PRL 105, 077402 (2010)

PHYSICAL REVIEW LETTERS

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Spin Oscillations in Antiferromagnetic NiO Triggered by Circularly Polarized Light
Takuya Satoh,1 Sung-Jin Cho,1 Ryugo Iida,1 Tsutomu Shimura,1 Kazuo Kuroda,1 Hiroaki Ueda,2 Yutaka Ueda,2B. A. Ivanov,3,4 Franco Nori,4,5 and Manfred Fiebig6
1
Institute of Industrial Science, University of Tokyo, Tokyo 153-8505, Japan
Institute for Solid State Physics, University of Tokyo, Kashiwa, Chiba 277-8581, Japan
3
Institute of Magnetism, Vernadskii Avenue 36B, 03142 Kiev, Ukraine
4
RIKEN Advanced Science Institute, Wako-shi, Saitama, 351-0198, Japan
5
Department of Physics, University of Michigan, Ann Arbor, Michigan 48109-1040, USA
6
HISKP, Universität Bonn, Nussallee 14-16, 53115 Bonn, Germany(Received 2 December 2009; published 11 August 2010)
2

Coherent spin oscillations were nonthermally induced by circularly polarized pulses in the fullycompensated antiferromagnet NiO. This effect is attributed to the action of the effective magnetic field
generated by an inverse Faraday effect on the spins. The novelty of this mechanism is that spin oscillations
are driven by the time derivative of the effective magnetic field which acts even on ‘‘pure’’ antiferromagnets with zero net magnetic moment in the ground state. The measured frequencies (1.07 THz and
140 GHz) correspond to the out-of-plane and in-plane modes of antiferromagnetic spin oscillations.
DOI: 10.1103/PhysRevLett.105.077402

PACS numbers: 78.20.Ls, 75.30.Ds, 75.50.Ee, 78.47.J

All-optical magnetization switching has been extensively studied in recent years. Demagnetization within
1 ps was discovered by irradiating ferromagnetic nickel
with femtosecond laser pulses [1]. This finding has stimulated intense theoretical and experimental investigations.
Many of the experiments on so-called ‘‘ultrafast magnetism’’ can be interpreted in terms of laser-induced heating,which is already exploited technologically in the form ofheat-assisted magnetic recording [2]. However, the recording rate is limited by slow thermal diffusion. Thus, magnetization control beyond the limit of such thermal control
is highly desirable.
A typical form of nonthermal magnetization control is
the inverse Faraday effect (IFE) [3,4] in which circularly
polarized light induces a magnetization that can be described as a light-induced effective magnetic field acting
on the body. A pump-probe technique with subpicosecond
time resolution has revealed a transient IFE at zero timedelay in itinerant ferromagnets [5–8]. However, the validity was questioned because the observation was restricted
to the temporal overlap of the pump and probe pulses [9].
The dynamic properties of antiferromagnets (AFMs) are
rapidly gaining importance [10,11]. They display inherently faster spin dynamics than ferromagnets [10–12] andoffer the advantage that the spin oscillation frequency
extends into the terahertz regime. In addition, ultrafast
manipulation of the antiferromagnetic order parameter
may be employed for ultrafast control of the magnetizationof an adjacent ferromagnet via the exchange-bias effect.
Recently, spin precession caused by the IFE has beenreported for ferrite garnets [13] and for canted AFMs
[11,14], which possess nonzero net magnetic moment
caused by the Dzyaloshinskii-Moriya interaction. The
presence of this magnetic moment is an important issue
for the recently proposed mechanism of inertia-driven
0031-9007=10=105(7)=077402(4)excitation of spin oscillations in canted AFMs [15]. However, fully nonthermal control of spin oscillations has notbeen demonstrated yet in ‘‘pure’’ AFMs, having a com~ ¼ 0) in the ground state.
pensated magnetic moment (MHere we report the first observation of coherent spin
oscillations in the compensated AFM NiO in a pump-probe
experiment. The oscillations consisted of 1.07 THz and
140 GHz components, which are assigned to out-of-plane
and in-plane modes of antiferromagnetic spin oscillations.
The sign of the oscillation was reversed with the reversal of
the pump helicity. This is interpreted within the  model asa direct action of the time derivative of the impulsive
magnetic field generated by a circularly polarized pulse
via the IFE on the zero-magnetization AFM. This mechanism (discussed in Refs. [16,17] but never observed before)
opens a novel way for the ultrafast control of spins incompensated AFMs.
NiO is a promising exchange-bias AFM because of its
simple structure and room-temperature antiferromagnetism. Therefore, the investigation of the time-resolved
responses of NiO is important for applications of ultrafast
optical switching and in fundamental research. The subpicosecond spin reorientation in NiO has been achieved bymodifying the magnetocrystalline anisotropy with linearlypolarized light [18]. However, this process depends on aresonant optical excitation and is thus limited by thermal
effects.
Above the Néel temperature (TN ¼ 523 K), NiO has aNaCl-type cubic structure (point group: m3m).
Below TN ,NiO has antiferromagnetic order. The Ni2þ spins align axes in f111g planes
ferromagnetically along the h112i
with antiferromagnetic coupling in between adjacentf111g planes [19]. Exchange striction leads to a contractionof the cubic unit cell along the h111i axes and reduces the This gives rise to four
crystallographic symmetry to 3m.

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Ó 2010 The American Physical Society

PHYSICAL REVIEW LETTERS

PRL 105, 077402 (2010)

types of twin (T) domains. The deformation is accompanied by magnetic birefringence between the f111g plane
and the h111i direction. NiO is a charge-transfer insulator
with a 4 eV band gap. The intragap optical transition in the
midinfrared to visible region is ascribed to the d-d transitions of the Ni2þ ð3d8 Þ electrons [20].
A NiO single crystal grown by the floating-zone method
was polished into (111)-oriented platelets with lateral dimensions of a few millimeters and a thickness of’100 m. To obtain T domains of 0.1–1 mm, the platelets
were annealed in an argon-oxygen mixture with small
oxygen partial pressure at 1400  C [21]. Four types of T
domains were distinguished in the cross-Nicol configuration [22]. For the pump-probe measurement, we selected a
 plane different from thesingle T domain with the (111)
sample surface (111), as shown in Fig. 1(a).
The temporal evolution of the polarization rotation andtransmission was measured at 77 K with a pump-probe
setup with no external magnetic field [Fig. 1(b)]. Linearlypolarized light from a Ti:sapphire laser with a wavelengthof 792 nm, a pulse width of 120 fs, and a repetition rate of
1 kHz was used as the probe. Circularly polarized opticalpulses with a wavelength of 1280 nm, generated by an
optical parametric amplifier, were used as the pump. The
pump and probe beams were incident at 7 and 0 , respectively, and focused onto the sample surface to spot sizes ofabout 100 and 40 m, respectively. The pump fluence was
10 mJ=cm2 , which corresponds to the absorption of about
one photon per 104 Ni2þ ions. The transmitted probe beam
was divided into two orthogonally polarized components

(a)

(c)

(111)

for obtaining the polarization rotation and the transmission
change.
To clarify the spin-related contribution, we examined the
response after photoexcitation with different time delays.
Figures 2(a) and 2(b) show the polarization rotation and thetransmission change, respectively, versus the time delay
between the probe beam and the pump beam. The inset in
Fig. 2 shows the polarization rotation of the probe beamnear zero delay. Here the signal is compared for ðþÞ andðÞ polarized pump beams at fixed laser fluence. In
Fig. 2, two processes can be distinguished: (1) a fast(quasi-instantaneous) change of the polarization rotation
within the time of the pulse action (inset) and (2) damped
oscillations of the polarization rotation which persists formuch longer times (upper frame).
In regime (1), for short time delays (&1 ps), the rotation
exceeded 20 mrad when the pump and the probe beams
overlapped temporally. The full width at half maximum of
the signal was about 200 fs, which reflects the duration of
the pump and probe pulses. In regime (2), damped oscillations of the signal were observed at times longer than
10 ps. For both time intervals, the sign of the signal
changes with reversal of the pump helicity, which is a clear
indication of the nonthermal origin of the effect. Note thesignificant difference in the amplitude of the rotation angle
observed at these two time scales (&0:2 and 1 ps) thatxlx (111)mz(easy axis)

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z

y

(d) x
m

z

y
l

:Ni

(b)

delay
probe
pump

y
WP

P

GI
o

7

sampleSi detector

FIG. 1 (color online). (a) Geometry of the experiment. The(111) direction coincides with the normal to the sample; the direction (x axis), y axis, and z axis, respectively, are the(111)
hard, medium, and easy axes for the T domain of our measurement (red triangle). (b) Schematic diagram of the experimental
setup. (P: polarizer; WP: Wollaston prism; GI: gated integrator).
(c),(d) Schematics of the oscillations of vectors l~ and m~ (blue andred arrows, respectively) for the out-of-plane and in-plane modesof the spin oscillations.

FIG. 2 (color online). Time-resolved (a) polarization rotationand (b) transmission change in NiO (111) for pump helicitiesðþ; Þ. Pump wavelength: e ¼ 1280 nm; probe wavelength:p ¼ 792 nm.

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PHYSICAL REVIEW LETTERS

likely reflects the difference of the mechanisms responsible
for them.
Process (1) can be considered as a typical example offemtomagnetism, arising at times much shorter than thethermalization time [23]. A description of this regime
involves either a direct transfer of photon angular momentum to the medium or a photoenhanced transfer between
orbital and spin momenta [8,13,23–25]. For NiO, the orbital momentum of the ground state (3 2 ) of the Ni2þ ð3d8 Þ
ion is quenched due to orbital nondegeneracy. In the virtually excited state, the orbital momentum is 1 dependingon the helicity ðÞ of the pump beam, which leads to theappearance of a transient magnetization. Recently,
ab initio calculations [26] of an ultrafast laser-induced
spin switch in NiO has demonstrated the possibility of
inducing a spin magnetic moment at <100 fs that results
in instantaneous magneto-optical effects.
In process (2), the sign of the oscillations in the polarization rotation changes with reversal of the pump helicity.
No oscillation is observed in the transmission, indicatingthat the oscillation in the rotation is magnetic
in origin. The
P
damped oscillations are fitted by i¼1;2 ai cosð2fi t þi Þ expðt=i Þ. The data in Fig. 2(a) yield a1 ¼
0:3 mrad, f1 ¼ 1:07 THz, 1 ¼ 1:0, 1 ¼ 15 ps, a2 ¼
0:375 mrad, f2 ¼ 140 GHz, 2 ¼ 2:2, and 2 ¼ 10 ps.
This behavior is not sinelike, as for canted AFMs [15]. A
small deviation from the cosinelike behavior [17] (seebelow) can be attributed to surface effects (like for opticalphonons [27]).
At these time scales some magnon modes are excited in
the spin system. The coherent spin oscillations modulate
the dielectric permittivity, leading to a rotation of the probe
polarization (see below). Since the net magnetization iszero in the ground state, the mechanism inducing spin
oscillations is different from that in ferrimagnets or incanted AFMs. Such excitation in NiO cannot be attributed
to the mechanism discussed in Ref. [15], for which thepresence of nonzero net magnetic moment in the groundstate is necessary. Instead, the dynamics of pure AFMs can~be described by the  model with the derivative dHðtÞ=dt
as a driving force [17]. Let us now discuss process (2)within the  model.
For the theoretical description of the spin excitations, weemploy a model of NiO with two sublattices with magne~ 1 and M~ 2 , jM
~ 1 j ¼ jM
~ 2 j ¼ M0 , coupled by thetizations M
antiferromagnetic next-nearest neighbor exchange interaction J [19]. For such AFMs, the antiferromagnetic vector~1 M~ 2 is the principal dynamical variable. Within
L~ ¼ Mthe  model, the equation for the normalized (unit) vector~ Lj~ can be written through the variation of thel~ ¼ L=j~ (see [16,28]):
Lagrangian L½l
L ¼



 ~2
~
@
@l
~  @ H~  l~  @l : (1) W ðlÞ
2Hex @t
Hex@t

Here the first two terms describe the free oscillations of theweek ending
13 AUGUST 2010spins, and the last term determines the action of the circularly polarized light described by an effective magnetic~ / ðE~  E~  Þ, corresponding to the IFE. The value
field HðtÞof the Lagrangian is presented per one spin. We have  ¼
gB =@ as the gyromagnetic ratio, g as the Landé factor, B
as the Bohr magneton, Hex ¼ zSJ=gB as the exchange
field of AFM, and z ¼ 6 as the number of next-nearest
neighbors. For NiO, J ¼ 221 K, which for S ¼ 1 gives
Hex ¼ zSJ=@ ¼ 27:4 THz. We used the simplest form of~ ¼ gB ðHa1 l2x þ Ha2 l2y Þ, writthe biaxial anisotropy W ðlÞ
ten in terms of the out-of-plane anisotropy field Ha1 andmuch smaller in-plane anisotropy field Ha2 [19]. Within~ 2 ¼ 2M0 m
~ ¼M
~1 þM
~
the  model, the magnetization M
is a slave variable and can be written as [16,28]
 ~ ~ H~  lÞ~ þ 1 @l  l~ ;~ ¼ ½H~  lð
Hex m
(2)
 @t
where the first term determines the canting of the sublat~ and thetices, caused by the effective magnetic field H,
second term describes the dynamic contribution.
~ gives the dynamical equations for
The variation of L½ll.~ In linear approximation over the deviation from theground state (l~ground k z; see Fig. 1), they readdHy @2 lydH@2 lx; 2 þ !22 ly ¼  x ; (3)þ !21 lx ¼ 
2
dt @t
dt
@t
pﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ
pﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ
where !1 ¼  2Hex Ha1 and !2 ¼  2Hex Ha2 are thefrequencies of the out-of-plane and in-plane antiferromagnetic spin oscillations, respectively, omitting the dissipation terms. For a short pulse (!1;2 t1), Eq. (3)describes a universal behavior for AFMs [17]. Namely,
after the pulse action, for t
t, the spins exhibit freeoscillations with frequencies !1;2 and amplitudes lx ðt ¼
0Þ
¼ H y t and ly ðt ¼ 0Þ ¼ H x t, where H x;y tRþ1
1 Hx;y ðtÞdt, determined by the form of the pulse. Thus,
the amplitudes are determined by the total fluence connected to the pulse field components, Hy and Hx , and theseamplitudes are not dependent on the pulse shape or duration (for our case, !t1). This situation is also common for the inertial mechanism for canted AFMs [15].
However, for canted AFMs the pulse produces an initial‘‘spin speed’’ d=dtjt¼þ0 , and for pure AFMs, the ‘‘initial
spin deviation’’ is jt¼þ0 , where  is an angular variable
for l.~ For this reason, cosinelike oscillations appear in
Fig. 2(a) (instead of sinelike, for the canted AFMs inves~ produces atigated before). The oscillation of the vector mmodulation of the antisymmetric part of the permittivity
tensor "ij , "aij / eijk mk , where eijk is the totally antisymmetric tensor. In linear approximation, the out-of-planemode produces "axz / my , and the in-plane mode produces "ayz / mx .
For our measurements, a T domain inclined to thesurface of the sample was chosen [see Fig. 1(a)], and thevalues of Hy and Hx were approximately equal, in agree-

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PHYSICAL REVIEW LETTERS

ment with the observation that a1 a2 . The measured
frequency f1 ¼ 1:07 THz is in good agreement with theout-of-plane mode of the antiferromagnetic spin oscillations. From the out-of-plane anisotropy, Ha1 ’ 23 GHz[19], one obtains f1 ¼ 1:1 THz. The 1.07 THz component
has been observed in far-infrared antiferromagnetic resonance [29,30] and Raman scattering [31]. The small inplane anisotropy field Ha2 1 GHz is not well known[19], but spin oscillations with a frequency f2 ¼ 140 GHz
have recently been observed in NiO by Brillouin scattering[32]. This strongly suggests that the oscillations in Fig. 2(a)at 1 ps are spin oscillations around the easy axis, which
are the usual spin-wave modes, triggered by the effective
magnetic field H~ generated via the IFE, with the time~
derivative of the field dH=dt
working as a torque acting~
on the vector l.
The simultaneous observation of the magnetic responseat both short times and long times, in processes (1) and (2),allows us to reach conclusions about the applicability ofdifferent approaches to describe the spin dynamics. The
Landau-Lifshitz equation for ferromagnets (or, equivalently, the -model equation for AFMs) describes the
dynamics of spin systems in terms of only the magnetization vector (or sublattice magnetizations, for AFMs). Theseequations are valid for quasiequilibrium states, where thesemagnetizations are formed by the exchange interaction.
This occurs (according to our observations) for times corresponding to process (2). On the other hand, our results
show that the -model approach (like other theories treating the dynamics of spin systems through the mean valueof the magnetization) is not sufficient to describe shorter
times t & 0:5 ps, namely, the behavior in regime (1). For
instance, the amplitudes of the oscillation lx;y ð0Þ do notcontain anisotropy fields, and they can be obtained byneglecting all relativistic interactions in the AFM, except
for the Zeeman interaction of the spins with the pulsed
magnetic field. In this approximation within the -model
approach, the projection of the magnetization parallel tothe field is conserved and cannot appear during the actionof a short (t1=!1;2 ) field pulse. For the  model,
direct calculations show that the static and dynamic contributions to the magnetization [Eq. (2)] compensate eachother in this short time interval [17]. On the other hand, thesignal observed at these times is much higher than forprocess (2). Thus, to describe the initial stage (1), one
needs to use a more detailed analysis involving the spinand orbital momenta of the solid and the angular momentum of photons [26].
In conclusion, the time-resolved magneto-optical response of NiO provides direct access to the magnetization
changes under the action of laser pulse irradiation. We
found that compensated antiferromagnetic NiO shows
spin oscillations triggered nonthermally by a circularly~
polarized pulse, with the time derivative dH=dt
as theweek ending
13 AUGUST 2010driving force acting on the antiferromagnetic vector l.~
The 1.07 THz and 140 GHz components are in good
agreement with reported values for antiferromagnetic
spin oscillations. We thus extend the potential of NiO as
an antiferromagnetic constituent in spintronic devices,from static and thermally limited spin-dynamical experiments into the range of all-optical magnetization control at
terahertz frequencies.
This work was supported by Kakenhi 19860020 and
20760008 (T. S.), SPP 1133 of the DFG (M. F.), NASU
220-10 (B. A. I.), and the NSA/LPS/ARO, NSF, Kakenhi,
MEXT, and JSPS (F. N.).

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