Spin Seebeck effect in antiferromagnets and compensated ferrimagnets

We theoretically investigate the spin Seebeck effect (SSE) in antiferromagnets and ferrimagnets, and show that the SSE vanishes in antiferromagnets but survives in ferrimagnets even at the magnetization compensation point despite the absence of its saturation magnetization. The nonvanishing SSE in ferrimagnets stems from two nondegenerate magnons. We demonstrate that the magnitude of the SSE in ferrimagnets is unchanged across the magnetization compensation point.

Figure 1

Schematic view of a hybrid structure composed of a nonmagnetic metal ($N$) and a ferrimagnet ($F$) with two sublattices $A$ and $B$.

Figure 2

Spin-wave spectra ($H_0=0$) with $\mathit{q}$ along the [111] direction calculated from Eq. (2) using parameters for (a) a uniaxial antiferromagnet NiO, and (b) a compensated ferrimagnet Er${}_3$Fe${}_5$O${}_{12}$. The wave vector $q$ is measured in units of the inverse of the nearest-neighbor distance.

Figure 3

Feynman diagram representing two processes relevant to the SSE in uniaxial antiferromagnets and ferrimagnets. (a) Spin current injected by ${\alpha }_{\mathit{q}}$ magnons ($I_s^{+}$). (b) Spin current injected by ${\beta }_{\mathit{q}}$ magnons ($I_s^{-}$). The signs of $I_s^{+}$ and $I_s^{-}$ are opposite. The solid and wavy lines represent magnon and itinerant spin-density propagators, respectively.

Figure 4

Temperature dependence of the SSE signal $I_s$ [red, Eq. (7)], saturation magnetization $M_s$ [blue, Eq. (9)], and total angular momentum $S_{\mathrm{tot}}$ [green, Eq. (10)], calculated for a compensated ferrimagnet Er${}_3$Fe${}_5$O${}_{12}$ using the same parameters as in Fig. 2b. The case for a $M_s$ pinned by the anisotropy field is shown; the data is normalized by its value at $T/T_{\mathrm{N}\text{é}\mathrm{el}}=0.1$. Inset: The case for a $M_s$ pinned by the external magnetic field is shown.

Figure 5

Temperature dependence of the effective magnon damping parameter ${\alpha }_{\mathrm{eff}}$ [red, Eqs. (B8) and (B9)], saturation magnetization $M_s$ [blue, Eq. (9)], and total angular momentum $S_{\mathrm{tot}}$ [green, Eq. (10)], calculated for a compensated ferrimagnet Gd${}_{22}$Fe${}_{70}$Co${}_8$. The data are normalized by the value at $T/T_{\mathrm{N}\text{é}\mathrm{el}}=0.05$.