We discuss recent theoretical results on the problem of current-induced spin torque in magnetic nanowires. Our main focus is on sharp domain walls, for which the domain-wall width is of the same order or smaller than the Fermi wavelength of electrons. Such a case is more suitable for magnetic semiconductors than metals.

We present the results of our calculations of the spin and spin current densities related to different modes of the scattering states. The accumulated transverse components of the spin density and the spin current oscillate in the vicinity of the wall and they essentially affect its dynamics whereas the longitudinal part of the spin current is responsible for another component of the spin torque, which creates a force for the current-induced motion of the domain wall along the nanowire.

We also analyze the dynamics of the sharp domain wall using the standard Landau-Lifshits-Gilbert formalism and the two-component spin torque calculated for this model. The model with a large constant of easy-plane anisotropy allows to simplify essentially the analysis of the domain wall motion, and our main calculations are performed for this particular model. We show that the domain wall changes its shape depending on the wall velocity, and we calculate this velocity as a function of the electric current. Within the model considered, there exists a critical current for the instability of magnetic system with respect to the spontaneous motion of the domain wall.

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