Current-Induced Motion of Narrow Domain Walls and Dissipation in Ferromagnetic Metals

Spin transport equations in a non-homogeneous ferromagnet are derived in the limit where the sd exchange coupling between the electrons in the conduction band and those in the d band is dominant. It is shown that spin diffusion in ferromagnets assumes a tensor form. The diagonal terms are renormalized with respect to that in normal metals and enhances the dissipation in the magnetic system while the off-diagonal terms renormalize the precessional frequency of the conduction electrons and enhances the non-adiabatic spin torque. To demonstrate the new physics in our theory, we show that self-consistent solutions of the spin diffusion equations and the Landau-Lifshitz equations in the presence of a current lead to a an increase in the terminal velocity of a domain wall which becomes strongly dependent on its width. We also provide a simplified equation that predicts damping due to the conduction electrons.