Thermal properties of magnons and the spin Seebeck effect in yttrium iron garnet/normal metal hybrid structures

In the study of the spin Seebeck effect (SSE) in structures with a ferromagnetic insulator (FMI) in contact with a normal metal it is important to know the distributions of the temperatures of the magnon, phonon, and electron systems. Studies of the SSE in yttrium iron garnet (YIG) have relied on the thermal properties of magnons in YIG calculated with expressions valid for low temperatures. Here we present a calculation of the magnon specific heat and thermal conductivity in YIG and show that the values at room temperature are very discrepant from numbers used in the literature. With our values we calculate the temperature profiles of the magnon and phonon systems in a FMI subject to a temperature gradient in the configurations used to study the transverse and longitudinal SSE. In both cases the results are quite different from those obtained in previous studies.

Figure 1

(a) Spin-wave dispersion in yttrium iron garnet at $T$ = 300 K. Upper (red) solid curve is calculated with a quadratic dispersion. The dotted line is calculated by Ref. [48] for $k$ along a [111] direction. Lower (blue) solid curve is calculated with Eq. (9). Note that the label of the horizontal axis in Fig. 2 of Ref. [49] is incorrect. (b) Variation with $x$ of the integrands in Eqs. (2) and (5).

Figure 2

Variation of the spontaneous magnetization of YIG with temperature. Circles represent the data of Anderson [51]. Lower solid curve (red) is calculated with the low-temperature expression Eq. (8). Dotted curve is calculated with Eq. (10) without magnon energy renormalization. Solid upper curve (blue) is calculated with Eq. (10) with magnon energy renormalization.

Figure 3

(a) Magnon specific heat: Upper curve (red) represents the calculation with the low-temperature result Eq. (3); lower curve (blue) is the result of calculation with Eq. (11). (b) Magnon thermal conductivity calculated with Eq. (12).

Figure 4

(a) and (b) Illustrations of the arrangements used to study the transverse and longitudinal spin Seebeck effects with a temperature gradient applied along or across the thickness of a ferromagnetic insulator (FMI) film. (b) and (c) Profiles of the temperatures of the phonon and magnon systems calculated with Eqs. (16) and (17), using the values of the magnon specific heat and thermal conductivity calculated for YIG at room temperature, for the configurations above.