Theory of Current-Driven Domain Wall Motion: Spin Transfer versus Momentum Transfer

A self-contained theory of the domain wall dynamics in ferromagnets under finite electric current is presented. The current has two effects: one is momentum transfer, which is proportional to the charge current and wall resistivity (${\rho }_{\mathrm{w}}$); the other is spin transfer, proportional to spin current. For thick walls, as in metallic wires, the latter dominates and the threshold current for wall motion is determined by the hard-axis magnetic anisotropy, except for the case of very strong pinning. For thin walls, as in nanocontacts and magnetic semiconductors, the momentum-transfer effect dominates, and the threshold current is proportional to $V_0/{\rho }_{\mathrm{w}}$, $V_0$ being the pinning potential.