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

An extended Landau–Lifshitz–Gilbert (LLG) equation is introduced to describe the dynamics of inhomogeneous magnetization in a current-carrying wire. The coefficients of all the terms in this equation are calculated quantum-mechanically for a simple model which includes impurity scattering. This is done by comparing the energies and lifetimes of a spin wave calculated from the LLG equation and from the explicit model. Two terms are of particular importance since they describe non-adiabatic spin-transfer torque and damping processes which do not rely on spin–orbit coupling. It is shown that these terms may have a significant influence on the velocity of a current-driven domain wall and they become dominant in the case of a narrow wall.