Acoustic ferromagnetic resonance and spin pumping induced by surface acoustic waves

Abstract

Voltage induced magnetization dynamics of magnetic thin films is a valuable tool to study anisotropic fields, exchange couplings, magnetization damping, and spin pumping mechanism. A particularly well-established technique is the ferromagnetic resonance (FMR) generated by the coupling of microwave photons and magnetization eigenmodes in the GHz range. Here we review the basic concepts of the so-called acoustic ferromagnetic resonance technique (a-FMR) induced by the coupling of surface acoustic waves (SAW) and magnetization of thin films. Interestingly, additional to the benefits of the microwave excited FMR technique, the coupling between SAW and magnetization also offers fertile ground to study magnon-phonon and spin rotation couplings. We describe the in-plane magnetic field angle dependence of the a-FMR by measuring the absorption/transmission of SAW and the attenuation of SAW in the presence of rotational motion of the lattice, and show the consequent generation of spin current by acoustic spin pumping.

Full text

Acoustic ferromagnetic resonance and spin pumping induced by surface acoustic waves
Jorge Puebla,1, ∗Mingran Xu,1, 2 Bivas Rana,1Kei Yamamoto,1, 3 Sadamichi Maekawa,1,3, 4 and Yoshichika Otani1, 2, †
1CEMS, RIKEN, Saitama, 351-0198, Japan
2Institute for Solid State Physics, University of Tokyo,
5-1-5 Kashiwanoha, Kashiwa, Chiba, 277-8581, Japan
3Advanced Science Research Center, Japan Atomic Energy Agency, Tokai 319-1195, Japan
4Kavli Institute for Theoretical Sciences, University of Chinese Academy of Sciences, Beijing 100049, Peoples Republic of China
(Dated: January 28, 2020)
Voltage induced magnetization dynamics of magnetic thin films is a valuable tool to study anisotropic fields,
exchange couplings, magnetization damping and spin pumping mechanism. A particularly well established
technique is the ferromagnetic resonance (FMR) generated by the coupling of microwave photons and magneti-
zation eigenmodes in the GHz range. Here we review the basic concepts of the so-called acoustic ferromagnetic
resonance technique (a-FMR) induced by the coupling of surface acoustic waves (SAW) and magnetization of
thin films. Interestingly, additional to the benefits of the microwave excited FMR technique, the coupling be-
tween SAW and magnetization also offers fertile ground to study magnon-phonon and spin rotation couplings.
We describe the in-plane magnetic field angle dependence of the a-FMR by measuring the absorption / trans-
mission of SAW and the attenuation of SAW in the presence of rotational motion of the lattice, and show the
consequent generation of spin current by acoustic spin pumping.
PACS numbers:
I. INTRODUCTION
Arguably, one of the most enlightening works by the late
physicist Charles Kittel1is the theoretical description of the
ferromagnetic resonance absorption, published first in 1947
[1] and extended to shape anistropies in 1948 [2]. At these
early works, Kittel described the magnetization dynamics ex-
erted in a ferromagnetic specimen subjected to a strong dc
field Hzand a weak perpendicular microwave field Hx, such
that the magnetization dynamics can be well described by
∂M/∂t =γ[M×H]; where γis the gyromagnetic ratio, M
the magnetization and His the external field with components
(Hx, Hy, Hz). If the dc field is in-plane and strong enough to
fully align the magnetization M, then the magnetization pre-
cess as a single magnetic domain, a phenomenon we know
nowadays as ferromagnetic resonance (FMR). The corre-
sponding frequency at the resonance condition f0is described
by the so-called Kittel formula f0=γ
2πpHz(Hz+µ0|M|).
Nowadays, the FMR is a versatile tool that allows study-
ing magnetization dynamics in thin films [3], spin waves [4],
magnetization switching [5] and spin pumping [6]. Remark-
ably, 10 years after his description of FMR, it was the same
Charles Kittel who first formulated the coupling of spin waves
(magnons) and lattice vibrations (phonons) at resonance con-
ditions, giving origin to the acoustic excited FMR [7]. One
initial conclusion was that microwave phonons were neces-
sary for reaching the resonance condition. Conveniently, mi-
crowave phonons can be generated by interdigital transduc-
ers fabricated on top of piezoelectric substrates. Additional
to the previous description of applications of standard FMR
∗Electronic address: jorgeluis.pueblanunez@riken.jp
†Electronic address: yotani@issp.u-tokyo.ac.jp
1Charles Kittel passed away the last 15th of May 2019 at the age of 102
(microwave field excited), Kittel suggested that magnetic bulk
crystals may show nonreciprocal acoustic properties, and in-
duce strong phonon attenuation.
Here, we first overview the main characteristics of acoustic
ferromagnetic resonance (a-FMR) excited by GHz frequency
surface acoustic waves (SAW). Then, we review the descrip-
tion of the magnetization coupling with elastic rotation and its
dependence when varying in-plane magnetic field [8,9]. Fur-
thermore, we recalled an example of the generation of spin
current by a-FMR, the so-called acoustic spin pumping. We
show that the order of magnitude of the spin current density is
of the same order of the more standard spin pumping mech-
anism excited by microwave photons. Additional to the most
recent works of a-FMR [8,9], we describe the less explored
coupling of magnetization with lattice rotation, first published
more than 40 years ago by one of the authors of the present re-
view [10]. Finally, beyond the a-FMR study we conclude with
an outlook for the coupling of SAW with magnetic and non-
magnetic materials for spintronic research and applications.
II. ACOUSTIC FERROMAGNETIC RESONANCE
A. Surface acoustic waves
As its name suggests, surface acoustic waves (SAW) are
elastic waves that travel parallel to the surface of an elastic
material, with a decay perpendicular to the surface into the
bulk with an approximated decay length equal to the acous-
tic wavelength λSAW . Figure 1(a) shows the schematics of
a two port interdigital transducer (IDT) device on a piezo-
electric substrate (LiNbO3, Lithium Niobate) for generation
of SAW, the wavelength of acoustic waves, λSAW , depends
on the periodicity of IDTs as also shown in the schematics.
The generation of SAW is done by the inverse piezoelectric
effect, where elastic deformation is produced by injection of
arXiv:2001.09581v1 [cond-mat.mes-hall] 27 Jan 2020

2
rf-voltage. The reading of SAW is done by the direct piezo-
electric effect, converting elastic deformation back to voltage
signal. The SAW frequency is defined by fSAW =vs
λSAW ,
where vsis the sound velocity of the piezoelectric material.
Figure 1(b) shows a scanning electron microscope (SEM) im-
age of IDTs with 400 nm width and λSAW = 1.6µm. The
IDTs are patterned by electron beam lithography and made of
Ti(5nm)/Au(30nm) by the lift-off method. Since the sound ve-
locity vs= 4000 m/s in LiNbO3, we expect the generation of
SAW with an approximate frequency fSAW = 2.5GHz. Fig-
ure 1(c) shows the characterization of the scattering parame-
ter for transmission S12 by a vector network analyzer (VNA),
giving a SAW resonance frequency fSAW = 2.38 GHz. The
voltage generation of SAW also induces generation of spuri-
ous electromagnetic waves (EMW); since the SAW and EMW
velocities are different, it is possible to filter out the EMW
by a technique called time-gating that employs Fourier trans-
form operations. IDTs act not only as the generator and re-
ceiver for acoustic phonons, but also as an antenna, receiving
the microwave signals through the air. And acoustic phonon
is propagating in a speed of vs, which is in thousand meters
per second level, while the velocity of EMW is approximately
3×108m/s. Hence, SAW signal arrive to the second IDT port
after the EMW. As an additional function of our VNA, we are
able to analyze the signal in time-domain. In order to rule out
the noise brought by the EMW, we set a gate in time-domain,
to take the signal which arrives in the interval expected ac-
cording the the SAW velocity vsand the lenght of our device.
And by using Fourier transform, we obtain frequency-domain
signal. The comparision of the signal with and without time
gating is presented in figure 1(c).
B. Magnetization coupling with elastic strain
When SAWs propagate on a ferromagnetic layer it produces
a time variant strain tensor field ˆε(t)in the lattice, which cou-
ples to the local magnetic environment via the magnetoelas-
tic effect; as a consequence a time varying magnetic field is
exerted. Here, we describe how this time varying magnon-
phonon coupling induces a-FMR.
Let us start by describing first the dynamics exerted on the
normalized magnetization vector m=M/|M|when an ef-
fective driving magnetic field µ0Heff is present. Such dy-
namics are described by the Landau-Lifshitz-Gilbert (LLG)
equation
∂m/∂t =γm×µ0Heff +αm×∂m/∂t (1)
where αis the Gilbert damping constant and the gyromagnetic
ratio γis taken as negative. In standard FMR the µ0Heff
is given by the magnetic field generated by microwave pho-
tons, commonly achieved by coplanar waveguides. In a SAW
excited a-FMR, the magnetoelastic coupling links the time
dependent lattice strain tensor ˆε(t)to the magnetic environ-
ment. To calculate µ0Heff as a function of the strain ten-
sor components εij and magnetization components miwhere
i, j =x, y, z; we phenomenologically postulate the ther-
modynamic relation of Gibbs µ0Heff =−∇mGtot, which
FIG. 1: (a) Illustration of experiment setup. The surface acoustic
waves (SAW) are generated by applying RF voltage on an interdigital
transducer port (IDT) via the inverse piezoelectric effect. A second
IDT port measures the transmittance of SAW via the direct piezoelec-
tric effect. (b) Scanning electron microscope (SEM) image of IDT
fingers with a nominal width of 400 nm. (c) Transmittance measure-
ment of SAW by vector network analyzer, the measurement shows a
SAW resonance frequency, fSAW = 2.38 GHz. We show the mea-
surement before (red open circles) and after (blue open squares) time
gating filtering removal of electromagnetic waves.
should be valid for linear response around equilibrium: Foll-
wing Dreher et al. [9], we have introduced Gtot =G+Gme
where Gis the free energy density normalized by |M|in a
ferromagnet, which may for instance be taken to be
G=−µ0H·m+Bdm2
z+Bu(m·u)2.(2)
Here Bd=µ0|M|/2is the shape anisotropy and Buis the
in-plane uniaxial anisotropy along the unit vector u. Al-
though one could further include other terms such as dipole-
dipole and exchange interactions, the detailed form of Gis
largely irrelevant in the following discussions and we omit
them here. Gme is the magnetoelasitc contribution to the
(|M|-normalized) free energy density, which for a cubic crys-
tal reads
Gme =b1(εxxm2
x+εyy m2
y+εzz m2
z)
+ 2b2(εxymxmy+εy zmymz+εz xmzmx),(3)
where b1,2are the magnetoelastic coupling constants. We
define a new coordinate system (x1, x2, x3) so that the mag-
netization components are accordingly (m1, m2, m3); where

3
the equilibrium direction of the magnetization m0lies in x3
(m3), while m1and m2are the small dynamical compo-
nents perpendicular to each other and perpendicular to m3
(see schematic in fig. 2(a)). Now we can expand the effective
field µ0Heff under the influence of magnetoelastic coupling
to first order in m1,2
µ0Heff =−

G11m1+G12 m2
G12m1+G22 m2
G3
+

µ0h1
µ0h2
µ0h3
.(4)
Here G3=∂m3G|m=m0and Gab =∂ma∂mbG|m=m0,
a, b = 1,2are constants whose details are not needed. The
transverse components of the strain induced field h1,2are
given shortly while the longitudinal component h3is irrele-
vant in our present setup. Since the components of the driving
field µ0Heff that induce a-FMR are those transverse to the
equilibrium of magnetization m0(m3), we rewrite the LLG
equation in its matrix form as
G11 −G3+iωα
γG12 −iω
γ
G12 +iω
γG22 −G3+iωα
γ!m1
m2=µ0h1
h2
(5)
Solving for the transverse components (m1,m2) to the mag-
netization in equilibrium m0, we have
|M|m1
m2=χh1
h2(6)
where χis the Polder susceptibility tensor which describes the
dependence on the material parameters and static magnetic
field following from the free energy density Gof Eq. (2)
χ=µ0|M| G11 −G3+iωα
γG12 −iω
γ
G12 +iω
γG22 −G3+iωα
γ!−1
.
(7)
h1and h2are the transverse components of the driving field
induced by elastic strain, such that
µ0h1=−2b1sin θcos θ[εxx cos2φ+εyy sin2φ−εzz ]
−2b2[cos 2θ(εxz cos φ+εyz sin φ)+2εxy
sin θcos θsin φcos φ],(8)
µ0h2=2b1sin θsin φcos φ[εxx −εyy ]−2b2[cos θ
(εyx cos φ−εxz sin φ) + εxy sin θcos 2φ].(9)
We observe that different from conventional FMR, the a-FMR
has a strong dependence in the angles θ(out of plane angle)
and φ(in plane angle) between the magnetization m0and the
strain components εij . Rayleigh waves in SAW contain the
strain components εxx,εxz , where the dominant component
is the longitudinal strain (εxx). For a pure longitudinal strain
εxx when the m0is in-plane configuration θ= 0◦, the max-
imum value of the driving field µ0h1(2) is at φ= 45◦where
the magnetoelastic torque is larger, and vanishes at φ= 0◦
and φ= 90◦, as schematically shown in fig. 2(b). This an-
gle dependence gives origin to the now characteristic four-
fold butterfly shape of the a-FMR excited by SAW [8,9,11].
FIG. 2: (a) Schematic representation of the coordinates of magnetiza-
tion components m1,m2and m3(m0). (b) Schematic representation
of stress fields of SAW from a top view. The maximum magnetoe-
lastic torque is induced at φ= 45◦, and vanishes at φ= 0◦and
φ= 90◦
While the SAW power absorption ∆PSAW (φ)is in general
proportional to the imaginary part of (h∗
1, h∗
2)χ(h1, h2)T[9],
its angular dependence in the in-plane configuration is well-
captured by the approximate formula [8]
∆PSAW (φ)∝[b1εxx sin φcos φ∓2b2εxz cos φ]2,(10)
where εxx,xz are the amplitudes of εxx,xz respectively and
∓corresponds to the SAW propagation along ±ˆ
xdirections.
Figure 3(a) shows the spectrum at resonance condition for
FMR driving of a Ni layer of 10nm within a Ni/Cu/Bi2O3
heterostructure (inset), with an external magnetic field angle
φ= 240◦. The full in-plane magnetic field angle dependence
of the SAW power absorption ∆PSAW shows the four-fold
butterfly shape of a-FMR in figure 3(b) which is well-fitted by
Eq. (10).
C. Possible role of magnetization coupling with lattice rotation
The four-fold butterfly shape is expected to be symmetric
for pure longitudinal strain εxx, however, an asymmetric dis-
tribution may arise due to the contribution of the shear strain
εxz. Such asymmetric SAW absorption of a-FMR has recently
received increasing attention [8,12]. The origin of the asym-
metric SAW absorption on these works was explained as inter-
ference of the longitudinal (εxx) and shear (εxz ) strain com-
ponents. Under this scenario one may expect that the shear
strain component should be dominant or at least comparable
to the longitudinal strain [12]. However, in the thin film limit,
kd << 1, where kis the wavevector and dthe film thickness,
the shear strain is strongly suppressed and longitudinal strain
is dominant.
Even though the shear strain εxz is strongly suppressed in
the thin film limit, Maekawa and Tachiki theoretically demon-
strated that a rotational deformation of the lattice ωxz =
1/2(∂ux/∂z −∂uz/∂x)survives and can couple to the mag-
netic anisotropy (out of plane, i.e. along z-direction) [10],
where the displacement vector components uxand uzare

4
FIG. 3: (a) Power absorption PSAW of SAW at resonance condi-
tion for FMR driving of a Ni layer of 10nm within a Ni/Cu/Bi2O3
heterostructure (inset). (b) Normalized in-plane magnetic field angle
dependence of ∆PSAW . Figure (b) is adapted from ref.[8].
given by
ux=Akte−ktz−2q2
q2+k2
t
e−klzcos(qx −ωt),(11)
uz=−Aq e−ktz−2ktkl
q2+k2
t
e−klzsin(qx −ωt),(12)
where A is the amplitude of the SAW, kt=pq2−(ω/vt)2,
kl=pq2−(ω/vl)2, with vtand vlbeing the transverse and
longitudinal sound velocities. One can compute ωxz as
ωxz =1
2Aq2ξ2(e−ktz) cos(qx −ωt).(13)
ξis given by the ratio of the velocities vtand vl. Follow-
ing [10], different from the standard magnetoelastic coupling,
here the rotational deformation ωxz couples to the uniaxial
crystal anisotropy (out of plane, z)Dasociated with a spin Si
in the i-th site, such that
−D[S2
iz +ωxz(SizSix +Six Siz)] (14)
If we insert Eq. (13) in Eq. (14) we obtain the Hamiltonian
describing the interaction between SAW and spins via the ro-
tational deformation ωxz
H=1
2Aq2ξ2DX
i
(e−ktliz )(SizSix+SixSiz ) cos(qlix −ωt)
(15)
FIG. 4: Asymmetric power absorption PSAW of SAW in (a)
Ni/Cu/Bi2O3and (b) Ni/Ag/Bi2O3. Figures are adapted from ref.[8].
where lxi is the x-component of the position vector for the i-th
site. The interaction described by Eq. (15) implies that SAW
may excite surface magnons via rotational motion, and induce
SAW attenuation even in the absence of shear strain.
Figure 4shows a comparison of the in-plane magnetic
field dependence of SAW attenuation for Ni/Cu/Bi2O3and
Ni/Ag/Bi2O3. Although, nominally both heterostructures
contain similar Ni and Bi2O3, and Cu and Ag posses simi-
lar acoustic attenuation, it is possible to observe a significant
difference in the asymmetric behavior of SAW absorption be-
tween the two heterostructures. In a previous report, we at-
tributed such difference in asymmetric SAW absorption to in-
terference of longitudinal and shear waves [8], as was also
suggested for other systems [12]. However, the authors have
recently become aware of a report suggesting enhancement
of magnetic anisotropy energy in the Ag/Ni interface [14].
Such enhancement of magnetic anisotropy most likely is the
result of spin reorientation due to intefacial spin orbit cou-
pling; however, further studies are necessary to clarify it. To-
gether with recent independent experiments [13], this asym-
metric absorption in figure 4, may be due to the lattice rotation
coupling with magnetization as described by Eq. (15).
III. ACOUSTIC SPIN PUMPING
As described by Tserkovnyak et al [15,16], magnetization
dynamics following the LLG equation can pump spin current
from a ferromagnetic layer into a nonmagnetic metal. Such
spin pumping is the result of loss of torque acting in the mag-
netization vector, and can be directly related to enhancements
in the Gilbert damping α. The conservation of angular mo-
mentum indicates that the damping of magnetization preces-
sion can pump angular momentum or spin current into an ad-
jacent layer. The spin current generated by acoustic ferromag-
netic resonance can be converted to charge current by either
inverse spin Hall effect (ISHE) [17,18] or inverse Edelstein

5
FIG. 5: (a) Inverse Edelstein effect (IEE) signal rectified at the
Cu/Bi2O3(red circles) and Ag/Bi2O3(blue triangles) interfaces. (b)
Angle dependence of the spin current density Jsfor Ni/Cu/Bi2O3.
Figures adapted from ref.[8].
effect (IEE) [8]. Figure 5(a) shows the IEE signal rectified at
the Cu/Bi2O3(red circles) and Ag/Bi2O3(blue triangles) in-
terfaces. The opposite signs of rectified signal reflect the op-
posite Rashba spin splitting at these two interfaces [19]. We
can use the IEE signal to estimate the generated spin current
density Jswith the following formula taken from [8]
Js=V(φ)
λIE E wRsinθ(16)
where V(φ)is the voltage signal detected while the mag-
netic field is applied at angle φ,λIE E is the inverse Edelstein
length, wis the sample width and Rthe electric sample re-
sistance. Figure 5(b) shows the angle dependence of the spin
current density for Ni/Cu/Bi2O3, with the following parame-
ters: λIE E = 0.17nm, w= 10µm, R= 42.87Ω. The angle
dependence of spin current density shows similar behavior of
that of the power absorption of SAW presented in figure 3(b).
The spin current density is in the order of 108A/m2, same
order of magnitude to spin current density generated by stan-
dard microwave photon FMR [6,20]. For completeness, we
show in figure 6the power dependence of IEE signal rectified
at the Cu/Bi2O3interface. As the input power increases the
IEE voltage increases monotonically. At low input powers the
signal can be approximated to a linear increase, however, at
high input power the signal increases nonlinearly.
FIG. 6: Power dependence of rectified Inverse Edelstein effect (IEE)
signal at the Cu/Bi2O3interface
IV. CONCLUSION AND OUTLOOK
We provided an overview of the basic characteristics of
SAW and description of the magnon-phonon coupling that
triggers acoustic ferromagnetic resonance. We extended our
discussion in a relatively yet unexplored coupling mecha-
nism of lattice rotation and magnetic anisotropies [10]. Such
coupling mechanism offers a novel direction for promoting
SAW asymmetric attenuation. Enhancement and modulation
of asymmetric electrical charge conductivity in electronic cir-
cuits allowed the development of the electronic diode technol-
ogy. The coupling mechanism between magnetic anisotropy
and lattice rotation paves the way to explore significant en-
hancements of asymmetric SAW attenuation in the GHz fre-
quency range, with potential for the development of the
magneto-acoustic analog to an electronic diode [13]. We de-
scribed and showed the spin current density generated by a-
FMR, the so-called acoustic spin pumping. The order of mag-
nitude of the spin current density Jsis comparable to that
produced by standard FMR technique. Here, acoustic wave
reflectors [21] may represent an opportunity for further en-
hancement of the generated spin current densities in acoustic
spin pumping. Beyond the specific topic presented here, SAW
can also couple to nonmagnetic layers via the so-called spin
rotation coupling and generate spin currents in the absence
of magnetic materials or external magnetic fields [22]. Initial
experimental evidence of spin rotation coupling has been re-
cently reported via spin transfer torque mechanism in Cu/NiFe
bilayer [23]. However, it would be interesting to demon-
strate the generation of SAW induced spin current in an all-
nonmagnetic structure. Coupling involving SAW has multi-
ple applications that range from wireless technology, sensing,
biology to control of elemental charges in condensed matter
and coupling to quantum states of matter [24], which offers
opportunities for interdisciplinary research and device devel-
opments.
This work was supported by Grants-in-Aid for Scientific

6
Research on Innovative Areas (No. 26103001, No. 26103002)
and JSPS KAKENHI (No. 19H05629). MX was supported
by JSPS KAKENHI (No. JP19J21720). KY would like to ac-
knowledge support of JSPS KAKENHI (JP 19K21040). SM
was financially supported by ERATO, JST, and KAKENHI
(No 17H02927 and No. 26103006) from MEXT, Japan.
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