirs of angular momentum 共free elec-
trons, orbital motion, and lattice兲 and their mutual ex-
change for the ultrafast optical manipulation of magne-
tism.
The effects of a pump laser pulse on a magnetic sys-
tem could be classified as belonging to one of the follow-
ing classes:
共1兲 Thermal effects: Because of the absorption of pho-
tons, energy is pumped into the medium. The
change in the magnetization corresponds to that of
spin temperature: M =M共T
s
兲. Since in the electric di-
pole approximation spin-flip transitions are forbid-
den, the direct pumping of energy from light to spins
is not effective. Instead, light pumps the energy into
the electron and phonon system. The time scale of
the subsequent magnetization change is determined
by internal equilibration processes such as electron-
electron, electron-phonon, and electron-spin inter-
actions, which for itinerant ferromagnets can be
very short, down to 50 fs. For dielectric magnets, in
contrast, this time is of the order of a nanosecond
due to the absence of direct electron-spin processes.
The lifetime of such thermal effects is given by ex-
ternal parameters such as thermal conductivity of a
substrate as well as the geometry of the sample.
共2兲 Nonthermal 共photomagnetic兲 effects involving the
absorption of pump photons 共Kabychenkov, 1991兲:
In this case the photons are absorbed via certain
electronic states that have a direct influence on mag-
netic parameters, such as, for example, the magne-
tocrystalline anisotropy. The change is instantaneous
共e.g., the rise time of the pump pulse兲. These param-
eters, in turn, cause a motion of the magnetic mo-
2733
Kirilyuk, Kimel, and Rasing: Ultrafast optical manipulation of magnetic order
Rev. Mod. Phys., Vol. 82, No. 3, July–September 2010
ments that obeys the usual precessional behavior.
The lifetime of this effect is given by the lifetime of
the corresponding electronic states. Note, however,
that if this time is much shorter than the precession
period, the effect will be difficult to detect.
共3兲 And finally, there are nonthermal optomagnetic ef-
fects that do not require the absorption of pump
photons but are based on an optically coherent
stimulated Raman scattering mechanism 共Kaby-
chenkov, 1991兲. The action of this mechanism can be
considered as instantaneous and is limited by the
spin-orbit coupling, which is the driving force be-
hind the change in the magnetization in this case
共⬃20 fs for a typical 50 meV value of spin-orbit cou-
pling兲. The lifetime of the effect coincides with that
of optical coherence 共100–200 fs兲. Note that in prac-
tice thermal effects are always present to some
extent.
II. THEORETICAL CONSIDERATIONS
A. Dynamics of magnetic moments: Landau-Lifshitz-Gilbert
equation
The interactions of magnetic moments with magnetic
fields are basic to the understanding of all magnetic phe-
nomena and may be applied in many ways. Homoge-
neously magnetized solids exhibit a magnetic moment,
which for a volume V is given by m=VM, where M is
the magnetization. If V is the atomic volume, then m is
the magnetic moment per atom; if V is the volume of the
magnetic solid, m is the total magnetic moment of the
body. The latter case is often called the “macrospin ap-
proximation.” Also, for the inhomogeneous case, the
magnetic solid can often be subdivided into small re-
gions in which the magnetization can be assumed homo-
geneous. These regions are large enough that the motion
of the magnetization can in most cases be described clas-
sically.
The precessional motion of a magnetic moment in the
absence of damping is described by the torque equation.
According to quantum theory, the angular momentum
associated with a magnetic moment m is
L = m/
␥
, 共1兲
where
␥
is the gyromagnetic ratio. The torque on the
magnetic moment m exerted by a magnetic field H is
T = m ⫻ H. 共2兲
The change in angular momentum with time equals the
torque:
dL
dt
=
d
dt
m
␥
= m ⫻ H. 共3兲
If the spins not only experience the action of the exter-
nal magnetic field but are also affected by the magneto-
crystalline anisotropy, shape anisotropy, magnetic dipole
interaction, etc., the situation becomes more compli-
cated. All these interactions will contribute to the ther-
modynamical potential ⌽, and the combined action of
all these contributions can be considered as an effective
magnetic field
H
eff
=−
⌽/
M. 共4兲
Thus the motion of the magnetization vector can be
written as the following equation, named after Landau
and Lifshitz 共Landau and Lifshitz, 1935兲:
dm/dt =
␥
m ⫻ H
eff
, 共5兲
which describes the precession of the magnetic moment
around the effective field H
eff
. As mentioned, H
eff
con-
tains many contributions:
H
eff
= H
ext
+ H
ani
+ H
dem
+ ¯ , 共6兲
where H
ext
is the external applied field, H
ani
is the an-
isotropy field, and H
dem
is the demagnetization field. Ex-
cept for H
ext
, all other contributions will be material de-
pendent. Consequently, optical excitation of a magnetic
material may result, via optically induced changes in the
material-related fields, in a change in H
eff
, giving rise to
optically induced magnetization dynamics.
At equilibrium, the change in angular momentum
with time is zero, and thus the torque is zero. A viscous
damping term can be included to describe the motion of
a precessing magnetic moment toward equilibrium. A
dissipative term proportional to the generalized velocity
共−
m/
t兲 is then added to the effective field. This dissi-
pative term slows down the motion of the magnetic mo-
ment and eventually aligns m parallel to H
eff
. This gives
the Landau-Lifshitz-Gilbert 共LLG兲 equation of motion
共Gilbert, 1955兲:
m
t
=
␥
m ⫻ H
eff
+
␣
兩m兩
m ⫻
m
t
, 共7兲
where
␣
is the dimensionless phenomenological Gilbert
damping constant.
Equation 共7兲 may be used to study the switching dy-
namics of small magnetic particles. If the particles are
sufficiently small, the magnetization may be assumed to
remain uniform during this reversal process, and the
only contributions to the effective field are the aniso-
tropy field, the demagnetizing field, and the applied ex-
ternal field. For larger samples, and in the case of inho-
mogeneous dynamics, such as spin waves with k⫽ 0, the
magnetic moment becomes a function of spatial coordi-
nates: m =m共r兲. The effective magnetic field in this case
also acquires a contribution from the exchange interac-
tion. In this case, nonhomogeneous elementary excita-
tions of the magnetic medium may exist, first proposed
by Bloch in 1930 共Bloch, 1930兲. These excitations are
called spin waves and involve many lattice sites. More
details on these aspects can be found in Hillebrands and
Ounadjela 共2002兲.
The LLG equation can also be used in the atomistic
limit to calculate the evolution of the spin system using
Langevin dynamics, which has proved to be a powerful
2734
Kirilyuk, Kimel, and Rasing: Ultrafast optical manipulation of magnetic order
Rev. Mod. Phys., Vol. 82, No. 3, July–September 2010
