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Microscopic Calculation of Spin Torques and Forces

Spin torques, that is, effects of conduction electrons on magnetization dynamics, are calculated microscopically in the first order in spatial gradient and time derivative of magnetization. Special attention is paid to the so-called β-term and the Gilbert damping, α, in the presence of electrons' spin-relaxation processes, which are modeled by quenched magnetic impurities. Two types of forces that the electric/spin current exerts on magnetization are identified based on a general formula relating the force to the torque.