Theory of magnon-driven spin Seebeck effect

The spin Seebeck effect is a spin-motive force generated by a temperature gradient in a ferromagnet that can be detected via normal metal contacts through the inverse spin Hall effect [K. Uchida et al., Nature (London) 455, 778 (2008)]. We explain this effect by spin pumping at the contact that is proportional to the spin-mixing conductance of the interface, the inverse of a temperature-dependent magnetic coherence volume, and the difference between the magnon temperature in the ferromagnet and the electron temperature in the normal metal [D. J. Sanders and D. Walton, Phys. Rev. B 15, 1489 (1977)].

Figure 1

(Color online) A ferromagnet with thickness $d$, length $L$, and magnetization $\mathbf{M}$ pointing in $\widehat{\mathbf{z}}$ direction connects two N contacts at temperature $T_{L/R}$ at the left and right ends. A Pt strip of dimension $l\times w\times h$ on top of F converts an injected spin current $\left({\mathbf{I}}_s={\mathbf{I}}_{sp}+{\mathbf{I}}_{fl}\right)$ into an charge current $I_c$ or Hall voltage $V_H$ by the inverse spin Hall effect.

Figure 2

(Color online) $\text{F}\mid \text{N}$ interface with (1) spin pumping current ${\mathbf{I}}_{sp}$ driven by the thermal activation of the magnetization in F at temperature $T_{\text{F}}$ and (2) fluctuating spin current ${\mathbf{I}}_{fl}$ driven by the thermal activation of the electron spins in N at temperature $T_{\text{N}}$.

Figure 3

(Color online) $g_{r,i}$ vs $U_0$ in log scale for different $\Delta$ values. Curves starting with values close to unity give the real part $g_r$ and curves starting from very low values display the imaginary part $-g_i$. The vertical axis is in units of the Sharvin conductance.