Green's function representation of spin pumping effect

Abstract

In this study, current pumping by an external potential is studied on the basis of the Keldysh Green's function method, and a pumping formula written in terms of retarded and advanced Green's functions is obtained. It is shown that pumping is essentially driven by a change of particle distribution before and after an external perturbation. The formula is used to study the spin pumping effect in the case of strong $s\ensuremath{-}d$ exchange interaction, and the driving field is identified to be the spin gauge field. At the lowest order in the precession frequency of magnetization, the spin gauge field works as a constant potential, and the system is shown to reduce to a static problem of spin current generation by a time-independent potential with off-diagonal spin components.