Underlying mechanism of the driving force for generating spin currents thermally in a ferrimagnetic insulator due to a temperature gradient

We previously proposed the idea that the effective thermal-energy transfer from the phonon system to the spin system in liquid phase epitaxial (LPE) films of Bi-substituted yttrium iron garnet (Bi:YIG), a ferrimagnetic insulator, takes place through enhanced spin-orbit coupling (SOC) with local 3d-electron spins in Fe3+ ions, and that the spin-thermoelectric (STE) generation in a paramagnetic platinum (Pt) layer is raised by increased spin pumping to the Pt layer from the Bi:YIG film. However, we could not specifically relate the underlying mechanism to the driving force for the generation of spin currents due to nonequilibrium dynamics of magnons driven by the temperature gradient ∇T in a magnetic insulator. In this paper, we discuss the origin of the driving force for generating spin currents, which are increased through enhanced SOC in LPE yttrium iron garnet films.