PHYSICAL REVIEW B 75, 155406 共2007兲

Ultrafast spin and lattice dynamics in antiferromagnetic Cr2O3
Takuya Satoh,* Bas B. Van Aken,† Nguyen Phuc Duong,‡ Thomas Lottermoser,§ and Manfred Fiebig储
Max-Born-Institut, Max-Born-Straße 2A, 12489 Berlin, Germany
共Received 7 November 2006; revised manuscript received 5 February 2007; published 9 April 2007兲
The spin and lattice dynamics of antiferromagnetic bulk Cr2O3 after excitation with an intense laser pulse
were investigated using amplitude and phase resolved optical second-harmonic generation as probe of themagnetic and crystallographic subsystems. Demagnetization occurs on three time scales ranging from
Ⰶ1 to ⬃ 7 ps. In comparison to ferromagnetic compounds, this is a two orders of magnitude faster response
and an additional spin-lattice interaction channel is observed.
DOI: 10.1103/PhysRevB.75.155406

PACS number共s兲: 78.47.⫹p, 42.65.Ky, 75.50.Ee, 78.20.Ls
II. MAGNETIC AND CRYSTALLOGRAPHIC SECONDHARMONIC GENERATION

I. INTRODUCTION: SPIN DYNAMICS
OF ANTIFERROMAGNETIC COMPOUNDSOne of the aspects steering the development of datastorage technologies is the speed at which the magnetic state
can be manipulated. Therefore, dynamical processes in magnetically ordered systems are a key issue of the rapidly
evolving field of spin electronics. For ferromagnetic systems,
it was shown that magnetic-field pulses allow repeatedswitching of the magnetization on the subnanosecond timescale, while optical experiments with pulsed lasers revealed
demagnetization processes down to the subpicosecond
range.1–3 In spite of the increasing interest in antiferromagnetic 共AFM兲 systems for practical applications,4,5 their magnetization dynamics is less well understood. This is mostly
due to the absence of a macroscopic magnetization which
impedes direct access to the AFM order parameter. Therefore, secondary effects are employed to study the spin dynamics of AFM systems on the ultrafast time scale: a weakferromagnetic moment accompanying the AFM order 共as in
FeBO3兲,6 a change of birefringence induced by AFM reordering 共as in orthoferrites兲,7 a change of reflectivity characteristic for the melting of an AFM insulating state 共as in
Pr0.7Ca0.3MnO3兲,8 or the exchange-bias effect 共as in
NiO / NiFe bilayers兲.9 However, the more indirect the coupling to the AFM order parameter is, the more difficult it getsto disentangle magnetic and crystallographic contributions to
the response signal and, thus, to distinguish between the dynamics of the spins and the lattice. The problem may besolved by resorting to nonlinear instead of linear opticaltechniques. Second-harmonic generation 共SHG兲 possesses
contributions that couple either to the “spinless” crystal or tothe magnetic order parameter. Therefore, it distinguishes
very efficiently between the crystallographic and magnetic
properties of, in particular, AFM compounds or ferromagnetic surfaces and interfaces.10–13
In this paper, we describe the temporal evolution of spins
and lattice in AFM Cr2O3 bulk crystals after excitation withan intense 250 fs laser pulse. The dynamical response of thetwo subsystems is probed in one experimental run by SHG
coupling to the AFM order parameter or to the crystal structure. The amplitude of the SHG signals reveals a different
response of spins and lattice. The phase between the SHG
contributions leads to the identification of three demagnetization channels on separate time scales. Distinct differences
to the dynamics of ferromagnetic systems are observed.
1098-0121/2007/75共15兲/155406共6兲

The simplest nonlinear optical process is SHG with
Si共2␻兲 = ␧0␹ijkE j共␻兲Ek共␻兲,共1兲

where Eជ 共␻兲 is the electric field of the incident light wave at
frequency ␻, while Sជ 共2␻兲 is the source of the light wave at
the frequency 2␻ emitted from the crystal.14 The light-matterinteraction is parametrized by the susceptibility ␹ˆ . The tensor
␹ˆ = ␹ˆ 共0兲 + ␹ˆ 共ᐉ兲 + . . . is expanded in the magnetic order parameter ᐉ. ␹ˆ 共0兲 represents the “crystallographic” contributions
found above and below the magnetic ordering temperature,
while ␹ˆ 共ᐉ兲 is the leading “magnetic” contribution found below the ordering temperature only.15 SHG from ␹ˆ 共ᐉ兲 and␹ˆ 共0兲 can thus be used to probe the spins and the lattice,respectively, and, thus, to reveal their coupling.
III. Cr2O3 AS MODEL COMPOUND

Our interest in Cr2O3 is twofold: On the one hand, recent
interest in this compound was triggered by its exchange-bias
properties,16 which can be controlled via the magnetoelectriceffect.17 The magnetoelectric interaction depends on the correlation between spins and lattice. This warrants an investigation of this correlation. On the other hand, Cr2O3 is an
AFM model compound whose static properties are wellknown.18 This is an ideal basis for investigating its dynamical properties. Note that the spin-wave dynamics of Cr2O3
has already been studied,19 however, without observing the
dynamics of the spin-lattice energy transfer.
Cr2O3 is a uniaxial antiferromagnet crystallizing in thecentrosymmetric point group 3̄m.18 The structure is composed of chains of Cr3+ ions aligned along the trigonal z axis.
The Cr3+ ions are surrounded by distorted octahedra of O2−ions with 3 as site symmetry. Cr2O3 orders antiferromagnetically at TN = 307.6 K.18 The sequence of Cr3+ spins along z in
the unit cell of opposite 180° domains is ⫹⫺·⫹⫺ and⫺⫹·⫺⫹, where the dot denotes an empty, undistorted
O2− octahedron. The AFM order breaks both time and space
inversion symmetry and leads to 3̄m as magnetic point
symmetry.20 The contributions from ␹ˆ 共0兲 and ␹ˆ 共ᐉ兲 to thesource term Sជ of the SHG wave described by Eq. 共1兲 were
derived in Ref. 20 and are summarized as follows: With lightincident along the trigonal z axis, only one independent com-

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SATOH et al.

IV. EXPERIMENTAL SETUP

FIG. 1. Experimental setup and SHG spectra of Cr2O3 measured
in one experimental run at 10 K for light incident along the z axis.
共a兲 Setup for pump-and-probe experiments with SHG in transmission as probe process. 共b兲 Settings of polarizer 共a quarter-wave
plate兲 and analyzer 共a polarization foil兲 needed to obtain the amplitude of and the phase between spin and lattice contributions to the
SHG signal. The y and x axes of Cr2O3 are defined by lying, respectively, perpendicular to and in the mirror plane of the crystal
with 3̄m symmetry 共Ref. 18兲. 共c兲 Spectra of the magnetic and crystallographic contributions to SHG. 共d兲 Spectra of their constructive
and destructive interferences.

ponent from the tensors ␹ˆ 共0兲 and ␹ˆ 共ᐉ兲 contributes to SHG,
which is henceforth simply denoted as ␹共0兲 and ␹共ᐉ兲, respectively. One gets

冢冣 冢

冣

␹共0兲共E2x − E2y 兲 + 2␹共ᐉ兲ExEy
Sx
2␻Sជ = Sy = 4 2 − 2␹共0兲ExEy + ␹共ᐉ兲共E2x − E2y 兲 ,
c
Sz
0

共2兲

for linearly polarized light, and

冢冣

冢

冣

关− ␹共0兲 + i␹共ᐉ兲兴E−2
S+2
␻
Sជ = S− = 4冑2 2 关+ ␹共0兲 + i␹共ᐉ兲兴E+2 ,
c
S0
0

共3兲

for circularly polarized light. According to Eq. 共2兲, a polarization analysis allows one to separate spin and lattice contributions to SHG: With light incident along the z axis andpolarized linear along one of the principal axes, the x- andthe y-polarized components of the corresponding SHG wave
couple to ␹共0兲 and ␹共ᐉ兲, respectively. On the other hand, useof circularly polarized light allows one to obtain the constructive and destructive interferences of SHG contributions
from ␹共0兲 and ␹共ᐉ兲.

Cr2O3 crystals grown by the flux method were oriented by
Laue diffraction and cut perpendicular to the trigonal z axis
by a diamond saw. Lapping by SiC powder was followed bychemical mechanical polishing with a colloidal silica slurry
共Syton兲. The finalized samples had a lateral size of a few
millimeters and a thickness of ⬃50 ␮m. They were mounted
in a cryostat, and areas located within one AFM domain werestudied in two types of transmission experiments: 共i兲 SHG
spectra were measured using 5 ns laser pulses at a repetition
rate of 10 Hz, which were emitted from an optical parametricoscillator pumped by the third harmonic of a Nd-doped yttrium aluminum garnet laser. 共ii兲 The temporal evolution of
the SHG signal was measured in a pump-and-probe experiment. The samples were excited at ប␻pump = 3.10 eV with
250 fs pulses at an intensity of 1 – 10 mJ/ cm2. The pulses
were generated at a repetition rate of 1 kHz by frequency
doubling amplified pulses at 1.55 eV emitted from a Ti:sapphire laser. Because of the proximity to the charge-transfer
gap of Cr2O3 at 3.3 eV, the absorption length of the pumppulses was ⬃7 ␮m.21
SHG by pulses emitted from an optical parametric amplifier pumped by the Ti:sapphire laser was employed for probing the dynamical properties. As shown in Fig. 1共a兲, thesamples were mounted in a cryostat and SHG from the region excited by the pump beam was measured in transmission. In order to ensure that a uniformly pumped area isprobed, the diameter of the probe beam is 50% smaller thanthat of the pump beam. Furthermore, the SHG energy
2ប␻probe was chosen such that the absorption length at2ប␻probe 共here 1.7 ␮m at 2.0 eV兲 was much smaller than theabsorption length at ប␻pump. Furthermore, because of thelarge absorption, the issue of phase matching can beneglected.14
The intensity of the probe beam was in the order of
10 mJ/ cm2, but this can still be regarded as “weak” in comparison to the pump beam because of the negligible absorption of the probe beam in the sample. In both setups, wave
plates and foil polarizers were applied to set the polarizationof the incoming light and to analyze the polarization of the
SHG light, respectively. Color filters were used in front of
the sample for suppressing SHG generated in optical components and behind the sample for separating the SHG lightfrom the fundamental light. The SHG signal was detected by
a GaAs photomultiplier tube and normalized to the squared
intensity of the transmitted fundamental light.
It is known that the phase of the SHG light can carry
important information about the magnetic state which is absent in the amplitude.11 We therefore require a setup in which
both the amplitude A of and the phase ␸ between spin andlattice contributions to the SHG signal are measured withhigh accuracy. This was achieved by mounting the components, which set and analyze the polarization of the lightwaves, in computer controlled mechanical rotors. This allowed us to measure the polarization configurations needed
for the determination of the SHG amplitudes and phases 关seeFig. 1共b兲兴 in one experimental run. Avoiding the temporal
drift of consecutively measured data sets, we were able todetermine the temporal evolution of ␸ with an accuracy of
0.1°.

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ULTRAFAST SPIN AND LATTICE DYNAMICS IN…
V. EXPERIMENT
A. Second-harmonic-generation spectra

Figures 1共c兲 and 1共d兲 show the spectral dependence of
SHG from Cr2O3 at 10 K in the range 1.7– 3.0 eV. As described, the four spectra were measured in a single experimental run in contrast to previous experiments. The configurations displayed in Fig. 1共b兲 were applied in order to obtainthem. The settings of polarizer and analyzer are based on
Eqs. 共2兲 and 共3兲. The magnetic and crystallographic contributions to SHG are generated with y-polarized fundamental
light and separated by detecting the y- and x-polarized component of the SHG light, respectively. The SHG intensities
are Imag ⬀ 兩Sy兩2 and Icryst ⬀ 兩Sx兩2, with Sជ 共2␻兲 as source termfrom Eq. 共1兲. The constructive and destructive interferencesof magnetic and crystallographic SHG contributions are obtained with circularly polarized incident light and no analyzer in the SHG beam. Here, the SHG intensities are I±⬀ 兩Sy ± iSx兩2. The amplitude of the magnetic contribution,
which is proportional to the AFM order parameter, and theamplitude of the crystallographic contribution 共for convenience denoted by L兲 areAmag = 冑Imag ⬀ ᐉ,

Acryst = 冑Icryst ⬅ L.

共4兲

The relative phase ␸ between the magnetic and crystallographic contributions22 is given bysin ␸ =

I+ − I− Imag + Icryst·.
I+ + I− 2冑ImagIcryst

共5兲

In Refs. 23 and 24, it was shown that the origin of magnetic
SHG in Cr2O3 is a twisted octahedral ligand field in combination with spin-orbit interaction which leads to two-photon
electric-dipole transitions coupling to the AFM order parameter. The value of ␸ is determined by local-field corrections
to the magnetic and crystallographic SHG susceptibilities.
This relation is a complex one and prevents the derivation ofquantitative values for ᐉ and L from ␸. However, as we will
see in the following, the phase of the SHG signal can still be
employed as qualitative probe of the magnetization and thelattice dynamics, which reveals important information about
the temporal evolution of the spin-lattice interaction that is
not acquired from the intensity of the SHG signal.
According to Eq. 共5兲, in order to minimize the error of⌬␸, the phase should be measured at a photon energy whereI+ Ⰷ I− and Imag ⬇ Icryst. Figure 1 reveals that SHG in therange 1.9– 2.2 eV or near 2.6 eV meets these requirements.
The optical parametric amplifier can emit light at
0.55– 0.77 eV 共“idler”兲 and at 0.77– 1.00 eV 共“signal”兲. For
probing at SHG energies ⬎2.0 eV, i.e., fundamental energy⬎1.0 eV, the frequency doubled idler wave needs to be usedas probe wave. However, the intensity of this wave is too
low, so that in spite of the larger SHG efficiency near 2.2 eV,
the fundamental signal wave was used for probing the ultrafast SHG response at 2.0 eV.
B. Pump-and-probe data

Figure 2共a兲 shows the temporal evolution of the change ofFIG. 2. Temporal evolution of SHG signals in a pump-andprobe experiment. 共a兲 Change of SHG intensity ⌬I at 2.0 eV versus
delay t after the photoexcitation. Based on Fig. 3共b兲, an instantaneous and two exponential contributions are fitted to the data 共seetext兲 and lead to the solid lines. Note that each curve is fitted withthe same time constants 共␶2 = 0.93 and ␶3 = 6.62 ps兲. 共b兲 Change of
linear reflectivity ⌬R at 2.0 eV versus delay t after the photoexcitation. 共c兲 Cross correlation of pump and probe pulses. 共d兲 Superposition of magnetic contribution to SHG and optical effects modifying the SHG intensity near t = 0.

SHG intensity ⌬I after exciting a Cr2O3 sample at 285 K
with a 250 fs pump pulse with an intensity of 10 mJ/ cm2.
The zero position of the delay t is defined by the maximumof the cross correlation in Fig. 2共c兲. Two regimes with abasically different SHG response are observed. At t
⬍ 0.3 ps, the response is universal: A transient decrease of all
SHG signals by about 10% occurs. At t ⬎ 0.3 ps, the temporal evolution of SHG is drastically different for the four configurations with ⌬I ranging from −22% to +18%.
In the interpretation of these data, optical effects modifying merely the efficiency of the SHG process must be distinguished from SHG variations that are due to a genuinechange of magnetization or lattice temperature.25 On the one
hand, the efficiency of the SHG process is modified bychanges of the linear optical constants that change the intensity of the fundamental light entering the sample and of the
SHG light leaving the sample. Figure 2共b兲 shows that thepump beam leads to a change of reflectivity ⌬R at the SHG
wavelength by 艋0.1% 共the same result is obtained at thefundamental wavelength兲. Modification of the linear opticalproperties can therefore be neglected in Fig. 2共a兲. On theother hand, the efficiency of the SHG process is modified by
nonlinear interaction between the pump and probe waves andby the massive excitation of nonequilibrium carriers in thepresence of the pump beam. In agreement with other pumpand-probe experiments based on SHG,12,13,26 the universal
dip at t = 0 in Fig. 2共a兲 is ascribed to these effects. The kink at
t = 0.3 ps in Fig. 2共d兲 indicates the transition from the range
dominated by optical effects to the range displaying genuine
spin and lattice dynamics.
Figures 3共a兲 and 3共b兲 show the temporal evolution of thefollowing parameters: 共i兲 the change of the AFM order parameter ⌬ᐉ, 共ii兲 the change of the corresponding lattice contribution ⌬L, and 共iii兲 the change of the relative phase be-

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FIG. 3. Temporal evolution of the change of 共a兲 amplitude and共b兲 phase. Data and solid lines are derived from Fig. 2共a兲 using Eqs.
共4兲 and 共5兲. The inset shows the extrapolation to t = 0 in comparison
to the SHG data. This reveals the instantaneous demagnetization
共arrow兲 discussed in the text.

tween spin and lattice contributions to SHG ⌬␸ as derived
from the raw data in Fig. 2共a兲 by means of Eq. 共5兲. The
progression in Fig. 3共a兲 does not uniquely reveal the numberof channels contributing to ⌬ᐉ共t兲 and ⌬L共t兲. However, this isdisclosed by the temporal evolution of ⌬␸ in Fig. 3共b兲. A
repeated change of the sign of the slope of ⌬␸共t兲 shows thatthree independent channels with alternating sign of the associated phase change contribute. Based on this observation,
three processes are fitted to the data at t ⬎ 0.3 ps in Fig. 2共a兲.
The processes are 共i兲 an “instantaneous” contribution on atime scale ␶1 Ⰶ 1 ps described by a step, 共ii兲 a “fast” exponential contribution with a characteristic time ␶2 = 0.93 ps,
and 共iii兲 a “slow” exponential contribution with a characteristic time ␶3 = 6.62 ps. The excellent agreement between data
and fits in Fig. 2 and, consequently, in Fig. 3 confirms thepresence of three channels. It further demonstrates that even
without establishing a quantitative relation between ⌬␸ and共⌬ᐉ , ⌬L兲, the phase serves as valuable probe of the magnetization and lattice dynamics.

⌬L reproduces the lattice temperature. This is confirmed by
the correspondence of ⌬L共t兲 and −⌬R共t兲. The reflectivity
change reproduces the temperature of the photogenerated
carriers27 and, thus, of the lattice because thermal equilibrium of electrons and lattice is acquired within ⬍1 ps.28 Furthermore, ⌬ᐉ reproduces the spin temperature, which is governed by spin-lattice interaction via the fast and the slow
processes. Spin-lattice interaction is evidenced by the factthat the lattice temperature is decreasing 共increase of ⌬L兲
while the spin temperature is increasing 共decrease of ⌬ᐉ兲,with ⌬L共t兲 and ⌬ᐉ共t兲 being described by the same relaxation
times ␶1 to ␶3. With 307.6 K as the Néel temperature,⌬ᐉ共30 ps兲 = −12% corresponds to a spin temperature increaseby 9 K at 285 K, which coincides with the value calculated
for lattice heating by the pump pulse.21,29 On the other hand,
the SHG intensity of the lattice contribution is mostly determined by the gradual increase of linear absorption withtemperature,21 which attenuates the SHG wave by about 1%10% per 100 K. Here, a temperature increase by 9 K is avery small effect and explains the near recovery of⌬L共30 ps兲. Note that electron-spin interaction is negligible
because Cr2O3 is an insulator. Thermal diffusion is also negligible because it occurs on a time scale of ⬎300 ps.28
The data in Fig. 3 reveal two remarkable differences tothe dynamical processes of ferromagnetic 共and ferrimagnetic兲 compounds: First, two demagnetization channels, theslow and the fast process, mediate the thermalization of spins
and lattice, whereas in ferromagnets only one such channel
was observed.3,30 The difference is striking but its origin is
yet unclear. Second, the demagnetization times ␶2,3 are 2
orders of magnitude shorter than the demagnetization time
for a ferromagnetic compound3 with the same magnetocrystalline anisotropy constant 共KA = 8 ⫻ 104 erg/ cm3 at room
temperature31兲 as Cr2O3. This is understood as follows. In
Ref. 3, it is shown that the demagnetization time for a ferromagnetic compound scales inversely with the ferromagnetic
resonance frequency, which is proportional to the magnetic
anisotropy energy: ␻FM ⬀ EA. In analogy, it is reasonable toassume that the demagnetization time for an AFM compound
scales inversely with the AFM resonance frequency. The
AFM resonance frequency is given by

␻AFM ⬀ 冑EAEex ,共6兲with Eex as exchange energy.32 For Cr2O3, one finds a ratio31
Eex / EA ⬃ 104, which leads to the 2 orders of magnitude faster
response observed.
Note that the excellent agreement of fits and data in Fig. 3
allows one to extend the progression of ⌬ᐉ共t兲 to t = 0 and to
separate the AFM contributions to SHG from optical modifications of the SHG efficiency in that range. The result in
the inset of Fig. 3 reveals the instantaneous contribution.
D. Temperature dependence

C. ModelFigure 3 leads us to the following scenario. Following
previous experiments, the instantaneous process is ascribedto emission of magnetic excitations such as magnons during
nonradiative decay of photoexcited carriers.3 Subsequently,

Figure 4共a兲 shows the temporal evolution of the change of
the AFM order parameter at three temperatures. The transient
drop of SHG intensity due to modification of the SHG efficiency by the pump pulse up to t ⬃ 0.3 ps appears at all temperatures. At 250 K, the instantaneous and the slow process

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temporal evolution of the phase change reveals additional
information: The inset of Fig. 4 shows that the slow process
still plays a role at 80 K, since a reproducible increase of ⌬␸on a time scale ␶3 = 5.2 ps is observed.
First, Fig. 4共b兲 confirms that an instantaneous demagnetization is present at all temperatures below TN, whereas
slower demagnetization processes become relevant near TN
only.3 Second, the fits reveals a continuous decrease of ␶3with temperature. According to Eq. 共6兲, this is consistent
with the increase of the magnetic anisotropy with decreasing−1. The correspondence is atemperature because of ␶3 ⬀ ␻AFM
qualitative, not a quantitative, one because the temperaturedependence of the magnetic specific heat30 can also influence
the temperature dependence of ␶3.
VI. CONCLUSION

FIG. 4. Temperature dependence of the magnetization dynamics. 共a兲 Evolution of the change of amplitude of magnetic SHG atthree temperatures. 共b兲 Change of magnetic amplitude at t = 30 ps asa function of temperature. Inset: evolution of the change of phase⌬␸ at 80 K.

are also observed but less pronounced than at 285 K. For theslow process, the fit reveals ␶3 = 6.23 ps. Because of thesmaller magnitude, the fast process can no longer be separated from the optical effects modifying the SHG intensity att ⬍ 0.3 ps. At 80 K, the magnitude of both the fast and theslow process is too small to be resolved, and only the instantaneous change of magnetization is observed. Again, theIn summary, the dynamical processes in AFM bulk Cr2O3
after excitation with an intense laser pulse were investigatedby ultrafast optical pump-and-probe experiments. SHG coupling either to the magnetic or the crystallographic subsystems allows us to separate the spin dynamics from thelattice dynamics and to study the interaction of these subsystems. Phase resolved SHG reveals that three thermalization processes contribute to the demagnetization on timescales of Ⰶ1, 0.93, and 6.62 ps at T = 285 K. The first process is associated with emission of magnetic excitations during nonradiative carrier decay, whereas the latter two describe the thermalization of the spin system by spin-latticeinteraction. Our results demonstrate that the magnetization
dynamics of even a simple AFM model compound differs
noticeably from that of ferromagnetic compounds.
In future experiments, the potential of nonlinear opticaltechniques to distinguish between contributions from different sublattices of a sample just on the basis of polarization
selection rules and spectroscopy will be used to investigate
the dynamical relations between sublattices in multiply ordered compounds. Here, multiferroics with a coexistence of
共anti兲ferroelectricity and 共anti兲ferromagnetism are candidatesof great current interest.
ACKNOWLEDGMENTS

The authors thank M. Matsubara for help with the reflection measurements. Subsidy from the SPP 1133 of the DFG
is appreciated. M.F. thanks T. Elsässer for continuous support.

*Present address: Department of Basic Science, The University ofBonn, Germany. Electronic address: fiebig@hiskp.uni-bonn.de

Tokyo, Komaba, Meguro-ku, Tokyo 153-8902, Japan.
†Present address: ECN, Afdeling zonne-energie, P.O. Box 1, 1755
ZG Petten, The Netherlands.
‡
Present address: ITIMS, Hanoi University of Technology, 1 Dai Co
Viet Road, Hanoi, Vietnam.
§
Present address: SSP-ERATO, Japan Science and Technology
Agency, Tsukuba, Ibaraki 305–8562, Japan.
储Present address: HISKP, Universität Bonn, Nussallee 14–16, 53115

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