Thermal spin current and spin accumulation at ferromagnetic insulator/nonmagnetic metal interface

Spin current injection and spin accumulation near a ferromagnetic insulator (FI)/nonmagnetic metal (NM) bilayer film under a thermal gradient is investigated theoretically. By using the Fermi golden rule and the Boltzmann equations, we find that FI and NM can exchange spins via interfacial electron-magnon scattering because of the imbalance between magnon emission and absorption caused by either the deviation of the magnon number from the equilibrium Bose-Einstein distribution or the difference in magnon temperature and electron temperature. A temperature gradient in FI and/or a temperature difference across the FI/NM interface generates a spin current which carries angular momenta parallel to the magnetization of FI from the hotter side to the colder one. Interestingly, the spin current induced by a temperature gradient in NM is negligibly small due to the nonmagnetic nature of the nonequilibrium electron distributions. The results agree well with all existing experiments.