Microscopic approach to current-driven domain wall dynamics

TL;DR

This paper reviews microscopic theories of current-driven domain wall dynamics in spintronics, focusing on quantum mechanical calculations of spin-transfer torque and the effects of conduction electrons and spin relaxation.

Contribution

It introduces a systematic quantum mechanical approach using non-equilibrium Green's functions to analyze domain wall motion induced by electric current.

Findings

Quantitative expressions for spin-transfer torque and force on domain walls.

Analysis of conduction electron effects on wall dynamics and resistivity.

Impact of electron spin relaxation on domain wall behavior.

Abstract

This review describes in detail the essential techniques used in microscopic theories on spintronics. We have investigated the domain wall dynamics induced by electric current based on the $s$-$d$ exchange model. The domain wall is treated as rigid and planar and is described by two collective coordinates: the position and angle of wall magnetization. The effect of conduction electrons on the domain wall dynamics is calculated in the case of slowly varying spin structure (close to the adiabatic limit) by use of a gauge transformation. The spin-transfer torque and force on the wall are expressed by Feynman diagrams and calculated systematically using non-equilibrium Green's functions, treating electrons fully quantum mechanically. The wall dynamics is discussed based on two coupled equations of motion derived for two collective coordinates. The force is related to electron transport properties, resistivity, and the Hall effect. Effect of conduction electron spin relaxation on the torque and wall dynamics is also studied.