A Focker-Planck description of the spin Seebeck effect

Thermally driven spin-wave spin current in a ferromagnetic material FM and the resulting electric signal in a metal probe placed on the FM are theoretically investigated by considering a thermally fluctuating spin at the interface of a FM-metal junction. We develop an analytical formulation to establish a Focker Plank equation for the probability distribution as a function of magnetization components of the material, for calculating the spin Seebeck signal detected by the metal probe, which converts spin current to charge current by the inverse spin Hall effect. The spin current is induced in the metal probe via an exchange interaction when the metal senses the temperature gradient.