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

TL;DR

This paper derives a quantum-mechanically grounded extended Landau-Lifshitz-Gilbert equation for ferromagnetic wires with current, highlighting non-adiabatic effects on domain wall dynamics without relying on spin-orbit coupling.

Contribution

It introduces a quantum-based derivation of the extended LLG equation, explicitly calculating coefficients for inhomogeneous magnetization and current effects, emphasizing non-adiabatic torque and damping.

Findings

Non-adiabatic torque significantly affects domain wall velocity.

Damping terms are derived from quantum mechanics, not spin-orbit coupling.

Non-adiabatic effects dominate in narrow domain walls.

Abstract

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.