Roles of non-equilibrium conduction electrons on magnetization dynamics of ferromagnets

The mutual dependence of spin-dependent conduction and magnetization dynamics of ferromagnets provides the key mechanisms in various spin-dependent phenomena. We compute the response of the conduction electron spins to a spatial and time varying magnetization ${\bf M} ({\bf r},t)$ within the time-dependent semiclassical transport theory. We show that the induced non-equilibrium conduction spin density in turn generates four spin torques acting on the magnetization--with each torque playing different roles in magnetization dynamics. By comparing with recent theoretical models, we find that one of these torques that has not been previously identified is crucial to consistently interpret experimental data on domain wall motion.