Current-Induced Motion of Narrow Domain Walls and Dissipation in Ferromagnetic Metals

TL;DR

This paper develops a theoretical framework for spin transport in ferromagnets, revealing how current influences domain wall motion and dissipation, with implications for magnetic device performance.

Contribution

It introduces a tensor form of spin diffusion equations in ferromagnets and demonstrates their impact on domain wall velocity and damping effects.

Findings

Current increases domain wall terminal velocity.

Spin diffusion tensor affects dissipation and precession.

Velocity depends strongly on domain wall width.

Abstract

Spin transport equations in a non-homogeneous ferromagnet are derived in the limit where the sd exchange coupling between the electrons in the conduction band and those in the d band is dominant. It is shown that spin diffusion in ferromagnets assumes a tensor form. The diagonal terms are renormalized with respect to that in normal metals and enhances the dissipation in the magnetic system while the off-diagonal terms renormalize the precessional frequency of the conduction electrons and enhances the non-adiabatic spin torque. To demonstrate the new physics in our theory, we show that self-consistent solutions of the spin diffusion equations and the Landau-Lifshitz equations in the presence of a current lead to a an increase in the terminal velocity of a domain wall which becomes strongly dependent on its width. We also provide a simplified equation that predicts damping due to the conduction electrons.