PHYSICAL REVIEW B 90, 064421 (2014)
Magnon thermal mean free path in yttrium iron garnet
Stephen R. Boona
1
and Joseph P. Heremans
1, 2
1
Department of Mechanical and Aerospace Engineering, The Ohio State University, Columbus, Ohio 43210, USA
2
Department of Physics, The Ohio State University, Columbus, Ohio 43210, USA
(Received 2 July 2014; revised manuscript received 6 August 2014; published 22 August 2014)
The magnetothermal properties of monocrystalline yttrium iron garnet (YIG) are reported. The magnon
contribution to both the thermal conductivity and specific heat at low temperatures has been determined by
measuring these properties under an applied magnetic field, which allows us to freeze the magnon modes
and isolate the phonon contribution relative to the zero-field behavior. These results are interpreted within the
framework of a simple kinetic gas model for magnon heat conduction that allows us to estimate the magnon
thermal mean free path, i.e., the inelastic scattering length scale for thermally driven bulk magnons. We observe
this parameter to reach as high as approximately 100 μm at 2 K. It tracks the acoustic phonon thermal mean
free path closely and decreases rapidly as the temperature is increased. This relatively short length scale suggests
that magnon modes at thermal energies in YIG are not solely or directly responsible for coherent macroscale
thermal spin transport (e.g., in the spin Seebeck effect) at high temperatures. Instead, these results support a
growing consensus that subthermal magnons, i.e., those at energies below about 30 ± 10 K, are important for
spin transport in YIG at all temperatures. These results also emphasize that magnon effects should be considered
wavelength dependent, and that magnon-magnon interactions may be just as important for thermal spin transport
as magnon-phonon scattering. This, in turn, has implications for understanding the characteristic temperature
and length scales involved in spin caloritronic phenomena.
DOI: 10.1103/PhysRevB.90.064421 PACS number(s): 66.70.−f , 44.10.+i, 72.10.Di
I. INTRODUCTION
The rapidly expanding field of spin caloritronics [1,2] has
generated a surge of interest in the magnetic and thermal
properties of a wide variety of materials. Via processes such as
the spin Seebeck (SSE) [3–5] and spin Peltier (SPE) [6] effects,
as well as the (inverse [7]) spin Hall effect (SHE) [8,9], a bevy
of spin-dependent transport mechanisms are now available
for probing the magnetic, electronic, and thermal properties
of various materials and heterostructures. The spin Seebeck
effect has been reported in two clearly different geometries, the
longitudinal SSE (LSSE), where magnon transport is parallel
to the temperature gradient, and the transverse geometry
(TSSE), where it is perpendicular. It was suggested, but
not proven, that the TSSE can be viewed as a variation of
LSSE with nonlocal spin detection. A key step in designing
and interpreting experiments in this field lies in developing
an appropriate understanding of the relevant interactions
between the elementary excitations (magnons, phonons, and,
in electrical conductors, spin-polarized electrons) whose fluxes
govern spin transport, and the corresponding length scales
over which these processes occur. For example, one important
parameter is the distance over which coherent spin currents
persist in various materials (the spin diffusion length), as
this distance correlates with the limiting length scale of
heterostructure components whose functions rely on spin
transport [10].
In order to isolate and understand the nature of various
possible interactions between fluxes of heat, charge, and mag-
netization in materials, it is convenient to examine materials in
which only one or two of the relevant elementary excitations
are active at a time. To study phonon-magnon interactions,
for example, it is desirable to examine materials that have
relatively large band gaps and high Curie temperatures, so
that the material remains both electrically insulating and
magnetically ordered within the desired temperature range
of study. For these reasons, certain transition metal oxides,
in particular yttrium iron garnet (Y
3
Fe
5
O
12
, or YIG), have
become ubiquitous in spin caloritronic experiments. This
material has a band gap of approximately 2.85 eV [11]; its
Curie (T
C
= 550 K [12]) and Debye (T
D
= 531 K, this
work) temperatures are remarkably close to each other, and
relatively high. The desired electronic and magnetic properties
are thus easily maintained at room temperature and below.
The absence of itinerant electrons in YIG means that the
localized core d electrons of the iron atoms are the primary
source of spin and magnetization dynamics in the material, and
thermal energy then propagates through only perturbations of
the magnetization (magnons) and/or real-space displacements
of the atoms (phonons).
Experimental measurements [13] of the magnon dispersion
in YIG by neutron diffraction, in addition to numerical
simulations, report that the magnons can be reasonably well
described by a quadratic dispersion:
ω = Da
2
k
2
, (1)
up to approximately 620 GHz (30 K). Here a is the size
of the unit cell (1.24 nm) and D corresponds to a spin-wave
stiffness parameter measured in units of temperature ranging
from about 46 K (for the limit where a
2
k
2
→ zero) to 35 K
(when a
2
k
2
= 0.01) [13]. Additional magnon modes appear
in the dispersion near 620 GHz. An “optical-like” magnon
mode appears near 150 K, and this mode hybridizes with
the “acousticlike” mode whose dispersion at this energy is
approximately linear. The linearity of this latter mode allows
for the calculation of a corresponding “pseudoacoustic” group
velocity v
M
= dω/dk, which is 8500 m/s at these energies
and temperatures.
1098-0121/2014/90(6)/064421(8) 064421-1 ©2014 American Physical Society