Theory of Current-Driven Domain Wall Motion: A Poorman's Approach

TL;DR

This paper presents a simplified, self-contained theory of domain wall motion in ferromagnets driven by electric current, highlighting the dominant effects depending on wall thickness and material properties.

Contribution

It introduces a straightforward theoretical framework distinguishing momentum and spin transfer effects on domain wall dynamics in different regimes.

Findings

Spin transfer dominates in thick walls, with threshold current linked to magnetic anisotropy.

Momentum transfer dominates in thin walls, with threshold current proportional to pinning potential.

The theory clarifies how current effects vary with wall thickness and material parameters.

Abstract

A self-contained theory of the domain wall dynamics in ferromagnets under finite electric current is presented. The current is shown to have two effects; one is momentum transfer, which is proportional to the charge current and wall resistivity ($\rhow$), and the other is spin transfer, proportional to spin current. For thick walls, as in metallic wires, the latter dominates and the threshold current for wall motion is determined by the hard-axis magnetic anisotropy, except for the case of very strong pinning. For thin walls, as in nanocontacts and magnetic semiconductors, the momentum-transfer effect dominates, and the threshold current is proportional to $\Vz/\rhow$, $\Vz$ being the pinning potential.