Microscopic Calculation of Spin Torques in Disordered Ferromagnets

Effects of conduction electrons on magnetization dynamics, represented by spin torques, are calculated microscopically in the first order in spatial gradient and time derivative of magnetization. Special attention is paid to the so-called $\beta$-term and the Gilbert damping, $\alpha$, in the presence of electrons' spin-relaxation processes, which are modeled by quenched magnetic (and spin-orbit) impurities. The obtained results such as $\alpha \ne \beta$ hold for localized as well as itinerant ferromagnetism.