  Spin current injection and spin accumulation near a ferromagnetic insulator
(FI)/nonmagnetic metal (NM) bilayer film under a thermal gradient is
investigated theoretically. 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 non-equilibrium distribution of magnons or
non-equilibrium between magnons and electrons. 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 non-equilibrium electron distributions. The results agree well with all
existing experiments.
