Ultrafast optical manipulation of magnetic order

TL;DR: In this article, the authors review the progress in this field of laser manipulation of magnetic order in a systematic way and show that the polarization of light plays an essential role in the manipulation of the magnetic moments at the femtosecond time scale.

Abstract: 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 nearly 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.

Summary

1. Introduction

• A key theme in restructuring economies in the developing world is opening stock markets to foreign portfolio investment.
• Furthermore, the scrutiny of foreign investors, foreign equity analysts, and foreign stock listing standards can help resolve agency problems, effectively transmitting higher quality reporting and governance standards to developing-country firms (Obstfeld 1998, Stulz 1999).
• More generally, an entire capital market may be thought of as submitting to the demands of foreign investors from higher-quality environments when it loosens restrictions on foreign equity investors.
• Roll (1988) suggests that low r-squared coefficients from regressing individual stock returns on common economic factors represent private firm-specific information.

3. Data

• The authors begin with the names of the component firms of the Standard and Poor’s Emerging Markets Database (EMDB).
• They represent significant firms from a cross-section of over forty emerging economies.
• Data restrictions, as discussed in subsequent sections, limit the number of countries the authors are able to use.
• The lack of sufficient Datastream or I/B/E/S records for such countries as Bahrain, Egypt, Morocco, Nigeria, Oman, Saudi Arabia, and Zimbabthe authors leads us to exclude them from their sample.
• The authors use as many countries, firms, and time periods as possible, and, as detailed below, some tests check for robustness over different subsamples of the available data.

3.1 Proxies for openness to cross border portfolio flows

• The authors compute three proxies for the openness of a particular developing country to foreign portfolio investment.
• As previously discussed, classic theories suggest that such events can ease access to the local stock market by foreign investors, and a variety of studies associate such events with decreases in the cost of capital.
• The authors restrict this new set of events to major liberalizations involving the stock market or affecting the ability of foreigners to buy and sell local equities.
• Table 1 displays their five sets of liberalization and openness events.
• The authors third type of openness measure is computed from the size of portfolio flows between a particular developing country and the U.S. U.S. investors represent a significant fraction of the portfolio capital flows to and from emerging markets.

3.2 Proxies for the information environment

• The authors create several measures of the information environment faced by the emerging market firms in their sample.
• This confirms their interpretation of the firm-specific variance as a measure 7.
• What remains is trading volume generated by differential informed judgment (or difference in opinions), and it is reflected in the regression intercept.
• This estimate of “disagreement” around earnings releases is their final information environment indicator.
• Again, the trade-off between greater precision and greater disagreement as a result of an enhanced information environment could cause either decreases or increases in their disagreement measure with greater openness.

4. Empirical results

• The authors have several measures of the information environment: firm-specific return volatility, number of analysts, forecast dispersion, forecast error, and abnormal market responses to earnings.
• The authors have three types of measures of openness: dates of liberalization, cross listings, closed end country fund listings, and breakpoints in net portfolio flows; the fraction of capitalization available to foreigners; and the flow of portfolio capital to and from the U.S.
• The authors report results of a variety of tests relating changes in openness to changes in the information environment.

4.1 Summary statistics

• Table 2 contains univariate summary statistics (mean, median, standard deviation, nobs) on the country openness measures and firm-specific volatility (Panel A) and the earnings-related information variables (Panel B).
• Furthermore, earnings-related information variables are available only once per firm-year so their summary statistics are computed on annual observations.
• Taiwan is a particularly interesting case as it features low investibility but high U.S. equity portfolio flows.
• The relatively developed Korean market features a median of only 7 analysts per firm.
• First, return volatility at earnings release shows strong positive correlation with most other information variables (number of analysts, forecast error and dispersion, abnormal volume).

4.2 “Before versus after” tests

• The authors sample of explicit (liberalization, cross listing, and country fund) and implicit (estimated portfolio flow breakpoints) events imply distinct “before” and “after” periods.
• It indicates that firm-specific volatility is generally lower prior to liberalization events.
• These results suggest that firm-specific volatility increases significantly after various liberalization events.
• F-tests confirm that equality of “before” and “after” dummy coefficients is strongly rejected, except for abnormal trading volume.
• It suggests that while there is some evidence of increase in “disagreement” component of trading volume around earnings releases after liberalization events, the change is not statistically significant.

4.3 Regressions relating information environment to time-series openness measures

• Recall that their second and third openness measures, the proportion of market cap available to foreigners and the flow of capital between the U.S. and a particular country, are monthly time series.
• The necessity of running regressions with annual medians, as described previously, may facilitate this: one lag of an openness variable provides a window of a year for gradual responses of information variable.
• This indicates that increased availability of a country’s equities to foreigners is associated with substantial changes in the information environment.
• In contrast, larger market cap is sensibly associated with a larger number of analysts.
• It may be the case that, upon becoming more open to foreign investment, an emerging market quickly draws foreign attention to immediate, specific earnings events while coverage of a more general nature takes time to develop.

4.4 A closer look at a cross section of individual firms from one country

• The authors tests to this point largely feature variables that have been aggregated across firms and months within a year.
• Second, the Korean market is a major target of foreign portfolio investors, ranking third among their sample countries in terms of U.S. portfolio investment.
• Specifically, the authors use the Korea Securities Research Institute (KSRI) database for stock returns and the Listed Company Database of the Korean Listed Companies Association for financial statements and ownership information.
• To study individual Korean firms, the authors parallel Tables 7 and 8 (based on country median data) and run regressions of individual firm volatility on openness variables and firm characteristics.
• This yields approximately 400 to 500 firms for each sample year.

4.5 In which direction does causality run?

• The authors earlier work shows that information variables often relate to contemporaneous and lagged values of their two time-series openness measures, investibility and total U.S. portfolio flow.
• This interpretation implies that liberalization and other acts of increasing access have a beneficial effect on the information environment, in addition to the decreased cost of capital documented by previous authors.
• As more information about firms in an emerging market becomes available, foreign demand for local stocks increases and puts pressure on local authorities to loosen access.
• In contrast, the causality between number of analysts and portfolio flow is bi-directional, with stronger causality from number of analysts to portfolio flow.

5. Summary and conclusions

• The authors have uncovered interesting associations between the state of the information environment and the degree of openness to foreign equity investment across a sample of emerging markets.
• When foreign equity investment is impeded, many aspects of the information environment recede.
• This suggests that different facets of the information environment respond differently to changes in the degree of openness and the actual extent of foreign equity flows across an emerging economy’s borders.
• An increase in preannouncement forecast dispersion may indicate that there are more analysts grappling with greater quantity and quality of information.

Figures

FIG. 4. Comparison of induced MO ellipticity open circles and rotation filled diamonds for a Cu 111 /Ni/Cu epitaxial film and Ni thickness and pulse energy as indicated. The inset depicts the polar configuration with pump 1 and probe 2 beams. From Koopmans et al., 2000.

FIG. 3. Remanent MO contrast measured for a nickel thin film as a function of time after exciting by a 60 fs laser pulse. The results demonstrate ultrafast loss of the magnetic order of the ferromagnetic material within a picosecond after laser excitation. From Beaurepaire et al., 1996.

FIG. 45. Color online Demonstration of compact all-optical recording of magnetic bits. This was achieved by scanning a circularly polarized laser beam across the sample and simultaneously modulating the polarization of the beam between left and right circular. From Stanciu, Hansteen, et al., 2007.

FIG. 44. The effect of single 40 fs circular polarized laser pulses on the magnetic domains in Gd22Fe74.6Co3.4. The domain pattern was obtained by sweeping at high-speed 50 mm/s circularly polarized beams across the surface so that every single laser pulse landed at a different spot. The laser fluence was about 2.9 mJ/cm2. The small size variation in the written domains is caused by the pulse-to-pulse fluctuation of the laser intensity. From Stanciu, Hansteen, et al., 2007.

FIG. 43. Color online Noninertial and inertial scenarios to transfer a point mass over a potential. The noninertial mechanism above requires a continuous driving force that pulls the mass over the potential barrier. A similar scenario is realized in magnetization reversal via precessional motion in ferromagnets. In contrast, in the inertial mechanism below , during the action of the driving force the coordinate of the particle is hardly changed, but the particle acquires enough momentum to overcome the barrier afterwards. From Kimel et al., 2009.

FIG. 20. Color online Temperature dependence of a the magnetization precession frequencies FMR and ex. As temperature decreases from 310 K toward TA, the exchange resonance mode ex open circles softens and mix with the ordinary FMR resonance FMR closed circles . The solid lines are a qualitative representation of the expected trend of the two resonance branches as indicated by Eqs. 25 and 27 . b Temperature dependence of the Gilbert damping parameter eff. The lines are guides to the eye. From Stanciu et al., 2006.

FIG. 34. Color online Magnetic excitations in DyFeO3 probed by the magneto-optical Faraday effect. Two processes can be distinguished: 1 instantaneous changes of the Faraday effect due to the photoexcitation of Fe ions and relaxation back to the high spin ground state S=5/2 and 2 oscillations of the Fe spins around their equilibrium direction with an approximately 5 ps period. The circularly polarized pump pulses of opposite helicities excite oscillations of opposite phase. Inset shows the geometry of the experiment. Vectors H+ and H− represent the effective magnetic fields induced by righthanded + and left-handed + circularly polarized pump pulses, respectively. From Kimel et al., 2005.

FIG. 33. Color online Precession following excitation with circularly polarized light. The two helicities + and − give rise to precession with an opposite phase and a different amplitude. During the 100 fs presence of the laser pulse the magnetization precesses in the dominating axial magnetic field HF created by the circularly pump pulse. Subsequent precession takes place in the effective magnetic field Heff , possibly modified by the photomagnetic effects, see Sec. V.A. From Hansteen et al., 2005, 2006.

FIG. 21. Excitation and relaxation of the AFM vector moment measured via changes in the magnetic birefringence. Here one can distinguish three processes: 1 electron-phonon thermalization with 0.3 ps relaxation time, 2 rotation of the AFM vector with 5 ps response time, and 3 oscillations of the AFM vector around its equilibrium direction with an approximate 10 ps period. From Kimel, Kirilyuk, et al., 2004.

FIG. 9. Color online Time-resolved electron photoemission. Top: Normalized photoelectron spectrum at 300 fs circles with fit solid line and distribution function f E ; t dashed line on a logarithmic scale and divided by f triangles on a linear scale at right. The inset sketches the TRPE experiment. Bottom: Photoelectron spectra at different delays are displayed in color fits in black and are offset vertically. From Lisowski et al., 2005.

FIG. 16. Ultrafast laser-induced dynamics in NiFe/NiO exchange-biased bilayer: a Easy-axis transient Kerr loops for the photoexcited sample at t=1 and 200 ps following pulse photoexcitation at t=0. The open circles inserted in the bottom trace show expected behavior in the absence of coherent magnetization rotation. b Illustration of the trajectory of the magnetization vector in the typical LLG calculation. The initial direction of M is directed along the z axis. M is subject to a damped rotation with a large y component and a finite outof-plane x component indicated schematically. The transient modulation of the z component, measured by experiment, is projected out explicitly in c . From Ju et al., 1999, 2000.

FIG. 15. Color online All-optical excitation of coherent precession. a t 0, the magnetization points in the equilibrium direction, given by the sum of the anisotropy, demagnetizing, and external fields; b 0 t 1 ps, the magnitude of M and/or the anisotropy change due to heating, thereby altering the equilibrium orientation; c the magnetization precesses around the new equilibrium direction that is slowly restored due to the heat diffusing away.

FIG. 49. Color online Laser-induced magneto-optical response from FeBO3: a Oscillations of the probe polarization as a function of the time delay between linearly polarized pump and probe pulses for different orientations of the pump polarization. The pump pulses propagate along the z axis shown in b . The probe pulse is not shown in b for simplicity. c The amplitude of oscillations as a function of the pump polarization azimuthal angle symbols and its fit using Eq. 71 line . The results are obtained at T=10 K, H=1.75 kOe, and I=10 mJ/cm2. From Kalashnikova et al., 2008.

FIG. 50. Color online Spin precession excited by circularly polarized pump pulses propagating along a the z axis and along b the y axis. +− − is the difference between the spin precession amplitude excited by right- and left-handed circularly polarized pump pulses. In both cases the magnetic field is applied along the x axis and the probe is at 10° from the pump propagation direction. The results are obtained at T=10 K and I=10 mJ/cm2. From Kalashnikova et al., 2008.

FIG. 27. Color online Graphical illustration of the process of photoinduced magnetic anisotropy caused by linearly polarized laser excitation and the subsequent precessional dynamics. From Hansteen et al., 2006.

FIG. 26. Color online Dependence of the precessional amplitude on the applied in-plane magnetic field Hext. Round and square symbols represent amplitudes extracted from measurements at ±Hext. From Hansteen et al., 2006.

FIG. 25. Color online Coherent precession of the magnetization triggered by linearly polarized laser pulses. a Time dependence of the precession for different planes of pump polarization , with an applied field of Hext =350 Oe in the plane of the sample. Circles represent measurements and solid lines simulations based on the Landau-Lifshitz equation. b Precessional amplitude as a function of the plane of pump polarization. Round and square symbols represent amplitudes extracted from measurements at ±Hext. The solid line is a best fit. From Hansteen et al., 2006.

FIG. 2. Color online Illustration of stimulated coherent Raman scattering, a possible microscopic mechanism responsible for an ultrafast optically generated magnetic field. Two frequency components of the electromagnetic radiation from the spectrally broad laser pulse take part in the process. The frequency 1 causes a transition into a virtual state with strong spin-orbit coupling. Radiation at the frequency 2 stimulates the relaxation back to the ground state together with the creation of a magnon.

FIG. 24. Color online Transient magnetization reversal dynamics measured for a pump fluence of 6.29 mJ/cm2. Insets show hysteresis loops measured at distinct pump-probe delays. The loops demonstrate the magnetization reversal after about 700 fs. From Stanciu, Tsukamoto, et al., 2007.

FIG. 35. The amplitude of the spin oscillations as a function of pump fluence. From Kimel et al., 2005.

FIG. 36. Color online Suppression of heat-driven oscillations of the net magnetization in a multidomain sample: a At t 0, the magnetizations M1 and M2 of oppositely magnetized domains are tilted due to the balance among magnetocrystalline anisotropy field Ha, shape anisotropy field Hs, and external field He. b After photoexcitation, t 0, heating induces out-of-phase oscillations of the z components of M1 and M2.

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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-
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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

Frequently asked questions

Q1. What have the authors contributed in "Ultrafast optical manipulation of magnetic order" ?

A review of femtosecond laser manipulation of magnetic order can be found in this paper, where a broad class of materials that includes both ferromagnetic and antiferromagnetically ordered metallic, semiconducting, and dielectric materials are considered. 

Q2. What future works have the authors mentioned in the paper "Ultrafast optical manipulation of magnetic order" ?

Regarding these potential applications, for that it will be essential to extend the present state of optical manipulation and control of magnetic order toward smaller nanoscale dimensions. Given the rapid developments in nano-optics and plasmonics, such possibilities do not seem to be too far fetched. 

Q3. What is the role of the hot electron gas in the demagnetization of metals?

The hot electron gas plays the role of a thermal bath for spins and thus facilitates both an intensification of spin-flip processes and the demagnetization. 

Q4. Why should an observation of circular or linear birefringence be accompanied by similar effects?

Because of the Kramers-Kronig relations, an observation of circular or linear birefringence in a certain spectral range should be accompanied by similar effects of polarization-dependent absorption in another spectral domain. 

Q5. Why are these domains suitable for stroboscopic pump-probe experiments?

Because of the coercivity, these magnetic domains are sufficiently stable in time and thus suitable for stroboscopic pump-probe experiments. 

Q6. Why is the spin flip in the ground state due to the fact that the light mixes a?

In other words, the spin flip in the ground state is due to the fact that circularly polarized light mixes a fraction of the excited-state wave function into the ground state Pershan et al., 1966 . 

Q7. What is the significance of the details of the magnetic structure for the understanding of these results?

Recent results that show that even linearly polarized laser pulses can lead to similar effects have indicated the importance of the details of the magnetic structure for the understanding of these optomagnetic results. 

Q8. What is the temperature dependence of the precession frequency and the Gilbert damping parameter?

The observed strong increase in the precession frequency and the Gilbert damping when the temperature approaches TA is ideal for ultrafast ringing-free precessional switching in magnetic and magneto-optical recording. 

Q9. What is the use of metallic magnets in various applications?

At the same time, metallic magnets are used in numerous applications, from power transformers and sensors to data storage and spintronics. 

Q10. What is the role of the bandwidth in the classification of metallic magnets?

To make a classification, the role of the bandwidth may be invoked: narrowband materials, such as insulators, oxides, and to some extent also f metals can be excited much more selectively than the broadband transition metals. 

Q11. How can a laser pulse control the precession of antiferromagnetic spins?

circularly polarized light can control the precession of antiferromagnetic spins in the terahertz domain see Fig. 40 . 

Q12. Why is the effect of a femtosecond pump pulse different?

Because of the fundamental differences in the magnetic and transport properties of metals and insulators, the effect of a femtosecond pump pulse on these two types of magnetic material is different. 

Q13. How can a laser-induced spin flip process be coherently stimulated?

such a laser-induced spin-flip process can be coherently stimulated if both frequencies 1 and 2 are present in the laser pulse see Fig. 2 . 

Q14. What is the way to model the ultrafast laser-induced spin dynamics in a metallic?

Another approach to modeling ultrafast laser-induced spin dynamics in a metallic magnet is to use the LLG equation on the atomic level Chubykalo-Fesenko et al., 2006; Kazantseva, Nowak, et al., 2008 .