論文 / 著書情報
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Title

Ultrafast Optomagnonics in Ferrimagnetic Multi-Sublattice Garnets

Authors

Andrzej Stupakiewicz, Takuya Satoh

Citation

Journal of the Physical Society of Japan, Vol. 90, No. 8, pp. 081008-111

Pub. date

2021, 7

Copyright(c) 2021 The Physical Society of Japan

DOI

https://doi.org/10.7566/JPSJ.90.081008

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This file is author (final) version.

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Ultrafast Optomagnonics in Ferrimagnetic Multi-Sublattice Garnets
Andrzej Stupakiewicz1* and Takuya Satoh2†
1
2

Faculty of Physics, University of Bialystok, 15-245 Bialystok, Poland

Department of Physics, Tokyo Institute of Technology, Meguro, Tokyo 152-8551, Japan

This review discusses the ultrafast magnetization dynamics within the gigahertz to terahertz
frequency range in ferrimagnetic rare-earth iron garnets with different substitutions. In thesegarnets, the roles of spin–orbit and exchange interactions have been detected using femtosecond
laser pulses via the inverse Faraday effect. The all-optical control of spin-wave and Kaplan–
Kittel exchange resonance modes in different frequency ranges is shown. Generation andlocalization of the electric field distribution inside the garnet through the metal-bound surface
plasmon-polariton strongly enhance the amplitude of the exchange resonance modes. The
exchange resonance mode in yttrium iron garnets was observed using circularly polarized
Raman spectroscopy. The results of this study may be utilized in the development of a wideclass of optomagnonic devices in the gigahertz to terahertz frequency range.
1. Introduction
Laser-induced magnetization dynamics is a flourishing area of research concerned with adeep understanding of previously unexplored and often strongly non-equilibrium phenomena,
enabling the coherent control of magnetization on ultrashort time scales [1]. Using modern laser
light sources, one can easily witness processes occurring on timescales down to femtoseconds.
This field offers an unprecedented capability to probe light–matter interactions and manipulatemagnetism at deep levels. Fundamental magnetic interactions, such as the exchange interaction
responsible for magnetic ordering and the spin–orbit coupling responsible for magnetic
anisotropy, have characteristic interaction times ranging from 1 ps to a few femtoseconds [2].
The practical applications include solving the most pressing issues related to modern
technological developments, future generations of electronic devices, ultrafast processing of
information, and development of spintronics and photonics.
Modern optical and magneto-optical methods offer new possibilities to study magnetization
dynamics with spatial and temporal resolutions over a wide frequency range [3–6]. The laserinduced magnetization dynamics represent a fundamentally challenging physics, since they are
typically strongly non-equilibrium, and the proper theoretical understanding is complicated by
the multitude of couplings between the microscopic constituents of matter. Additionally, there
is a fundamental distinction between the mechanisms allowing the manipulation of themagnetization by means of ultrashort laser pulses, and these phenomena can be classified into
two types. First, the thermal effects, which are based on the ultrafast demagnetization withheating of the medium leading to the change in its magnetic properties, observed usually inmetallic systems [7,8]. Second, non-thermal effects, which operate without heating the medium,are usually observed in the form of the inverse Faraday effect (IFE) [9,10] and thephotomagnetic effect [11–13] in magnetic dielectrics, such as iron garnets with different
dopants. The non-thermal effect are the most intriguing due to the dissipation-free mechanismof magnetization dynamics and all-optical switching of magnetization with lowest heat load.
The non-thermal photomagnetic effect is based on absorption of photons during opticalexcitation of the strongly anisotropic ions using linear polarization of light. Such excitation
allows one to generate an effective field of photo-induced magnetic anisotropy, which in1

general can have lifetime much longer than the laser pulse width itself and magnitude
comparable to the intrinsic anisotropy; it is sufficient to trigger angle precession of themagnetization. On the contrary, the IFE does not require the absorption of the pump light in thematerials. The lifetime of the effective magnetic field arising from the IFE is only as long as
the pulse width, which is typically couple of tens to hundred femtoseconds. This fact allows theuse of IFE as a mechanism of laser-induced control of magnetization for fundamental research
and applications.
The first explanation of all-optical helicity-dependent magnetization switching [14] wasbased on the IFE using femtosecond circularly polarized laser pulses [15]. However, further
investigations showed that the helicity dependence of all-optical switching, previously regarded
as the confirmation of the non-thermal origin of effects, occurs due to circular dichroism,
resulting in different heating efficiencies [16]. Difficulties with manipulation of magnetization
in metals by IFE are associated with high absorption in the visible and near-infrared regions ofspectra and as a result, weak IFE amplitude. However, the idea of using an impulsive magnetic
field created by laser pulses for non-thermal manipulation of magnetization by IFE seems to bepromising for highly transparent and magneto-optically active materials, such as ferrimagnetic
dielectrics (e.g., garnets).
The IFE is the creation of an effective magnetic field in magnetic media during the action ofa circularly polarized laser pulse. This effect was originally predicted by Faraday in the second
part of his work concerning the interaction between light and magnetization [17]. In later
theoretical works [18,19], it was shown that circularly polarized light can induce the “DC”
magnetic field along the propagation direction of the incident light:
𝐇𝐇(0) = 𝑎𝑎[𝐄𝐄(𝜔𝜔) × 𝐄𝐄 ∗ (𝜔𝜔)],(1)

where a is the magneto-optical constant. The same constant a is used in the direct Faraday effectand indicates magneto-optical coupling. Thus, the process of DC magnetic field generation via
photons is called the IFE, which underlines the same magneto-optical constant presented in Eq.
(1). The microscopic mechanism of the IFE was explained using impulsive stimulated Raman
scattering [20,21]. This mechanism is based on a laser pulse stimulation of an optical transition
from the ground state to a virtual excited state, which is split due to the spin–orbit coupling.
Then the same laser pulse stimulates the transition back to the ground state, in which themagnetic state is changed.
The present review consists of five parts: (1) Introduction, (2) Experimental details
describing the magnetic ordering in rare earth (RE) iron garnets and pump-probe magnetooptical method to laser-induced magnetization dynamics; (3) Laser-induced wide frequency
range of magnetization dynamics in iron garnets, presenting the results of the excitation ofprecession of magnetization at different frequency ranges corresponding to the spin-wave andexchange resonance modes in RE iron garnets by IFE; (4) Generation and localization ofmagnetization precession under excitation of the exchange resonance mode in magnetoplasmonic Au/garnets, dedicated to the amplification of amplitude of magnetization precession
with a nanoscale localization in depth of the garnet during excitation of exchange resonancemode via surface plasmon-polariton (SPP) resonance in Au/garnet structure; (5) Exchange
resonance mode in yttrium iron garnet (YIG), devoted to study of the exchange resonance modein YIG using circularly-polarized Raman spectroscopy.
2. Experimental Details
2.1 RE iron garnets
2

The magnetic order in a pure YIG (Y3Fe5O12) is attributed to the localized spins of its
magnetic ions and their super-exchange interaction with the surrounding oxygen ions. Due tothe spatial overlap of the electron wave functions of the neighboring ions, the oxygen’s 2p states
mediate the interaction between 3d5 states of the iron ions close by [22]. The super-exchangeof the overlapping orbitals brings about an extra energy term, whose nature depends on therelative arrangement of the electron’s spins, the strongest being the super-exchange interaction
between inequivalent tetrahedral (d) and octahedral [a] sites [Fig. 1(a)]. As the Fe3+ are arranged
in two separate tetra- and octahedral sublattices and the spins within each sublattice areferromagnetically ordered, one can consider the sublattices to have own magnetizations (ofvarious magnitudes). However, the iron sublattices themselves are coupled
antiferromagnetically and the total magnetization is a sum of each sublattice contribution,
producing a ferrimagnetic ordering. Various possibilities in garnet substitution, especially bymagnetic RE ions in dodecahedral {c} sublattice provide the opportunity to vary properties overa wide range.
Generally, the f shell can have more electrons, and in some cases, the RE ions produce larger
magnetic moments than transition metal (TM) ions. However, because of their larger ionic radiiand consequently longer RE-RE distances, their coupling is weaker than that of TM ions. This
leads to differences in the temperature dependence of magnetization of sublattices. Doping withions having large spin–orbit splitting parameter into dodecahedral sites can produce an increasein the Faraday rotation angle. Generally, the Faraday rotation in Bi-substituted RE iron garnets
is strongly dependent on the wavelength in the visible range [23]. An enhanced Faraday rotation
is usually accompanied by a large absorption [24,25]. In particular, a giant Faraday rotation iscaused by an increase in the spin–orbit splitting in the excited states because of the formationof hybrid molecular orbitals between the 3d orbital in Fe3+ and the 2p orbital in O2-, mixed withthe 6p orbital in Bi3+, which has a large spin–orbit interaction parameter. In such materials, themagnetic moment of the RE sublattice originates from 4f localized electrons, in contrast to theiron sublattice, where the magnetism occurs by means of 3d delocalized conduction electrons.
Consequently, the RE sublattice is polarized by the iron sublattice, and the magnetic moments
become antiparallel through exchange interactions. One can expect that the exchangeinteraction between iron sublattices will be stronger than the exchange interaction between ironand RE (e.g., Gd and Yb ions) sublattices. We note here that the exchange between RE
sublattices will be negligible in comparison to the above.
In our experiments, we used 380-µm-thick Gd4/3Yb2/3BiFe5O12 (GdYb-BIG), 200-µm-thick
Gd2BiFe5O12 (Gd-BIG), and 160-µm-thick YIG single crystals [26–28]. In this review, we also
consider 7-µm-thick Lu1.69Y0.65Bi0.66Fe3.85Ga1.15O12 (LuIG) garnet grown on GGG substrate[29]. In these garnets, Gd, Yb, Lu, Y, and Bi ions are surrounded by eight oxygen ions in adodecahedral sublattice {c}.

3Fig. 1. (Color online) (a) Garnet lattice with octahedral-[a], dodecahedral-{c} and tetrahedral-(d) sites.
(b) Visualization sketch of the magnetization precession and schematic illustration of the samples withexperimental geometry.

2.2 Time-resolved magneto-optical method
As shown in Fig. 1(b), time-resolved pump-probe measurements were performed in atransmission geometry to investigate the ultrafast magnetization dynamics in ferrimagnetic RE
iron garnets [26,27]. Pump pulses with a duration of 50 fs from an amplifier at a 500 Hz
repetition rate were directed at an angle of incidence of approximately a few degrees from thesample normal. The probe laser pulses at a repetition rate of 1 kHz were incident normal to thesample. In order to keep off influence of most intense pump pulse on detector, the propagation
direction of the pump pulse is generally not identical to that of the probe pulse. The wavelengthof the pump beam was adjustable by an optical parametric amplifier in the near-infrared rangeof 1000–1500 nm, whereas the probe wavelength was fixed at 800 nm. The pump beam withan energy density of ~40 mJ/cm2 was focused to a spot approximately 100 μm in diameter,while the 50 times weaker probe beam on the sample was twice as small in diameter. The delay
time ∆𝑡𝑡 between the pump and probe pulses can be adjusted up to 2.5 ns. The polarization of
the pump pulse was adjusted between circular polarization with different helicities. The
polarization plane of the probe beam was linear. An external in-plane magnetic field 𝐻𝐻∥ wasapplied to the sample. We measured the time-resolved Faraday rotation angle 𝜃𝜃F of the probe
as a function of the delay time ∆𝑡𝑡. The angle of the Faraday rotation 𝜃𝜃F is proportional to theout-of-plane component of magnetization 𝑀𝑀𝑥𝑥 in a sample.
3. Laser-Induced Wide Frequency Range of Magnetization Dynamics in Iron Garnets

Here, we will consider the results of the non-thermal laser-induced ultrafast magnetization
precession in Lu-iron garnet [29], and our results obtained for Gd- [27], and GdYb- [26] irongarnets. The magnetization precession in the picosecond and nanosecond time scales was
optically excited via the IFE using the circular polarization of pump pulses. Two types of4

magnetization precession with different time scales were observed [Fig. 1(b)]: a low-frequency(ferromagnetic resonance (FMR) and spin-wave) mode with a frequency in the gigahertz (GHz)range for a duration of approximately 2.5 ns, and a high-frequency (HF) (exchange resonance)mode with a frequency in the sub-terahertz (sub-THz) range, which was present immediately
after the initiation of the magnetization precession and lasted for approximately 30 ps.
3.1 Magnetization precession in ferrimagnets
The collective oscillations of excited spins in magnetic materials, such as the magnetization
precession or spin waves, can be used to extract the information about the essential magnetic
properties and phenomena. A clear understanding of the oscillations in the ferrimagnet can beobtained from the analysis of the equation of motion of each sublattice under an external
magnetic field. Generally, the number of possible self-modes of oscillation is equal to thenumber of sublattices, which is in turn related to the number of different magnetic ions. The
simplest case is a ferrimagnet with two sublattices. Neglecting the anisotropy field,
demagnetizing field, and damping, the equations of motion for the two-sublattice systems 𝐌𝐌𝟏𝟏
and 𝐌𝐌2 under the external magnetic field 𝐇𝐇 are
𝑑𝑑𝐌𝐌1= −𝛾𝛾1 [𝐌𝐌1 × (𝐇𝐇1 + 𝐇𝐇)],
𝑑𝑑𝑑𝑑
𝑑𝑑𝐌𝐌2
= −𝛾𝛾2 [𝐌𝐌2 × (𝐇𝐇2 + 𝐇𝐇)].
𝑑𝑑𝑑𝑑

(2)

The exchange fields are 𝐇𝐇1 = −𝜆𝜆𝐌𝐌2 and 𝐇𝐇2 = −𝜆𝜆𝐌𝐌1 , where 𝜆𝜆 is the molecular field
coefficient between the two sublattices. 𝛾𝛾1 , 𝛾𝛾2 (> 0) are the gyromagnetic ratio. We set 𝐌𝐌1 =𝑦𝑦𝑦𝑦�𝑚𝑚1𝑥𝑥 𝑒𝑒 𝑖𝑖𝑖𝑖𝑖𝑖 , 𝑚𝑚1 𝑒𝑒 𝑖𝑖𝑖𝑖𝑖𝑖 , 𝑀𝑀1 � , 𝐌𝐌2 = �𝑚𝑚2𝑥𝑥 𝑒𝑒 𝑖𝑖𝑖𝑖𝑖𝑖 , 𝑚𝑚2 𝑒𝑒 𝑖𝑖𝑖𝑖𝑖𝑖 , −𝑀𝑀2 � , and 𝐇𝐇 = (0, 0, 𝐻𝐻∥ ) and solve theequations of motion for 𝐌𝐌1 and 𝐌𝐌2 . Here, 𝑀𝑀1 > 𝑀𝑀2 > 0 and 𝐻𝐻∥ > 0. Two solutions of thesecular equation are possible, representing two types of oscillations [30,31]: FMR with apositive frequency 𝜔𝜔FMR = 𝛾𝛾eff 𝐻𝐻∥ , and exchange resonance with a negative frequency′
𝜔𝜔ex = −[𝜆𝜆(𝛾𝛾2 𝑀𝑀1 − 𝛾𝛾1 𝑀𝑀2 ) − 𝛾𝛾eff
𝐻𝐻∥ ].

(3)

𝜔𝜔FMR = 𝛾𝛾eff �[4𝜋𝜋(𝑀𝑀1 − 𝑀𝑀2 )(𝑁𝑁𝑥𝑥 − 𝑁𝑁𝑧𝑧 ) + 𝐻𝐻∥ − 𝐻𝐻A ]𝐻𝐻∥ .

(4)

Here, we also assume that the molecular fields 𝐇𝐇1 and 𝐇𝐇2 are much stronger than the external
field 𝐇𝐇. Further, assuming a thin film with the thickness direction parallel to x axis, uniaxial
anisotropy field 𝐻𝐻A along x axis, demagnetizing field (demagnetization factor 𝐍𝐍), and in-planemagnetic field 𝐻𝐻∥ (> 𝐻𝐻A ) along z axis, the FMR frequency can be obtained by the Kittel formula[32]

For zero-orbital contribution to the magnetic moment of the ion, the gyromagnetic ratio for each′sublattice can be the same: 𝛾𝛾1 = 𝛾𝛾2 = 𝛾𝛾 and 𝛾𝛾eff = 𝛾𝛾eff= 𝛾𝛾. These types of precession are
illustrated in Fig. 2. The parameter 𝜆𝜆dc responsible for the exchange resonance mode is amolecular-field parameter between (d) and {c} [22]. 𝜆𝜆dc is typically higher than 𝜆𝜆ac , which
5implies a stronger interaction. A positive 𝜆𝜆dc corresponds to an antiferromagnetic interaction.
Thus, the exchange resonance modes have an antiferromagnetic nature.

Fig. 2. (Color online) Schematic of (a) FMR (a) and (b) exchange resonance modes for a two-sublatticeferrimagnet.

3.2 Spin-wave mode excitation via the IFE
In order to determine the mechanism and characteristics of the laser-induced magnetization
precession, we carried out measurements as functions of the pump polarization and the static
applied magnetic field. Such measurements allow one to determine the excited magnetization
precession mode, such as that under the change in frequency of the precession. The Bisubstituted iron garnets have the giant static Faraday rotation. Thus, all experimental data,
which are presented below, were obtained using the GdYb-BIG sample at room temperature.
However, the behaviors of the main intrinsic parameters of magnetization dynamics in the GdBIG sample at room temperature were similar. Figure 3 shows the experimental geometry andthe magnetization precession as a time-resolved Faraday rotation angle for left-handed (σ+ ) andright-handed (σ− ) circularly polarized pump pulses with in-plane external magnetic field 𝐻𝐻∥ =1.2 kOe.

Fig. 3. (Color online) Time-resolved Faraday rotation for different helicities of the circularpolarizations of the pump beam in an applied magnetic field 𝐻𝐻∥ = 1.2 kOe at room temperature for the
GdYb-BIG sample. Insets show the graphical illustration of the excitation of magnetization precession
by effective IFE field HIFE.

6

Figure 4(a) shows the linear dependence of amplitude of magnetization precession fordifferent pump laser pulses. Such behavior is typical for excitation of magnetization dynamics
via IFE because this effect does not require photon absorption during laser excitation. For
significantly higher pulse energies, the effect saturates. The dependence of the magnetization
precession amplitude, which was extracted from time-traces measurements, as a function of aquarter-wave plate angle (compensator polarization) for the pump polarization is shown in Fig.
4(b). The magnetization precessions with opposite phases were triggered by σ+ and σ−polarizations. Generally, the opposite phase precession of magnetization for different pumppolarization (especially for different helicity of circular polarization) in ferrimagnets is thefingerprint of the non-thermal excitation. This result is consistent with a laser-induced IFE
magnetic field HIFE along the direction perpendicular to the sample plane during a femtosecond
laser pulse excitation in an iron garnet [9]. In this case, the magnetization vector precesses
around the effective magnetic field (Heff) as a result of the action of different contributions: theexternal in-plane magnetic field and magnetic anisotropy field (inset in Fig. 3).

Fig. 4. (Color online) Dependence of the amplitude of magnetization precession as a function of (a)pump fluence and (b) compensator pump polarization (45° - left-handed cirlular polarization σ−, 135°left-handed cirlular polarization σ+, and 90° - linear polarization E) at 𝐻𝐻∥ = 1.2 kOe in the GdYb-BIG
sample.

In order to interpret the nature of the magnetization precession with respect to FMR mode,time-resolved measurements of magnetization dynamics have been performed with different
amplitudes of external magnetic field larger than value of the magnetic anisotropy field HA =620 Oe. The transient Faraday rotation as a function of delay time with various 𝐻𝐻∥ are shownin Fig. 5. Behavior of these curves suggest the beating effect which can be determined using
the analysis of spectrum frequencies of the magnetization precession. For this, we have
performed the fast Fourier transform (FFT) which shows the spectrum of distinct frequenciesof the magnetization precession (see the inset in Fig. 5).

7

Fig. 5. (Color online) Time-resolved Faraday rotation as a function of the delay time for different
amplitudes of external magnetic field 𝐻𝐻∥ . The red solid lines are fitted using Eq. (5). The inset is the
FFT spectrum for 𝐻𝐻∥ = 1.2 kOe.

As presented in Ref. 10 for a similar garnet, the excitation and propagation of spin-wave
modes using IFE has been shown. In such case, the spin-wave excitation in this garnet can
induce a spatial distribution of the magnetization orientation within the spot of the pump beam,thus leading to a beating precession process. The two frequency components 𝑓𝑓1 and 𝑓𝑓2
originated from the backward-volume magnetostatic waves (BVMSWs) with wavevectors k.
Thus, the results of laser-induced magnetization precession can be described as following
function [10]:𝜃𝜃F (Δ𝑡𝑡) = 𝐴𝐴 ∫ 𝑑𝑑𝐤𝐤ℎ(𝐤𝐤) sin(𝐤𝐤 ⋅ 𝐫𝐫 − 2𝜋𝜋𝜋𝜋(𝐤𝐤)Δ𝑡𝑡)exp(−2𝛼𝛼𝛼𝛼𝛼𝛼(𝐤𝐤)Δ𝑡𝑡),(5)

where 𝐴𝐴 is the amplitude and ℎ(𝐤𝐤) is the FFT of the intensity distribution at the pump spot, and𝛼𝛼 is Gilbert damping. The results of the numerical calculations using Eq. (5) confirmed theresults of the experiments and the FFT spectrum (inset in Fig. 5). In addition, experimental
time-traces datasets were fitted using Eq. (5) and are shown in Fig. 5 (red solid lines). With
increasing external magnetic field, significant changes were observed in the two frequencies 𝑓𝑓1
and 𝑓𝑓2 over the entire range of applied fields as shown in Fig. 6(a). In order to verify BVMSW
modes, the dispersion dependence for frequency 𝑓𝑓(𝐤𝐤) have been calculated [Fig. 6(b)]. In
addition, as shown, BVMSW mode can exist for 𝐤𝐤 perpendicular to the in-plane orientation ofmagnetic field 𝐻𝐻∥ [33].

8

Fig. 6. (Color online) (a) Experimental data for the frequencies corresponding to spin-wave modes(circle dots) and FMR data (square dots) as a function of the external magnetic field. Red solid line
represents the ferromagnetic resonance frequency results from the calculations using the Kittel formulaEq. (4). (b) Dispersion spectra of the spin-wave mode at 𝐻𝐻∥ = 4.2 kOe. Here, 𝑘𝑘 is defined as the inverseof the wavelength.

To compare the obtained spin-wave modes, we measured and calculated the frequency of
FMR mode with the Kittel formula using Eq. (4), using 𝐻𝐻A = 620 Oe and 4𝜋𝜋𝜋𝜋S =4𝜋𝜋(𝑀𝑀Fe − 𝑀𝑀RE ) = 1140 G. The magnetization of RE sublattices 𝑀𝑀RE was defined by themagnetization of Gd sublattice due to the zero contribution of the magnetization Yb ions atroom temperature. In Fig. 6(a), it is clearly seen that the frequencies of laser-induced
magnetization precession are lower than the measured and calculated FMR frequency [Fig.
6(a)].
3.3 Laser-induced exchange resonance between iron sublattices in garnets
Based on the Néel theory of ferrimagnetism, antiparallelly oriented non-equal magnetic
moments reside in the exchange field created by themselves. In this case, the precession ofsublattice magnetizations in the exchange field is the so-called Kaplan–Kittel exchange
resonance [30]. Typically, in comparison with the FMR, a high value of the exchange fieldleads to a high frequency for such oscillations, which corresponds to the far-infrared (FIR)
range. The FIR absorption and transmission spectra were measured for a number offerrimagnets [34,35], and the exchange resonance frequency was determined. Nevertheless,there is poor information on the optical excitation of the exchange resonance in the visible and
NIR regions of the spectrum.
The possibility of the excitation of ultrafast magnetization precession using the IFE without
heating in LuIG has been reported [29]. In this case, the exchange resonance mode was excited
9between iron sublattices (tetrahedral and octahedral) 𝐌𝐌d and 𝐌𝐌a in LuIG with a frequency
range of 400–700 GHz.

Fig. 7 (Color online) (a) Exchange resonance mode excited by σ+ and σ− circularly polarized pumplight at room temperature. The inset graphs show the amplitude dependence on the pump fluence andthe spectral dependence of this mode. (b) Schematic illustration of the excitation of the exchange
resonance. The figure is reproduced with permission from Ref. 29 (@2010 American Physical Society).

The nature of this mode is related to the canting of the two sublattices away from their mutual
exchange interactions. The exchange resonance mode shows a 180°-phase shift between the
excitations with σ+ and σ− circularly polarized light [Fig. 7(a)]. No variations were observedin the amplitude or frequency of changes in a sufficiently small external field up to 3 kOe.

In this case, femtosecond pump pulses with circularly polarized light were used to excite themagnetic-dipole forbidden exchange resonance between the magnetizations of two ironsublattices via the IFE. The tetrahedral and octahedral iron sublattices experience inequivalent
optically induced effective magnetic fields because of the different magneto-opticalsusceptibilities, resulting in a canting between magnetizations of the sublattices [Fig. 7(b)]. In
Ref. 29, the contribution of dodecahedral ions was negligible, which play an important role,
especially in Gd-substituted iron garnets.
3.4 Laser-induced exchange resonance between RE and iron sublattices in garnets
We experimentally demonstrated the laser-induced precessional motion of the magnetization
with a frequency of approximately 410 GHz in GdYb-BIG at room temperature via the IFE[26]. In this HF mode, we observed a precession of oppotiste phases with respect to the pumphelicity [Fig. 8(a)]. Figure 8(b) shows the precession dependencies for different amplitudes ofmagnetic field. In addition, the spin-wave mode was excited along with the HF mode. In a
duration of approximately 20 ps, we observed the simultaneous relaxation of the HF mode andthe excitation of the spin-wave mode at a frequency of a few GHz.
10

Fig. 8. (Color online) (a) Time-resolved Faraday rotation as a function of delay time for an external
magnetic field of 1.2 kOe induced by σ+ (open points) and σ− (full points) circularly polarized pumplight at room temperature in the GdYb-BIG sample. (b) Exchange resonance frequency as a function of
the external magnetic field measured at room temperature.

The frequency of the HF mode [Fig. 8(b)] linearly decreased with increasing intensity of theexternal magnetic field. Such dependence agrees with Eq. (3); however, the maximum
achievable change in frequency was only 3.8%. The value of slope 1.74 MHz/Oe is lower thanthat for free electron motion, i.e., 𝛾𝛾 = 2.8 MHz/Oe. This dynamic behavior is a consequenceof the exchange resonance between the magnetic ions in the RE and iron sublattices 𝐌𝐌RE and𝐌𝐌Fe . In this case, the frequency of exchange resonance is lower than the frequency resulting
from exchange resonance between the iron sublattices (650 GHz at room temperature [29]). In
contrast to our results for GdYb-BIG garnet, in LuIG garnet, changes were not observed in theexchange frequency for changes in the external field up to 3 kOe [29]. In RE garnets with nonzero contribution to the magnetization from the dodecahedral sites at room temperature, theexchange field between the iron and RE sublattices is weaker than that between the octahedraland tetrahedral iron sublattices. Therefore, influence of external magnetic field in relation to
exchange resonance between RE and iron sublattices will be weaker than in case of the spinwave or FMR modes [Fig. 6(a)].
3.5 Temperature dependence of the exchange resonance mode11

Because of the high value of the exchange field, the dependence on the external magnetic
field is not strong. Hence, the variation in temperature seems to be a suitable way to confirm
the excitation of such modes as a consequence of the temperature dependence of the exchange
field.
To confirm the prediction related to the excitation of the exchange resonance mode,temperature experiments were performed. Figure 9 shows the time-resolved Faraday rotation
curves measured with the Gd-BIG sample at the picosecond time scale for different
temperatures. This sample was simple for temperature investigation owing to the single RE
sublattice of Gd. For temperatures lower than T = 100 K, the modulation of the spin-wave modein the HF sub-THz mode can be observed. The time decay of the HF mode over temperatures
ranging from 10 K to 70 K was approximately 20 ps. After 20 ps, the HF precession relaxed,
and the spin-wave mode was simultaneously excited, decaying at approximately 100 ps at 12 K.
The initial phases of the HF and spin-wave modes heavily depend on the helicity of the circularpump polarization, which is typical for excitations via the IFE (Fig. 2 in Ref. 27).

Fig. 9. (Color online) Time-resolved Faraday rotation for different temperatures in Gd-BIG sample.

In general, RE iron garnets can be treated as two-sublattice ferrimagnets, one made up of Fe
ions occupying both tetrahedral (d) and octahedral [a] sites (𝑀𝑀d − 𝑀𝑀a = 𝑀𝑀Fe ) and the other of
RE ions occupying dodecahedral {c} sites (𝑀𝑀c = 𝑀𝑀Gd ). In our case, total magnetization is given
by 𝑀𝑀Fe − 𝑀𝑀Gd . We obtained the temperature dependence of the Gd and Fe sublatticemagnetizations using molecular field theory with a single molecular-field coefficient [27]. The
Gd ions exhibit antiferromagnetic exchange coupling with the Fe ions, and the Gd ions tend toalign their spins against the net moment of the Fe ions. Because this coupling is relatively weak,
the Gd ion ordering is significant only at low temperatures (<60 K), at which the Gd sublattice
is much more strongly magnetized than the Fe sublattice [27].
As the temperature decreases below 𝑇𝑇comp , the frequency of the HF mode tends to increase
with an increasing 𝑀𝑀s , which suggests an excitation of the Kaplan–Kittel exchange resonance.
In the Gd-BIG sample, this resonance exists because of the exchange interaction between the12Gd and Fe sublattices. The magnetizations of these sublattices are noncollinear (inset in Fig.
10) during the entire precession (Fig. 9). Below 60 K, the Fe ions are strongly coupled, andexcitations between them are difficult [22]. Thus, in garnets, the Gd–Fe coupling is relatively
weak, and the Gd–Gd coupling is even weaker and hence neglected. The magnetization
precession in our garnets occurs in a molecular field close to 500 kOe [36,37].
By fitting the time-resolved Faraday rotation data (Fig. 9) with two frequencies, we wereable to determine the temperature dependence of both mode frequencies. As the totalmagnetization increased, the HF mode increased in frequency within the GHz–THz range via
exchange resonance excitation (see Fig. 10).

Fig. 10. (Color online) Temperature dependence of the exchange resonance mode (points) for the GdBIG sample. The solid line 𝑓𝑓ex (𝑇𝑇) was obtained using Eq. (3).

The temperature dependence of the HF mode provides direct evidence of this resonance. We
can calculate the temperature dependence of the HF mode using Eq. (3) for the exchange
resonance between the Fe and Gd sublattices. The gyromagnetic ratio 𝛾𝛾 is the same for thesesublattices (𝛾𝛾 = 𝛾𝛾Gd = 𝛾𝛾Fe ) because for Gd ions, 𝐿𝐿 = 0. The red solid line in Fig. 10 is calculatedusing Eq. (3). The experimental data and theoretical calculations show a good agreement.
4. Generation and Localization of Magnetization Precession under Excitation of the
Exchange Resonance Mode in Magneto-Plasmonic Au/Garnets
Magneto-plasmonics is one of the most promising manipulation methods of spins in thenanometer localization in space [38,39]. In magneto-plasmonic dielectric-based
heterostructures, the non-magnetic (noble) metallic layer provides high-quality collective
resonances of the free electron gas, whereas magnetic properties are introduced usually by theiron garnets with different substitutions [6]. The latter enables external control of the interface
resonances by means of either static magnetic field or the laser-induced effective magnetic field
generated via the IFE [15,20,21,26,27]. In Au/garnet heterostructure, two materials with very
distinct timescales are combined. The transient electronic response of Au is fast, on the subpicosecond timescale, whereas garnet lacks free electrons and its relatively slow magnetooptical response is tied to the spin and phonon subsystems.

13

In the previous part of this review, we demonstrated that a circularly polarized light pulse
impulsively excites magnetization precession in GdYb-BIG crystal with HF of exchange
resonance mode at about 410 GHz. We assumed that the IFE-induced magnetization dynamics
can be enhanced with a localization of the electromagnetic field in such garnet upon the SPP
excitation. For that, we studied the SPP-assisted magnetization dynamics in a magnetoplasmonic crystal consisting of 380 μm-thick GdYb-BIG crystal which was complemented witha periodically perforated 50 nm-thick Au overlayer (800 nm period), allowing for the excitationof the SPP mode at the Au/air and Au/garnet interfaces [inset in Fig. 11(a)]. In experiments weused the magneto-optical pump-probe technique with 60 fs temporal resolution. The pumpbeam wavelength was tuned in the near-IR range [Fig. 11(a) as a purple stripe], while the probe
beam wavelength was fixed at 800 nm [red spot on Fig. 11(a)]. The SPP dispersion is shown in
Fig. 11(a). By tuning the wavelength and the incidence angle, SPPs can be excited, thus
controlling the localization of the hotspot [Fig. 11(a)]. Once the magnetization precession in agarnet is excited via the IFE, the delayed probe beam measures the transient Faraday rotation.
Figure 11 (b) shows the dependences of HF precession of exchange resonance mode atdifferent values of the pump wavelength, and the angle of rotation of the quarter-wave plate forpump pulse. The corresponding values are marked with colored circles in Fig. 11(c). Figure11(c) shows the dependences of the amplitude and phase of the magnetization precession on
the angle of rotation of the quarter-wave plate for two pump wavelengths: 1300 nm (noresonance) and 1380 nm (the vicinity of the SPP resonance at Au/garnet interface). In the nonresonant case (black curves), magnetization precession should be excited in the volume of theferrite garnet due to the ellipticity of the pump pulse. Accordingly, the precession amplitude
will be zero with linear pump polarization, and will increase with a deviation from the zero
position of the quarter-wave plate, while the phase will change by π for opposite angles ofrotation of the plate [Fig. 11(c)]. On the other hand, upon excitation SPP, the precession ofmagnetization will be excited in the subsurface layer due to the effective plasmon field. Indeed,
at a pump wavelength of 1380 nm (red curves), the characteristics of the dependences change[Fig. 11(c)]. This behavior can be explained by the fact that when ellipticity is added to thepolarization of the pump pulse, in addition to the magnetization precession in the near-surface
layer, the magnetization precession is also excited in the garnet. The phases of these excitations
are different; therefore, the resulting angle of the Faraday rotation is determined by theirinterference.

14

Fig. 11. (Color online) (a) SPP dispersion map of an Au/GdYb-BIG garnet heterostructure. The purple

stripe and the red spot show the spectral tunability of the pump and probe pulses, respectively. (b) Timeresolved Faraday rotation with the background removed, together with the fit lines for linear pumppolarization at different pump wavelengths. The green data points show the magnetization dynamics
excitation with circularly polarized light via IFE. (c) The amplitude and phase of the magnetization
precession as a function of the incident pump polarization, where λ/4 wave plate angle of 0° corresponds
to the p-polarized excitation. The colored circles correspond to the data shown in (b) with respective
colors. The figure is reproduced with permission from Ref. 40 (@2018 American Chemical Society).

To clearly demonstrate the effect of SPP excitation on the amplitude and phase ofmagnetization precession, we measured their dependence on the pump wavelength. Bymeasuring the variations in the Faraday rotation of the probe pulse with the time delay between
the pump and probe, we extracted the amplitude and phase of the exchange resonance mode atdifferent pump-pulse wavelengths. The amplitude spectrum of the exchange resonance mode isshown in Fig. 12 for circular and linear pump polarizations.
Spectral dependences of the circularly polarized pump pulse were monotonic and showedno resonance features. On the contrary, with a linearly polarized pump pulse both in theamplitude and phase of precession, strongly pronounced features were observed near the SPP
excitation (pump wavelength of 1400 nm, see Fig. 12). The precession phase at resonancechanges by π, which is equivalent to a change in the sign of the amplitude (solid and dashedcurves in Fig. 12). We note that in near 1200 nm wavelength, a feature is also observed in theprecession phase and amplitude. In this case, the excitation of two different SPPs should occur
at different interfaces [40].

15Fig. 12. (Color online) Phase and amplitude of exchange resonance mode versus the wavelength for Ccircular (black curve) and P-linear (red curve) pump pulse polarizations. The phase shift of π is identicalto the amplitude sign changes, as shown by red dashed curves. The figure is reproduced with permission
from Ref. 40 (@2018 American Chemical Society).

Here, unlike all the previously demonstrated examples, the SPP affects the sub-THz coherent
magnetization dynamics by the spatial confinement of the IFE in a metal–dielectric hybrid
structure. As we demonstrated experimentally and through modeling, the SPP electric fieldrotates in the incidence plane as the SPP propagates along the Au/GdYb-BIG interface andinduces a static transversal IFE magnetic field localized on the scale of 100 nm [40]. In the caseof circular pump polarization, magnetization precession is excited in depth of a garnet crystal
with a thickness of 𝑑𝑑bulk = 380 μm (absorption in this wavelength range is low). On the other
hand, as shown by numerical calculations [40], with SPP-excitation at the Au/garnet interface,precession should be efficiently excited in a near-surface layer with a depth of about 𝑑𝑑SPP ≈100 nm. Taking into account the difference in precession amplitudes (Faraday rotation ∆𝜃𝜃) withresonant and non-resonant excitation ∆𝜃𝜃SPP /∆𝜃𝜃bulk ≈ 0.1 , we obtain following relation
between the precession excitation efficiencies with and without SPP excitation:
𝑑𝑑

𝑑𝑑bulk bulk

∆𝜃𝜃SPP

𝑑𝑑SPP ∆𝜃𝜃bulk≈ 400. Taking advantage of the tunability of the pump wavelength, theexcitation efficiency at the SPP resonance was enhanced by two orders of magnitude.
5. Exchange Resonance Mode in YIG

Among other rare-earth iron garnets, YIG single crystal possesses superior properties, suchas the narrowest FMR linewidth (α ≈ 10−5 ) and a Curie temperature Tc of 560 K, and has been
regarded as an indispensable magnetic material [41–45]. Y3+ ions in the dodecahedral {c} sites
are non-magnetic. Therefore, YIG forms a two-sublattice ferrimagnet. Previous studies on YIG
have mostly focused on FMR or acoustic magnons in the GHz range. Limited information has
been provided about the Kaplan–Kittel exchange resonance mode in the THz frequency range[41]. Recently, several theoretical investigations have revealed full magnon band structures[46–50]. Only inelastic neutron scattering spectroscopy has been experimentally identified forTHz magnons in YIG [51–54]. Therefore, the THz-magnon should be investigated using Raman
spectroscopy.
16Raman spectroscopy was performed in a 180° backscattering geometry with a 785 nm
excitation laser. The polarization of the incident and scattered light is denoted as parallel (∥)
and crossed (⊥) for linearly polarized configurations and RL, LR, RR, and LL for circularly
polarized configurations. The hand of the circularly polarized light (R or L) was defined as thesense of polarization rotation in the sample plane, regardless of the direction of propagation.

Fig. 13. (Color online) Raman spectra in the 240–270 cm−1 range with (a) RR- and (b) LL-polarized
configurations in the 80–140 K temperature range in YIG (111). The red, green, and purple curves fit
the magnon and two T2g phonons, respectively. The blue curve denotes the sum of the red, green, andpurple curves. The figure is reproduced with permission from Ref. 28 (@2020 American PhysicalSociety).

The Raman spectra in the 240–270 cm−1 range are depicted in Figs. 13(a) and 13(b) for the
RR- and LL-polarized configurations, respectively [28]. In both configurations, a tiny signal
was observed and assigned to the resonance exchange mode because of the significant
temperature dependence of the frequency shift. At 80 K, the Raman shift was 260 cm−1, whichcorresponds to 7.8 THz.
In Fig. 14(a), the frequency shifts of the THz magnon in the RR- and LL-polarized
configurations are plotted as a function of temperature [28] and compared with the results
obtained from the neutron scattering measurements [51–54] and simulations [49,50]. The
tendency is the same, but a frequency deviation exists between the Raman results and the others.
Raman spectroscopy provides a more precise frequency resolution than other techniques. A
frequency of 8.0 THz at 4 K was obtained by extrapolating the magnon frequency using thetemperature dependence of magnetization [55]. Equation (3) is equivalent to (12𝑆𝑆d −8𝑆𝑆a )|𝐽𝐽ad | = 10|𝐽𝐽ad |, where a- and d-site spins are 𝑆𝑆a = 𝑆𝑆d = 5/2 and 𝐽𝐽ad is the exchange
constant between the a- and d-site sublattice. This yields 𝐽𝐽ad = −38 K according to 10|𝐽𝐽ad | =8.0 THz.
17

Fig. 14. (Color online) Temperature-dependent frequency shift in the resonance exchange mode (a). The
red and black lines with error bars denote the exchange resonance mode observed in our Raman spectrawith RR- and LL-polarized configurations, respectively. Selection rule for the resonance exchange modeof YIG observed with crossed-, RR-, and LL-polarized configurations at 260 cm−1 (7.8 THz) and 80 K(b). The figure is reproduced with permission from Ref. 28 (@2020 American Physical Society).

The Raman selection rule was investigated at 80 K, as shown in Fig. 14(b). The Raman
intensity ratio of the resonance exchange mode was [𝐼𝐼∥ : 𝐼𝐼⊥ : 𝐼𝐼RL : 𝐼𝐼RR ] = [0: 1: 0: 1]. This finding
is consistent with the magnon Raman tensor in antisymmetric form as
𝑅𝑅 = �

0−𝑖𝑖𝑚𝑚𝑧𝑧

𝑖𝑖𝑚𝑚𝑧𝑧�,
0(7)which corresponds to linear (first-order) magnetic excitations [56–60]. The consistency of theexchange resonance mode to the FMR mode excited through light scattering indicates that thesemodes possess the same symmetry. In the exchange resonance mode, all the atomic spins
belonging to the same sublattice simultaneously rotate with their spins always parallel and withthe same amplitude, which is analogous to the FMR mode. The spins in the other sublattices
behave in the same manner. Therefore, the exchange resonance and FMR modes correspond to
the A2 mode [61]. However, unlike the FMR mode, the net magnetization 𝐌𝐌a + 𝐌𝐌d of theexchange resonance mode did not occur. Therefore, the exchange resonance mode is considered
to be unobservable via optical methods [62]. Nevertheless, the exchange resonance mode wasobserved in the Raman method as a linear magnetic excitation, which usually results from the18

precession of 𝐌𝐌. This is because the Faraday rotation is more sensitive to the a-site Fe sublatticethan the d-site Fe sublattice. The exchange resonance mode resulted from the precessionalmotion of 𝐌𝐌a [29].
6. Conclusions
In this review, we have presented the experimental studies and theoretical approaches in RE
iron garnets by using ultrafast time-resolved magneto-optical spectroscopy and Raman
spectroscopy. Technology for fabricating high-quality garnets at thicknesses of micro- to nanoscales provides an extremely wide variety of compositions. Using magnetic RE-ions
substitution for YIG at dodecahedral sites (e.g. Gd, Yb, Lu) in the garnet matrix enables themagnetic ordering and modes of magnetization precession to be varied. We reviewed the nonthermal optically excited precession of magnetization via the IFE and Raman process in RE
iron garnet single crystals.
We showed that different frequency modes of the magnetization precession in the GHz and
THz ranges strongly depend on the polarization of the pump laser and amplitude of external
magnetic field. The low frequency modes in the GHz regime correspond to the spin wave in
Bi-substituted iron garnets excitation via the IFE. The HF mode is related to a Kaplan–Kittel
exchange resonance mode between magnetic sublattices in ferrimagnetic garnets. The
mechanism underlying the exchange interaction plays an important role in understanding thephysical origin of magnetism in materials on the atomic level.
A novel approach was using of the garnet crystal with exchange resonance mode at range of
sub-THz frequency to study of SPP-driven of magnetization precession with a nanoscale
localization. Our experiments and modeling verify the localization of the magnetization
dynamics excitation within a 100 nm-thin layer of a transparent dielectric garnet. Taking
advantage of the tunability of the pump wavelength, we demonstrated two orders of magnitudeenhancement of the excitation efficiency at the SPP resonance. Combining spatial localization
with the non-thermal spin–photon coupling, our results open the way toward high-density, lowloss ultrafast optomagnonics.
A wide frequency range of magnetization precession from GHz up to THz and large spatial
propagation variations may be useful for wavenumber, magnetic resonance, and dispersion
control, as well as offering options for tuning the ultrafast dynamic response with a giant
Faraday rotation. Our results demonstrated near-infrared pulse-induced phenomena that areusually observed in the far-infrared range of energies corresponding to atomic interactions incondensed matter. Many related issues remain open for further investigation in optomagnonics.
Acknowledgment
A.S. acknowledges support from the grants of the Foundation for Polish Science
POIR.04.04.00-00-413C/17-00 and the National Science Centre of Poland (Grant DEC2017/25/B/ST3/01305). T.S. was financially supported by the Japan Society for the Promotionof Science (JSPS) KAKENHI (Grant Nos. JP19H01828, JP19H05618, and JP19K21854) and
Frontier Photonic Sciences Project of National Institutes of Natural Sciences (NINS) (Grant No.
19

01212002). The authors are particularly grateful to S. Parchenko, A. Chekhov, I. Razdolski, I.
Yoshimine, and W.-H. Hsu for their research support.
*

E-mail: and@uwb.edu.pl†

E-mail: satoh@phys.titech.ac.jp

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22