Effect of spin diffusion on current generated by spin motive force

Spin motive force is a spin-dependent force on conduction electrons induced by magnetization dynamics. In order to examine its effects on magnetization dynamics, it is indispensable to take into account spin accumulation, spin diffusion, and spin-flip scattering since the spin motive force is in general nonuniform. We examine the effects of all these on the way the spin motive force generates the charge and spin currents in conventional situations, where the conduction electron spin relaxation dynamics is much faster than the magnetization dynamics. When the spin-dependent electric field is spatially localized, which is common in experimental situations, we find that the conservative part of the spin motive force is unable to generate the charge current due to the cancelation effect by the diffusion current. We also find that the spin current is a nonlocal function of the spin motive force and can be effectively expressed in terms of nonlocal Gilbert damping tensor. It turns out that any spin independent potential such as Coulomb potential does not affect our principal results. At the last part of this paper, we apply our theory to current-induced domain wall motion.