A brief review of field- and current-driven domain-wall motion

A brief review of field- and recently developed current-driven domain-wall motion in a ferromagnetic nanowire is presented from a theoretical point of view. In the first part, the wall motion driven by an external magnetic field is studied on the basis of the Landau-Lifshitz-Gilbert equation and the collective coordinate method. The domain wall is treated as planar and rigid, called a one-dimensional model, and the wall motion is described by the relevant collective coordinates, centre position X and the polarization angle phi(0) of the wall. We also consider the interaction between the collective coordinates and spin waves excited around the wall and provide applicable criteria for the collective coordinate method in the domain-wall system. In the second part, we devote ourselves to studying the effect of conduction electrons on the domain-wall dynamics in a ferromagnetic metal. Microscopic calculations of the spin-transfer torque, dissipative spin torque (beta-term), non-adiabatic force and Gilbert damping are presented on the basis of the linear response theory and its extension. In the third part, the current-driven domain-wall motion described by the collective coordinates is studied. The effect of external pinning is also examined. There are several depinning mechanisms and threshold currents in different pinning regimes.