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An extended Landau-Lifshitz-Gilbert (LLG) equation is introduced to describethe dynamics of inhomogeneous magnetization in a current-carrying wire. Thecoefficients of all the terms in this equation are calculatedquantum-mechanically for a simple model which includes impurity scattering.This is done by comparing the energies and lifetimes of a spin wave calculatedfrom the LLG equation and from the explicit model. Two terms are of particularimportance since they describe non-adiabatic spin-transfer torque and dampingprocesses which do not rely on spin-orbit coupling. It is shown that theseterms may have a significant influence on the velocity of a current-drivendomain wall and they become dominant in the case of a narrow wall.

The quantum-mechanical basis of an extended Landau-Lifshitz-Gilbert equation for a current-carrying ferromagnetic wire