Spin and charge transport induced by magnetization dynamics in diffusive ferromagnetic metals

In ferromagnetic metals, the temporal and spatial dependence of the magnetization vector generates spin-dependent electric and magnetic fields. We study spin and charge transport by using the linearalized Boltzmann equation in response to these fields. A generalized spin-diffusion equation is derived and then exactly solved for a nanowire where the spatial dependence of the magnetization is one dimensional. It is found that the relative length scales between the domain-wall width and the spin-diffusion length are important in determining the local electromotive force and the enhanced damping induced by magnetization dynamics.