Theory of current-driven magnetization dynamics in inhomogeneous ferromagnets

We give a brief account of recent developments in the theoretical understanding of the interaction between electric currents and inhomogeneous ferromagnetic order parameters. We start by discussing the physical origin of the spin torques responsible for this interaction and construct a phenomenological description. We then consider the electric current-induced ferromagnetic instability and domain-wall motion. Finally, we present a microscopic justification of the phenomenological description of current-driven magnetization dynamics, with particular emphasis on the dissipative terms, the so-called Gilbert damping $\alpha$ and the $\beta$ component of the adiabatic current-driven torque.