Anisotropic Magnon Spin Transport in Ultra-thin Spinel Ferrite Thin Films -- Evidence for Anisotropy in Exchange Stiffness

Abstract

We report measurements of magnon spin transport in a spinel ferrite, magnesium aluminum ferrite $\mathrm{MgAl_{0.5}Fe_{1.5}O_4}$ (MAFO), which has a substantial in-plane four-fold magnetic anisotropy. We observe spin diffusion lengths $> 0.8$ $\mathrm{\mu m}$ at room temperature in 6 nm films, with spin diffusion length 30% longer along the easy axes compared to the hard axes. The sign of this difference is opposite to the effects just of anisotropy in the magnetic energy for a uniform magnetic state. We suggest instead that accounting for anisotropy in exchange stiffness is necessary to explain these results.

Full text

Anisotropic Magnon Spin Transport in Ultra-thin Spinel Ferrite Thin Films –
Evidence for Anisotropy in Exchange Stiffness
Ruofan Li,1Peng Li,2Di Yi,2, 3 Lauren Riddiford,2, 4 Yahong Chai,5, 6
Yuri Suzuki,2, 4 Daniel C. Ralph,7, 8 , ∗and Tianxiang Nan5, 6, 7 , †
1Laboratory of Atomic and Solid State Physics, Cornell University, Ithaca, NY 14853, USA
2Geballe Laboratory for Advanced Materials, Stanford University, Stanford, CA 94305, USA
3State Key Lab of New Ceramics and Fine Processing,
School of Materials Science and Engineering, Tsinghua University, Beijing 100084, China
4Department of Applied Physics, Stanford University, Stanford, CA, 94305, USA
5School of Integrated Circuits and Beijing National Research Center for Information
Science and Technology (BNRist), Tsinghua University, Beijing 100084, China
6Institute of Microelectronics, Tsinghua University, Beijing 100084, China
7Laboratory of Atomic and Solid-State Physics, Cornell University, Ithaca, NY 14853, USA
8Kavli Institute at Cornell for Nanoscale Science, Ithaca, NY 14853, USA
We report measurements of magnon spin transport in a spinel ferrite, magnesium aluminum
ferrite MgAl0.5Fe1.5O4(MAFO), which has a substantial in-plane four-fold magnetic anisotropy.
We observe spin diffusion lengths >0.8µmat room temperature in 6 nm films, with spin diffusion
length 30% longer along the easy axes compared to the hard axes. The sign of this difference is
opposite to the effects just of anisotropy in the magnetic energy for a uniform magnetic state. We
suggest instead that accounting for anisotropy in exchange stiffness is necessary to explain these
results.
Using magnons, the quanta of spin waves, for informa-
tion transmission offers the potential for low energy dis-
sipation compared to traditional electronic transport[1].
Magnon spin transport has been demonstrated experi-
mentally in both insulating ferrimagnets [2–14] and anti-
ferromagnets [15–17]. The magnon spin diffusion length,
the characteristic propagation length, has been stud-
ied under various conditions of temperature [11, 18–20],
magnon chemical potential [21–23], and external mag-
netic field [11, 20, 24]. Previous measurements on ferri-
magnetic insulators have focused on yttrium iron garnet
(YIG), either with thick films (>100 nm) which are fully
relaxed relative to the substrate [3, 5, 20] or with thinner
films [25]. In either case, YIG has very weak magnetic
anisotropy, and no anisotropies have been observed in the
spin transport.
Here we report measurements of magnon transport in
a low-loss spinel material that has been recently stabi-
lized in epitaxial thin-film form, magnesium aluminum
ferrite MgAl0.5Fe1.5O4(MAFO) [26–30]. When grown
epitaxially on an MgAl2O4substrate, MAFO possesses
a substantial in-plane cubic anisotropy (∼13 mT with
easy axes in the <110> directions), while maintain-
ing low magnetic damping into the regime of ultrathin
films. We report that magnon spin transport depends
strongly on the propagation direction relative to the
anisotropy axes, with a spin diffusion length 30% greater
for magnon propagation along the easy axes compared
to the hard axes. We argue that this difference has
the wrong sign to be explained taking into account only
the usual magnetic anisotropy energy which applies to
spatially-uniform states, but require also a consideration
of anisotropy in the exchange stiffness for nonuniform
states. Our results suggest that spin transport measure-
ments can be used as a sensitive probe of the exchange
stiffness and that manipulation of this stiffness (e.g., via
strain) provides an alternative strategy for controlling
magnon spin diffusion.
We employ a measurement geometry commonly used
for measuring magnon spin transport – parallel Pt wires
with different separation distances deposited on top of
the magnetic insulator to be investigated (Fig. 1(a))
[3, 5, 7, 10, 11, 15, 17]. The Pt wires have widths 200
nm, lengths 10 µm, and spacings that range from 0.4 to
3.2 µm. A charge current passing through one of the Pt
wires results in the excitation of magnons in the mag-
netic film below the wire by the spin Hall effect (SHE)
[31] and, because of a thermal gradient arising from Joule
heating, also by the spin Seebeck effect (SSE) [32]. The
excited magnons diffuse through the film to the other Pt
wire where they are detected by means of a voltage sig-
nal generated by the inverse spin Hall effect (ISHE) [33].
To measure magnon spin transport in different directions
relative to the underlying crystalline film we measure sep-
arate devices on the same chip with different orientations
of the Pt wires (Fig. 1(b)).
The magnetic insulators we probe are (001)-oriented 6-
nm-thick MAFO thin films that are epitaxially grown on
MgAl2O4(MAO) substrates [26] (see Supplemental Ma-
terial [34] for sample growth and fabrication). Tetragonal
distortion due to epitaxial strain acting on MAFO (3%
lattice mismatch) induces an in-plane 4-fold magnetic
anisotropy with an effective field strength of 13 mT as
shown by ferromagnetic resonance (FMR) measurements
on a MAFO film of similar thickness (5 nm) grown under
the same conditions (Fig. 1(c)). The angular dependence
arXiv:2105.13943v1 [cond-mat.mtrl-sci] 28 May 2021

2
of the anisotropy field is consistent with cubic symmetry,
and the easy axes are along <110>. The Gilbert damp-
ing in MAFO as measured by FMR remains small and
isotropic with respect to the angle of in-plane magnetic
field relative to the crystal axes [26].
d
V
I
MAO
MAFO
Pt Pt
𝜙
M
(a)
[100]
[1!
10]
[110]
[010]
(b)
[100]
[010]
(c)
FIG. 1. Measurement geometry and magnetic anisotropy of
MAFO (a) Schematic layout of the experimental setup (not
to scale). (b) Schematics for measuring magnon transport
along different directions relative to the crystal axes of the
MAFO film (c) FMR resonance field at 9 GHz as a function
of the angle (φH) between applied in-plane magnetic field and
the [100] crystal axis for a MAFO thin film of 5 nm thickness
grown under the same conditions as the 6 nm film. The solid
line represents a cos(4φH)fit to the measured data.
For the magnon spin-transport measurements, we pass
a low-frequency current (5.9 Hz) through one Pt wire,
exciting magnons in the MAFO film via both the SHE
and SSE. All the measurements were performed at room
temperature, using different angles and magnitudes of in-
plane applied magnetic field, and different spacings be-
tween the injector and detector Pt wires. The component
of the nonlocal voltage (VNL) detected in the distant Pt
wire that originates from SHE (VSHE) has a linear depen-
dence on the current (I), while the component from SSE
(VSSE), which arises due to a temperature gradient from
Joule heating, varies quadratically with I. These two
kinds of nonlocal voltages can therefore be distinguished
by detecting the first (V1ω=R1ωI) and second-harmonic
(V2ω=R2ωI2) responses using lock-in amplifiers. De-
pending on their origin, the nonlocal resistances can be
then written as
R1ω=RSH E +R0,1ω(1)
R2ω=RSSE +R0,2ω(2)
where RSHE and RSSE represent the nonlocal resistances
that we wish to measure arising from the SHE and SSE,
while R0,1ωand R0,2ωare offset resistances due to in-
ductive and capacitative couplings in the sample and the
measurement setup.
To subtract out the constant-impedance parts (R0,1ω
and R0,2ω), we collected V1ωand V2ωas a function of the
in-plane magnetic angle φfor a field magnitude of 75 mT,
as shown in Fig. 2(a). φis defined as the complement of
the angle between the magnetization of MAFO and the
applied current axis (see Fig. 1(a)). For the electrically-
generated nonlocal signal VSHE , both the injection and
the detection of the magnons have a cos(φ)dependence
coming from SHE and ISHE respectively, resulting in a
total dependence approximately ∝cos2(φ)(Fig. 2(a)).
In the case of the thermally-generated nonlocal signal
VSSE, the magnon injection is generated by Joule heating,
which has no angular dependence, while the detection of
the magnons through ISHE varies with angle φ, which
gives rise to an approximately cos(φ)angular dependence
(Fig. 2(c)).
(a)
(d)
(b)
(c)
FIG. 2. (a) First-harmonic RSH E and (c) second-harmonic
RSSE nonlocal signals as functions of the magnetic-field angle
φfor a field magnitude of 75 mT and samples with d= 0.6, 1,
and 1.4 µm, with the Pt wires oriented along the [100] direc-
tion. Solid lines are the fits to cos2(φ)and cos(φ)dependence
for first and second-harmonic signals respectively. Magnitude
of (b) first-harmonic and (d) second-harmonic nonlocal sig-
nals as functions of distance between the Pt wires oriented
along the [100] and [1¯
10] directions. The solid lines are fits to
Eq. 3.
Although generally magnon conductance decreases
with decreasing thickness in magnetic insulator films due
to increased damping [35], nevertheless even in 6 nm of
MAFO we observe long-range magnon transport across
3.2 µm gaps. The spin diffusion length can be extracted
from the decay of RSHE and RSSE as a function of the
separation (d) between the Pt wires (injector and detec-
tor). This decay can be well fitted to a magnon diffusion

3
model [3]:
RNL =C
λ
exp (d/λ)
1−exp (2d/λ)(3)
where RNL could be either RSHE and RSSE,Cis a
distance-independent constant, and λis an effective spin
diffusion length in the direction perpendicular to the Pt
wires.
We have investigated the effects of anisotropy by com-
paring spin diffusion lengths for the orientation of the
wires along [100], [110], [010] and [1¯
10] axes. Fig. 2(b)
shows the first-harmonic non-local resistances for the
[100] and [1¯
10] wire orientations plotted as a function
of the wire spacing. The dots in the plots correspond to
the experimental data while the solid lines show the fits
to Eq. (3). A similar decay of the nonlocal resistance vs.
spacing was also observed for the second-harmonic signal
as shown in Fig. 2(d). The spin diffusion lengths, λ1ωand
λ2ω, extracted from the fits for first and second-harmonic
signals are shown in Fig. 3 for the different crystal-axis
orientations.
FIG. 3. Spin diffusion lengths extracted from the decay of
the first (blue circles) and second-harmonic (red triangles)
nonlocal signals for wires along corresponding axes. Error
bars represent the standard deviations of the fits.
For both λ1ωand λ2ωwe observe significantly larger
(> 30%) spin diffusion lengths along the <110> family
of axes (easy axes) compared to the <100> axes (hard
axes). We also find that the extracted values of λ2ωare
slightly larger than λ1ω, which has also been observed
previously for YIG thin films [20]. This difference can be
explained as due to the different mechanisms by which
the nonequilibrium magnon distributions are generated
for the two signals. Furthermore, due to a lateral thermal
gradient near the Pt injector bar, the second-harmonic
voltage can have contributions from both local and non-
local SSE signals, while for the first-harmonic signal the
SHE excites the magnons only locally [5]. The angular
dependencies of λ1ωand λ2ωcorrespond to the same 4-
fold symmetry as the in-plane magnetic anisotropy, con-
sistent with the cubic symmetry of MAFO (Fig. 1(c)).
If one assumes that the primary cause of anisotropic
magnon transport in MAFO is simply the anisotropy in
the magnetic energy for a uniform magnetic state, it is
surprising that the spin diffusion length is longer in the
direction of the magnetic easy axis, rather than the re-
verse. The magnetic anisotropy energy for a uniform
magnetic state should cause the same qualitative behav-
ior as an increased applied magnetic field along the easy
axis. Both previous measurements on YIG [20, 24], and
our own measurements on MAFO (Fig. 4) show that
the magnitude of the nonlocal spin signal decreases as a
function of the increasing magnitude of an applied mag-
netic field, corresponding to a decreased spin diffusion
length with increasing magnetic field. This behavior has
been ascribed within the context of the SSE to the influ-
ence of the magnetic field increasing the energy of long-
wavelength magnons [24]. Quantitatively, the effect of a
magnetic field is also far too weak to explain the scale of
the effect that we measure. Figure 4 shows that a 140
mT magnetic field decreases the spin signal by only 18%,
indicating that an in-plane cubic anisotropy of 13 mT
could not generate the 30% difference we observe.
FIG. 4. The ratio of first harmonic nonlocal signal with its
maximum value as a function of applied magnetic field at
φ= 0 for samples with d = 1 µmand Pt wires oriented along
(a) hard axis (b) easy axis. The inset in each plot shows the
orientation of the Pt wires and applied magnetic field with
respect to the crystal axis.
The sign of the effect we observe is also surpris-
ing within the usual theoretical framework for model-
ing the energies and group velocities of long-wavelength
magnons. The only type of anisotropy that is ordinarily
considered is the anisotropy energy for a uniform mag-
netic state, accounted for in terms of an anisotropy field
2µ0Han. For a 4-fold in-plane magnetic anisotropy, the
dispersion curve for long-wavelength magnons (taking
into account both exchange and magnetic dipole contri-
butions) takes the form [36–38]
ω(k, φk, φH) = gµB
~pB1B2,(4)

4
with
B1=B+µ0Meff(1 −Pk) + Dk2+1
4µ0Han(3 + cos(4φH))
(5)
B2=B+µ0MeffPksin2(φk) + Dk2+µ0Han cos(4φH),
(6)
and where k=|~
k|is the magnitude of the wavevector,
φkis the angle of the wavevector relative to an easy axis,
φHis the angle of the average magnetization relative to
the [100] direction, B= 0.075 T in our angle-dependent
measurements, Meff is the saturation magnetization, D
is the exchange stiffness, and Pk= 1 −[(1 −e−kd )/(kd)]
with das the film thickness. For our MAFO samples,
µ0Meff = 1.5T, 2µ0Han = 13 mT, d= 6 nm. For oxide
ferrimagnets, a typical value of the exchange stiffness is
D= 5 ×10−17 T m2. The effect of the anisotropy field
is to increase the energy of magnons with small values of
kfor φknear the easy axis, but to cause little change in
the energy of magnons with larger kdue to the increas-
ing importance of the exchange and dipole terms. As
a result, the group velocity, vg=dω(k, φk, φH)/dk is al-
ways decreased by an increase in the magnetic anisotropy
energy. A larger value of Han will also decrease the ther-
mal magnon population. Both effects should decrease the
spin diffusion length in the direction of a magnetic easy
axis.
We therefore draw the conclusion, based on both the
sign and magnitude of the effect we observe, that the
anisotropic nonlocal spin signal must be caused by crys-
talline anisotropies which are different from simply the
magnetic anisotropy energy for a uniform magnetic state.
We considered whether the scattering time for spin relax-
ation might depend on the orientation of ~
kwith respect
to the anisotropy axes. But if this were the case, we
would expect the scattering to also depend on the ori-
entation of ~
kwith respect to the an applied magnetic
field. We do not observe deviations from the behavior
VSHE ∝cos(φ)and VSSE ∝cos2(φ)and therefore con-
clude that scattering time is not ~
korientation dependent
(See Supplemental Material [34] for residuals in the an-
gular fits).
We suggest, instead, that the anisotropy of our sig-
nal is dominated by anisotropies in the exchange ener-
gies associated with the MAFO crystal structure. In-
stead of assuming an isotropic exchange stiffness as in
Eqs. (4-6), we can model the exchange stiffness Das a
function of the orientation ~
krelative to the crystal axes
for the long wavelength spin waves that contribute most
to the non-local measurements; more specifically Dis
larger for ~
kalong the magnetic easy axis so as to increase
group velocity in those directions. The possibility of an
anisotropic exchange stiffness has been considered pre-
viously [39–41]. For non-relativistic exchange processes,
the spin stiffness should not depend on the orientation of
the magnetization with respect to the crystal axes (φH),
but it can depend on the orientation of the wavevector
relative to the crystal axes (φk). This is the symmetry
required to explain our results without significant devia-
tions from the observed dependence on the angle of mag-
netic field (VSHE ∝cos(φ)and VSSE ∝cos2(φ)).
The existence of anisotropy in exchange stiffness can
also help to explain the differences in the magnitude of
the spin transport signal extrapolated to small spacings
dbetween source and detector wires – the fact that the
spin signals in the limit of small dbecome larger for trans-
port along the hard axis compared to the easy axis. The
anisotropies in both the exchange stiffness and the energy
of the uniform magnetic state have the sign to increase
the energies of long-wavelength magnons with ~
kalong
the easy axes, so the population of those magnons will
be decreased relative to magnons with ~
kalong the hard
axes.
We are not aware of previous observations of
anisotropy in exchange stiffness by broadband ferro-
magnetic resonance (FMR) or Brillouin light scattering
(BLS), the two most common techniques for making di-
rect measurements of exchange stiffness in thin-film sam-
ples [42–45]. Broadband FMR measures the exchange
stiffness in only one direction (~
kperpendicular to the
plane of the thin film) since it requires measuring spin-
wave standing waves within the film thickness. To sep-
arate the effects of anisotropy in exchange stiffness from
a simple magnetic anisotropy energy using BLS would
likely require measurements as a function of the magni-
tude of ~
k.
In summary, we have measured magnon-mediated
spin transport in epitaxially-grown ultrathin (6 nm)
MgAl0.5Fe1.5O4thin films. The small isotropic Gilbert
damping parameter (∼0.0015) of these films, their soft
magnetism (in-plane coercive field < 0.5 mT), and
low processing temperature (∼450 ℃) make MAFO an
particularly attractive platform for the study of magnon
transport and integrated magnonic devices. Unlike
previous studies of YIG samples, tetragonally-strained
epitaxial MAFO posseses substantial in-plane cubic
magnetic anisotropy. We find also a strong anisotropy
in magnon-mediated spin transport, with spin diffusion
lengths 30% larger along the easy axes as compared
to that along the hard axes. The sign of this effect is
opposite to what would be expected due simply to the
magnetic anisotropy energy of a uniform magnetic state,
so we suggest that the anisotropy in spin transport is
dominated instead by anisotropy in exchange stiffness.
An exchange stiffness that is larger for ~
klong the
magnetic easy axis can explain not only the longer spin
diffusion lengths for transport along the easy axes but
also larger nonlocal spin signals in the limit of small
spacing that we observe for transport along the hard
axes. Nonlocal spin wave transport measurements might
therefore serve as a sensitive probe of exchange-stiffness
anisotropy in thin-film samples. Since crystalline

5
anisotropies can be tuned by strain, we also suggest
that strain-mediated manipulation of exchange stiffness
might provide a strategy for modulating spin transport
in magnetic thin films.
We thank Andrei Slavin and Vasyl Tyberkevych for
a critique of an initial draft of this paper, and Satoru
Emori, Jiamian Hu, Pu Yu, Dingfu Shao and Evgeny
Tsymbal for helpful discussions. Research at Cornell
was supported by the Cornell Center for Materials Re-
search with funding from the NSF MRSEC program
(Grant No. DMR-1719875). This work was performed
in part at the Cornell NanoScale Facility, a member
of the National Nanotechnology Coordinated Infrastruc-
ture, which is supported by the NSF (Grant No. NNCI-
2025233). Research at Tsinghua was supported by the
National Natural Science Foundation (52073158), and
the Beijing Advanced Innovation Center for Future Chip
(ICFC). Research at Stanford was funded by the Van-
nevar Bush Faculty Fellowship of the Department of De-
fense (contract No. N00014-15-1-0045). L.J.R. acknowl-
edges support from the Air Force Office of Scientific Re-
search (Grant No. FA 9550-20-1-0293) and an NSF Grad-
uate Research Fellowship.
∗dcr14@cornell.edu
†nantianxiang@mail.tsinghua.edu.cn
[1] A. V. Chumak, V. I. Vasyuchka, A. A. Serga, and
B. Hillebrands, Magnon spintronics, Nature Physics 11,
453 (2015).
[2] J. D. Adam, Analog signal processing with microwave
magnetics, Proceedings of the IEEE 76, 159 (1988).
[3] L. J. Cornelissen, J. Liu, R. A. Duine, J. B. Youssef, and
B. J. van Wees, Long-distance transport of magnon spin
information in a magnetic insulator at room temperature,
Nature Physics 11, 1022 (2015).
[4] B. L. Giles, Z. Yang, J. S. Jamison, and R. C. Myers,
Long-range pure magnon spin diffusion observed in a
nonlocal spin-seebeck geometry, Phys. Rev. B 92, 224415
(2015).
[5] J. Shan, L. J. Cornelissen, N. Vlietstra, J. Ben Youssef,
T. Kuschel, R. A. Duine, and B. J. van Wees, Influence of
yttrium iron garnet thickness and heater opacity on the
nonlocal transport of electrically and thermally excited
magnons, Phys. Rev. B 94, 174437 (2016).
[6] M. Collet, O. Gladii, M. Evelt, V. Bessonov, L. Soumah,
P. Bortolotti, S. O. Demokritov, Y. Henry, V. Cros,
M. Bailleul, V. E. Demidov, and A. Anane, Spin-wave
propagation in ultra-thin YIG based waveguides, Applied
Physics Letters 110, 092408 (2017).
[7] J. Shan, P. Bougiatioti, L. Liang, G. Reiss, T. Kuschel,
and B. J. van Wees, Nonlocal magnon spin transport in
NiFe2O4thin films, Applied Physics Letters 110, 132406
(2017).
[8] H. Qin, S. J. Hämäläinen, K. Arjas, J. Witteveen, and
S. van Dijken, Propagating spin waves in nanometer-
thick yttrium iron garnet films: Dependence on wave
vector, magnetic field strength, and angle, Phys. Rev.
B98, 224422 (2018).
[9] C. Liu, J. Chen, T. Liu, F. Heimbach, H. Yu, Y. Xiao,
J. Hu, M. Liu, H. Chang, T. Stueckler, S. Tu, Y. Zhang,
Y. Zhang, P. Gao, Z. Liao, D. Yu, K. Xia, N. Lei,
W. Zhao, and M. Wu, Long-distance propagation of
short-wavelength spin waves, Nature Communications 9,
738 (2018).
[10] J. Liu, L. J. Cornelissen, J. Shan, B. J. van Wees,
and T. Kuschel, Nonlocal magnon spin transport in yt-
trium iron garnet with tantalum and platinum spin injec-
tion/detection electrodes, Journal of Physics D: Applied
Physics 51, 224005 (2018).
[11] K. Oyanagi, T. Kikkawa, and E. Saitoh, Magnetic
field dependence of the nonlocal spin Seebeck effect in
Pt/YIG/Pt systems at low temperatures, AIP Advances
10, 015031 (2020).
[12] V. E. Demidov, S. Urazhdin, A. Anane, V. Cros, and
S. O. Demokritov, Spin–orbit-torque magnonics, Journal
of Applied Physics 127, 170901 (2020).
[13] S. T. B. Goennenwein, R. Schlitz, M. Pernpeintner,
K. Ganzhorn, M. Althammer, R. Gross, and H. Huebl,
Non-local magnetoresistance in YIG/Pt nanostructures,
Applied Physics Letters 107, 172405 (2015).
[14] K. Ganzhorn, T. Wimmer, J. Barker, G. E. W. Bauer,
Z. Qiu, E. Saitoh, N. Vlietstra, S. Geprägs, R. Gross,
H. Huebl, and S. T. B. Goennenwein, Non-local magnon
transport in the compensated ferrimagnet GdIG (2017),
arXiv:1705.02871.
[15] R. Lebrun, A. Ross, S. A. Bender, A. Qaiumzadeh,
L. Baldrati, J. Cramer, A. Brataas, R. A. Duine, and
M. Kläui, Tunable long-distance spin transport in a crys-
talline antiferromagnetic iron oxide, Nature 561, 222
(2018).
[16] W. Xing, L. Qiu, X. Wang, Y. Yao, Y. Ma, R. Cai, S. Jia,
X. C. Xie, and W. Han, Magnon transport in quasi-two-
dimensional van der waals antiferromagnets, Phys. Rev.
X9, 011026 (2019).
[17] J. Han, P. Zhang, Z. Bi, Y. Fan, T. S. Safi, J. Xiang,
J. Finley, L. Fu, R. Cheng, and L. Liu, Birefringence-
like spin transport via linearly polarized antiferromag-
netic magnons, Nature Nanotechnology 15, 563 (2020).
[18] L. J. Cornelissen, J. Shan, and B. J. van Wees, Tem-
perature dependence of the magnon spin diffusion length
and magnon spin conductivity in the magnetic insulator
yttrium iron garnet, Phys. Rev. B 94, 180402 (2016).
[19] K. Ganzhorn, T. Wimmer, J. Cramer, R. Schlitz,
S. Geprägs, G. Jakob, R. Gross, H. Huebl, M. Kläui, and
S. T. B. Goennenwein, Temperature dependence of the
non-local spin Seebeck effect in YIG/Pt nanostructures,
AIP Advances 7, 085102 (2017).
[20] J. M. Gomez-Perez, S. Vélez, L. E. Hueso, and
F. Casanova, Differences in the magnon diffusion length
for electrically and thermally driven magnon currents in
Y3Fe5O12 , Phys. Rev. B 101, 184420 (2020).
[21] L. J. Cornelissen, K. J. H. Peters, G. E. W. Bauer, R. A.
Duine, and B. J. van Wees, Magnon spin transport driven
by the magnon chemical potential in a magnetic insula-
tor, Phys. Rev. B 94, 014412 (2016).
[22] L. J. Cornelissen, J. Liu, B. J. van Wees, and R. A. Duine,
Spin-current-controlled modulation of the magnon spin
conductance in a three-terminal magnon transistor, Phys.
Rev. Lett. 120, 097702 (2018).
[23] K. S. Das, F. Feringa, M. Middelkamp, B. J. van Wees,

6
and I. J. Vera-Marun, Modulation of magnon spin trans-
port in a magnetic gate transistor, Phys. Rev. B 101,
054436 (2020).
[24] L. J. Cornelissen and B. J. van Wees, Magnetic field de-
pendence of the magnon spin diffusion length in the mag-
netic insulator yttrium iron garnet, Phys. Rev. B 93,
020403 (2016).
[25] J. Liu, X.-Y. Wei, G. E. W. Bauer, J. B. Youssef, and
B. J. van Wees, Electrically induced strong modulation of
magnons transport in ultrathin magnetic insulator films
(2020), arXiv:2011.07800.
[26] S. Emori, D. Yi, S. Crossley, J. J. Wisser, P. P. Bal-
akrishnan, B. Khodadadi, P. Shafer, C. Klewe, A. T.
N’Diaye, B. T. Urwin, K. Mahalingam, B. M. Howe,
H. Y. Hwang, E. Arenholz, and Y. Suzuki, Ultralow
damping in nanometer-thick epitaxial spinel ferrite thin
films, Nano Letters 18, 4273 (2018).
[27] J. J. Wisser, S. Emori, L. Riddiford, A. Altman, P. Li,
K. Mahalingam, B. T. Urwin, B. M. Howe, M. R. Page,
A. J. Grutter, B. J. Kirby, and Y. Suzuki, Ultrathin inter-
facial layer with suppressed room temperature magneti-
zation in magnesium aluminum ferrite thin films, Applied
Physics Letters 115, 132404 (2019).
[28] J. J. Wisser, A. J. Grutter, D. A. Gilbert, A. T.
N’Diaye, C. Klewe, P. Shafer, E. Arenholz, Y. Suzuki,
and S. Emori, Damping enhancement in coherent ferrite–
insulating-paramagnet bilayers, Phys. Rev. Applied 12,
054044 (2019).
[29] J. J. Wisser, L. J. Riddiford, A. Altman, P. Li, S. Emori,
P. Shafer, C. Klewe, A. T. N’Diaye, E. Arenholz, and
Y. Suzuki, The role of iron in magnetic damping of
Mg(Al,Fe)2O4spinel ferrite thin films, Applied Physics
Letters 116, 142406 (2020).
[30] L. J. Riddiford, J. J. Wisser, S. Emori, P. Li, D. Roy,
E. Cogulu, O. van ’t Erve, Y. Deng, S. X. Wang, B. T.
Jonker, A. D. Kent, and Y. Suzuki, Efficient spin current
generation in low-damping Mg(Al,Fe)2O4thin films, Ap-
plied Physics Letters 115, 122401 (2019).
[31] L. Vila, T. Kimura, and Y. Otani, Evolution of the spin
Hall effect in Pt nanowires: Size and temperature effects,
Phys. Rev. Lett. 99, 226604 (2007).
[32] K. Uchida, S. Takahashi, K. Harii, J. Ieda, W. Koshibae,
K. Ando, S. Maekawa, and E. Saitoh, Observation of the
spin Seebeck effect, Nature 455, 778–781 (2008).
[33] E. Saitoh, M. Ueda, H. Miyajima, and G. Tatara, Conver-
sion of spin current into charge current at room temper-
ature: Inverse spin-Hall effect, Applied Physics Letters
88, 182509 (2006).
[34] See supplemental material at [url] for additional sample
information and measurement details.
[35] M. B. Jungfleisch, A. V. Chumak, A. Kehlberger,
V. Lauer, D. H. Kim, M. C. Onbasli, C. A. Ross,
M. Kläui, and B. Hillebrands, Thickness and power de-
pendence of the spin-pumping effect in Y3Fe5O12/Pt het-
erostructures measured by the inverse spin Hall effect,
Phys. Rev. B 91, 134407 (2015).
[36] B. A. Kalinikos, M. P. Kostylev, N. V. Kozhus, and
A. N. Slavin, The dipole-exchange spin wave spectrum
for anisotropic ferromagnetic films with mixed exchange
boundary conditions, Journal of Physics: Condensed
Matter 2, 9861 (1990).
[37] R. D. McMichael and P. Krivosik, Classical model of
extrinsic ferromagnetic resonance linewidth in ultrathin
films, IEEE Transactions on Magnetics 40, 2 (2004).
[38] K. Sekiguchi, S.-W. Lee, H. Sukegawa, N. Sato, S.-H. Oh,
R. D. McMichael, and K.-J. Lee, Spin-wave propagation
in cubic anisotropic materials, NPG Asia Materials 9,
e392 (2017).
[39] K. Belashchenko, Anisotropy of exchange stiffness and its
effect on the properties of magnets, Journal of Magnetism
and Magnetic Materials 270, 413 (2004).
[40] R. Skomski, A. Kashyap, J. Zhou, and D. J. Sellmyer,
Anisotropic exchange, Journal of Applied Physics 97,
10B302 (2005).
[41] M. Heide, G. Bihlmayer, and S. Blügel, Dzyaloshinskii-
moriya interaction accounting for the orientation of mag-
netic domains in ultrathin films: Fe/W(110), Phys. Rev.
B78, 140403 (2008).
[42] F. Schreiber and Z. Frait, Spin-wave resonance in high-
conductivity films: The Fe-Co alloy system, Phys. Rev.
B54, 6473 (1996).
[43] S. Klingler, A. V. Chumak, T. Mewes, B. Khodadadi,
C. Mewes, C. Dubs, O. Surzhenko, B. Hillebrands, and
A. Conca, Measurements of the exchange stiffness of
YIG films using broadband ferromagnetic resonance tech-
niques, Journal of Physics D: Applied Physics 48, 015001
(2014).
[44] J. Hamrle, O. Gaier, S.-G. Min, B. Hillebrands,
Y. Sakuraba, and Y. Ando, Determination of exchange
constants of heusler compounds by brillouin light scat-
tering spectroscopy: application to Co2MnSi, Journal of
Physics D: Applied Physics 42, 084005 (2009).
[45] A. Haldar, C. Banerjee, P. Laha, and A. Barman, Bril-
louin light scattering study of spin waves in NiFe/Co ex-
change spring bilayer films, Journal of Applied Physics
115, 133901 (2014).