PHYSICAL REVIEW B 101, 134413 (2020)
Editors’ Suggestion

Ultrafast light-driven simultaneous excitation of coherent terahertz magnons
and phonons in multiferroic BiFeO3
Pritam Khan ,1,2,* Masataka Kanamaru,1 Keita Matsumoto ,1,3 Toshimitsu Ito ,4 and Takuya Satoh

1,3,†

1

Department of Physics, Kyushu University, Fukuoka 819-0395, Japan
Department of Physics, Bernal Institute, University of Limerick, V94T9PX, Ireland
3
Department of Physics, Tokyo Institute of Technology, Tokyo 152-8551, Japan
4
National Institute of Advanced Industrial Science and Technology, Tsukuba 305-8565, Japan
2(Received 7 February 2020; accepted 11 March 2020; published 13 April 2020)
The ultrafast switching of magnetization in multiferroic materials by a femtosecond laser could provide
various advantages in photonics and magnonics. An efficient approach to control the light-matter interactionis the modulation of ultrafast coherent magnons and phonons in the high-frequency range. Spontaneous Raman
and infrared spectra reveal the excitation of magnons and optical phonons in multiferroic BiFeO3 in the sub-fewterahertz range. However, coherent control of such quasiparticles has not been achieved yet. In this study, wedemonstrate that linearly polarized laser pulses simultaneously excite coherent magnons [out-of-plane () andin-plane () cyclone modes] and optical phonon (E mode) in BiFeO3 . Experimental results in conjugation withphenomenological theory, by considering three uniformly distributed magnetic domains, reveal that impulsive
stimulated Raman scattering is responsible for the generation of coherent magnons and phonons in BiFeO3 . The
observation of these terahertz magnon and optical phonon modes paves the way for the development of ultrafast
magnetoelectro-optical devices.
DOI: 10.1103/PhysRevB.101.134413
I. INTRODUCTION

The multiferroics, unique materials simultaneously exhibiting ferroelectric and (anti)ferromagnetic orders [1–3], arepromising candidates for the fabrication of next-generation
spintronic devices with added functionalities [4]. Recently,
oxide multiferroics have attracted considerable attention owing to the magnetoelectric coupling between the orders bymanipulating magnetic properties by electric field [5] andferroelectric polarization by magnetic field [6]. BiFeO3 stands
out as a canonical material in the multiferroic magnetoelectricresearch because it exhibits ferroelectricity and antiferromagnetism at room temperature [7–11]. Spontaneous Raman[12–17] and infrared (IR) [18–26] spectroscopic measurements on BiFeO3 have revealed the excitation of magnons andphonons. BiFeO3 also exhibits nontrivial light-matter interaction, which yields exotic phenomena, such as visible-light
photovoltaic effect [27,28], photoinduced ultrafast magneticfield-dependent terahertz (THz) emission [29], and giant
electrochromic behavior [30]. Recently, ultrafast pump-probe
spectroscopy has been successfully used to investigate the excitation of coherent magnons and acoustic phonons in BiFeO3
in the range below 100 GHz [31,32]. Although such observations are quite enticing, excitations of coherent magnon andoptical phonon modes in the sub-few-THz regime have notbeen reported. For practical application, the development of
ultrafast magnetoelectro-optical devices requires the generation of optically controlled polarization-sensitive magnon and*†pritam.khan@ul.ie
satoh@phys.titech.ac.jp2469-9950/2020/101(13)/134413(7)phonon modes at considerably higher frequencies of the THz
regime.
In this study, femtosecond pump-probe spectroscopy
was employed to generate high-frequency ultrafast coherent
magnons and optical phonon in a BiFeO3 single crystal andto understand their excitation and detection mechanisms. We
obtained magnon modes in sub-THz frequency range whereasa phonon mode was observed in few-THz range. The signed
amplitude of magnons and phonon exhibit sinusoidal dependence on the pump azimuth angle, which is originated from
impulsive stimulated Raman scattering (ISRS). Temperaturedependent pump-probe measurements further indicate that themagnon modes of 530, 560, and 740 GHz (at 300 K) belong
to 1(2) , 1(1) , and 2(1,2) symmetries, respectively.
II. MATERIAL AND METHODS
A. Sample fabrication and characteristics

The experiments were performed on a 150-μm-thicksingle-crystal BiFeO3 , grown by using a modified floatingzone method with laser diodes, parallel to the ẑ  [111]pc
orientation [33]. At room temperature, BiFeO3 exhibits arhombohedral R3c distorted perovskite structure with a magnetic point group of 3m. In addition, it exhibits a G-type antiferromagnetic order below the Néel temperature of 640 K [34]with a cycloidal spiral structure having a large modulation
period of 62 nm [35,36]. BiFeO3 is high-temperature ferroelectric with a Curie temperature of 1100 K and spontaneouselectric polarization of approximately 100 μC/cm2 along thez direction [37]. We chose a ferroelectric single domain where
the electric polarization is oriented along the sample normal(z axis). The cycloidal rotation was assumed to be along the134413-1©2020 American Physical Society

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PHYSICAL REVIEW B 101, 134413 (2020)

shown in Fig. 1. In the pump-probe measurement, optically
excited coherent magnons and phonons were observed byusing the polarimetric detection technique [41–43] with balanced detectors enabling the extraction of the contributions ofan induced change in ellipticity of the probe polarization. The
pump azimuth angle θ was defined as the angle between the xaxis and the direction of the pump polarization (electric field).
The detection was performed with a circularly polarized probe
in two different geometric configurations, X - and Y -probe
configurations [42], where the detection angles were set toρ = 0 and π /4, respectively.
III. RESULTS AND DISCUSSION
FIG. 1. Schematic of sample orientation pump-probe measurement with a linearly polarized pump and circularly polarized probe.
Here θ and ρ are the pump azimuth and the detection angle,
respectively.

x̂  [101̄]pc direction, whereas ŷ  [1̄21̄]pc was perpendicular
to the plane of cycloidal rotation.
B. Ultrafast pump-probe measurements

To observe the ultrafast spin and lattice dynamics in
BiFeO3 , we performed femtosecond time-resolved pumpprobe measurements in the transmission geometry. A pumppulse generated by a Ti:sapphire laser with a regenerative
amplifier and optical parametric amplifier (Spectra-Physics)
at a repetition rate of 500 Hz, wavelength of 1300 nm, andduration of 70 fs was incident at an angle of 10° with respect
to the sample normal (z axis). The pump photon energy is
below the lowest Fe3+ d-d or p-d transition energy [38–40].
Probe pulses with a wavelength of 800 nm and repetition rateof 1 kHz were incident perpendicularly to the sample. The
linearly polarized pump beam was focused to a spot diameterof approximately 100 μm, which yielded a fluence of approximately 25 mJ/cm2 . The circularly polarized probe beam
had approximately twice smaller spot diameter. A schematicof the pump-probe measurement and sample orientation are

Figure 2 shows the time evolution of the ellipticity change(η) in probe polarization in BiFeO3 at 300 K, for an excitation at a pump azimuth angle of θ = −π /4 and detectionin the Y -probe configuration. We observed oscillatory signals having different characteristic frequencies, as shown in
Figs. 2(a) and 2(b), with an abruptness at delay t ∼ 2.8 ps.
The abrupt signal is observed because of the overlap of theprobe pulse with the pump pulse, which is reflected from theback surface of the sample, counterpropagated, and reflectedagain from the front surface [41]. We performed fast Fouriertransform (FFT) of the oscillatory signals at positive delays.
The resulting amplitude spectra are shown in the insets ofFigs. 2(a) and 2(b). The FFT spectra reveal a high-amplitude
mode at 2.4 THz in Fig. 2(a) and three low-amplitude modes
at 530, 560, and 740 GHz in Fig. 2(b).
Experimental results in conjugation with the symmetry
consideration reveal that the ISRS is responsible for theexcitation of the 2.4-THz phonon mode having E symmetry, which is consistent with the mode in previous reports
observed by spontaneous Raman [16] and IR [18] spectroscopies. Detailed results and analysis on the selection rule
for the excitation and detection of the coherent phonon arepresented in Figs. S1 and S2 of Supplemental Material (SM)[44] (see also Refs. [16,45] therein).
The temperature dependence of the 2.4-THz frequency isshown in Fig. 3. The FFT spectra of the oscillation curves
corresponding to the 2.4-THz mode are shown in Fig. 3(a).

FIG. 2. Temporal evolutions of the ellipticity changes (η) in transmitted probe polarizations in BiFeO3 (T = 300 K) at two different
probe delays up to (a) 20 and (b) 60 ps. The insets show the FFT amplitude spectra of the signals at the corresponding delays, which reveal
center frequencies of (a) 2.4 THz and (b) 530, 560, and 740 GHz.
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FIG. 3. (a) FFT amplitude spectra of the 2.4-THz mode at various temperatures. (b) Variation of E phonon (2.4 THz) at different
temperatures. Here, the black line represents the FWHM of the phonon mode.

The ellipticity curves associated with THz mode is shownin Fig. S3 of SM [44]. Figure 3(b) reveals that the 2.4-THz
phonon mode exhibits frequency softening (∼4%) within thefull width at half maximum (FWHM) of the FFT spectra
shown in Fig. 3(a), when the temperature is increased.
To understand the temperature dependence of sub-THz
modes, ellipticity changes are recorded at various temperatures as shown in Fig. S4 of SM [44]. The corresponding FFT
spectra of the sub-THz frequencies at different temperaturesare shown in Fig. 4(a). The amplitude of the 530-GHz modeis small and overshadowed by the 560- and 750-GHz mode
to be observed. In a stark contrast to 2.4-THz phonon mode,
sub-THz modes exhibit stronger temperature dependences(the frequencies decrease drastically with the increase intemperature), as shown in Fig. 4(b) within the FWHM of the
FFT spectra in Fig. 4(a). The comparison of the temperaturedependences of the frequencies to those of the previously
reported IR transmission spectra of BiFeO3 [22–26] showsthat the 530-, 560-, and 740-GHz modes are consistent withthe 1(2) , 1(1) , and 2(1,2) magnon modes, respectively.
To elucidate the selection rule for the excitation and detection of coherent magnons, we performed time-resolved
measurements in X - and Y -probe configurations at various
pump azimuth angles θ , as shown in Fig. S5 of SM [44].

Figures 5(a) and 5(b) show the signed amplitudes of the1(1) and 2(1,2) modes in the X - and Y -probe configurations,
respectively. Both modes exhibit the same dependence on thepump azimuth [i.e., cos(2θ ) and sin(2θ ) in the X - and Y -probe
configurations, respectively]. As stated above, the amplitudeof the 1(2) mode is small. However, a FFT analysis at selected
pump azimuth reveals the appearance of this mode at θ = 0
and π /2 in the X -probe configuration and at θ = ±π /4 in
the Y -probe configuration as shown in Figs. 5(c) and 5(d).
Therefore, the selection rule for the 1(2) mode is similar to
those for the 1(1) and 2(1,2) modes.
Further, we use the phenomenological theory of ISRS tocorrelate the experimental results for BiFeO3 . In principle,
the light-matter interaction can be expressed by the interaction
free-energy density [46,47],
F =−

1
∗
i j (M, L)Ei E j ,
16π

(1)

where i j (M, L) is the dielectric tensor, a complex functionof M and L (we define a ferromagnetic vector M = M1 +M2 and antiferromagnetic vector L = M1 − M2 by using
the two sublattice magnetizations M1 and M2 ), and Ei isthe time-dependent amplitude of the electric field Ei (t ) =Re[Ei (t ) exp(iωt )].

FIG. 4. (a) FFT amplitude spectra of the sub-THz oscillations at various temperatures. (b) Variations of 1(2) (530 GHz), 1(1) (560 GHz),and 2(1,2) (740 GHz) magnon modes as functions of the measurement temperature. Here, the blue and red lines represent the FWHM of the2(1,2) and 1(1) magnon modes, respectively.
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PHYSICAL REVIEW B 101, 134413 (2020)

FIG. 5. Dependences of the signed amplitudes of the (a) 1(1) and (b) 2(1,2) magnon modes measured in the X -probe (green circles) andY -probe (blue circles) configurations as functions of the pump azimuth angle (T = 300 K). The solid red curves represent the sinusoidal fits ofthe experimental data. FFT amplitude spectra of 530-GHz 1(2) magnon mode at selected pump azimuth angles in the (c) X - and (d) Y -probe
configurations.

First, we expand the dielectric tensor
power series of M and L [46,48],ij =i j (M, L)

into a(0)MLMM
i j + iki jk Mk + iki jk Lk + gi jkl Mk Ml
ML+ gLL
i jkl Lk Ll + pi jkl Mk Ll ,(2)

where ki jk and gi jkl are the magneto-optical coupling constants, which mediate the inverse Faraday effect and inverse
Cotton-Mouton effect (ICME), respectively [46]. As |M| |L|, we can neglect the quadratic term of M, i.e., the fourthterm in the right-hand side of Eq. (2). Considering the 3msymmetry, the components of k M , k L , gLL , and pML are shownin SM [44] (see also Ref. [49] therein). The antiferromagnetic
vector L exhibits a cycloid rotation in the xz plane [35]. For
simplicity, we separately consider the x and z componentsof L. We also neglect local ferromagnetic components [50].
We start with L = (Lx , 0, 0), and thus the components ofi j (M, L) can be expressed as in Table I.

In the table, m and l are the dynamic components of M
and L, respectively. The out-of-plane () and in-plane ()cyclone modes have mz , ly and my , lz nonzero dynamic
components, respectively [36,51,52].
We define the effective magnetic fields for m and l as
∂F
,
∂m
∂F
heff = −∂lHeff = −

xx
yy
xy
yx

 mode (mz , ly = 0)

 mode (my , lz = 0)

p3 Lx mz
−p3 Lx mz
g9 Lx ly + ik2 mz
g9 Lx ly − ik2 mz

p4 Lx my−p2 Lx myg4 Lx lz
g4 Lx lz(4)

respectively. We define Ex (t ) = E0 (t ) cos θ and Ey (t ) =E0 (t ) sin θ exp(iϕ) (0  θ < π , − π2  ϕ < π2 ). As the pulse
widths of the femtosecond lasers are significantly smaller
than the period of the magnon oscillations, [E0 (t )]2 → I0 δ(t ),where I0 ≡ ∫ [E0 (t )]2 dt. By using Table I, we can express thecomponents of Heff and heff as

TABLE I. Dielectric tensor components of BiFeO3 for L =(Lx , 0, 0).
Tensor element(3)

Hxeff = 0,1
Hyeff =
I0 δ(t )(p4 Lx cos2 θ − p2 Lx sin2 θ ),16π
1
Hzeff =
I0 δ(t ){p3 Lx cos(2θ ) + k2 sin ϕ sin(2θ )},16π
hxeff = 0,1
I0 δ(t )g9 Lx cos ϕ sin (2θ ),16π
1hzeff =
I0 δ(t )g4 Lx cos ϕ sin (2θ ).
16πhyeff =

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(5)
(6)
(7)
(8)
(9)
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PHYSICAL REVIEW B 101, 134413 (2020)
TABLE II. Selection rules for the excitations of coherent
magnons in the X - and Y -probe configurations.

The equations of motions of m and l are [53]1dm(t )= − γ (M × Heff + L × heff ),dt
2
1
dl (t )
= − γ (M × heff + L × Heff ).
dt
2

(11)

Probe
X
Y

(12)

We neglect the damping terms because they are not important in the analysis. Further, we integrate Eqs. (11) and (12)around t = 0, which yields
1m =γ I0 Lx2 [g4 cos ϕ sin(2θ )ŷ − g9 cos ϕ sin(2θ )
z],
32π
(13)



1
l =
γ I0 p3 Lx2 cos(2θ ) + k2 Lx sin(2θ ) sin ϕ ŷ
32π
 

p2 − p4 2
2
Lx 
z .
(14)
+ p9 Lx cos(2θ ) −2

1
γ I0 Lx2 [g4 sin(2θ )ŷ − g9 sin(2θ )
z],
32π

1
γ I0 p3 Lx2 cos (2θ )ŷl lin =32π p2 − p4 2z .
Lx + p9 Lx2 cos(2θ ) −2

cos(2θ )sin(2θ )sin(2θ )Further, we consider the second case for L = (0, 0, Lz ).
Similarly (the calculations are shown in SM [44]), under theconditions A and A
1, the components of m and l can be
expressed as1
γ I0 g4 Lz2 cos (2θ ) cos (ω t ),32π1
γ I0 g4 Lz2 sin (2θ ) cos (ωt ),mylin (t ) = −32π1
γ I0 A g4 Lz2 sin (2θ ) sin (ωt ),lxlin (t ) =32π1lylin (t ) =γ I0 A g4 Lz2 cos (2θ ) sin (ω t ).
32π
mxlin (t ) =For a linearly polarized light, ϕ = 0, and thus Eqs. (13) and(14) can be simplified tomlin =

(15)

1 [46,47,54]. At t = 0,A = mlzy ; usually, A and A
my and mz have finite values, and thus are proportional tocos(ω t ) and cos(ωt ), respectively, whereas ly and lz oscillate with a phase difference of π /2 and exhibit sin(ω t ) andsin(ωt ) dependences, respectively,≈ A (g4 )2 Lz3 cos(2θ ) sin(ω t ),1
γ I0 g4 Lx2 sin (2θ ) cos (ωt ),32π
1
γ I0 g9 Lx2 sin (2θ ) cos (ω t ),mzlin (t ) = −32π1
γ I0 A g9 Lx2 sin (2θ ) sin (ω t ),lylin (t ) =32π1
γ I0 A g4 Lx2 sin (2θ ) sin (ωt ).
lzlin (t ) =32π
mylin (t ) =

(18)
(19)
(20)

xx − yy ∝ p3 Lx mz + p9 Lx my∝ p3 g9 Lx3 sin(2θ ) cos(ω t ) + p9 g4 Lx3 sin(2θ )(21)

xy + yx ∝ g9 Lx ly + g4 Lx lz∝ A (g9 )2 Lx3 sin(2θ ) sin(ω t )
(22)

(27)

ηY ∝ g4 Lz lx − p1 Lz my∝ A (g4 )2 Lz3 sin(2θ ) sin(ωt )− p1 g4 Lz3 sin(2θ ) cos(ωt )(17)

As the coupling between the light and magnetization is described solely by the tensor g, we confirm that both modes are
originated from the ICME. The changes in probe polarization,i.e., ellipticity (η), can be expressed as+ A (g4 )2 Lx3 sin(2θ ) sin(ωt ).

(26)∝ A (g4 )2 Lz3 cos(2θ ) sin(ω t )+ p1 g4 Lz3 cos(2θ ) cos(ω t )

ηY ∝

(25)

ηX ∝ g4 Lz ly + p1 Lz mx(16)l× cos(ωt ) ∼ (A, )0 ,(24)

Likewise, we obtain the changes in probe polarization,

We define exchange enhancement factors A = myz and

ηX ∝

(23)

≈ A (g4 )2 Lz3 sin(2θ ) sin(ωt ).

(28)

By combining Eqs. (21), (22) and (27), (28) and considering the contributions of Lx and Lz , we obtain the selection
rules for the magnon modes, as shown in Table II.
According to Table II, for the  modes, the experimental
results well match with the theoretical calculations in both X and Y -probe configurations. However, the experimental andtheoretical results for the  mode in the X -probe configuration contradict.
In the above analysis, we assumed that BiFeO3 has asingle magnetic domain with a spin cycloidal rotation along
the x̂  [101̄]pc direction. Next, we assume that BiFeO3 has
three uniformly distributed domains where the spin cycloidal
rotations are along the [101̄]pc , [1̄10]pc , and [01̄1]pc directions[55]. A detailed description with the contribution of all threedomains and probe light polarization changes by Lx and Lz
under the condition A and A
1 are presented in SM [44]while the resulting selection rules are shown in Table III.
Thus, the consideration of the contributions of all threedomains leads to experimental results well matched with thetheoretical calculations.

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PHYSICAL REVIEW B 101, 134413 (2020)

TABLE III. Selection rules for the excitations of coherent
magnons in the X - and Y -probe configurations assuming the contributions of multidomains.
Probe
X
Y





cos(2θ )sin(2θ )cos(2θ )sin(2θ )the out-of-plane (1(2) , 1(1) ) and in-plane (2(1,2) ) cyclone
magnon modes with frequencies of 530, 560, and 740 GHz
at 300 K, respectively. These results pave the way for further
studies on electromagnon excitations under the influence ofelectric and magnetic fields, which could reveal the inherent
relationship between the ferroelectric and antiferromagnetic
orders in THz optomagnonics.
ACKNOWLEDGMENTS

IV. CONCLUSIONS

The dynamics of coherent magnon and phonon modes in
the multiferroic BiFeO3 were investigated by time-resolved
ellipticity measurements. Spin and lattice oscillations in
BiFeO3 were excited nonthermally by the linearly polarized
light. The subsequent detection by the circularly polarizedprobe, along with the symmetry analysis by considering thecontribution of three uniformly distributed magnetic domains,
indicated that the ISRS was responsible for the driving of

We thank S. Miyahara, A. Koreeda, Y. Fujii, T. Yoshimura,and N. Fujimura for valuable discussions and M. Fiebig
and Ch. Tzschaschel for helping in the low-temperature
pump-probe measurements. This study was supported by
the Japan Society for the Promotion of Science (JSPS)
KAKENHI (Grants No. JP15H05454, No. JP16F16358,
No. JP19H01828, No. JP19H05618, No. JP19J21797, No.
JP19K21854, and No. JP26103004), JSPS Core-to-Core Program (A. Advanced Research Networks).

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