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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).
Xiao et al. (Mon,) studied this question.