Threshold Current of Domain Wall Motion under Extrinsic Pinning, $\beta$-Term and Non-Adiabaticity

TL;DR

This paper provides a theoretical analysis of the threshold current needed for domain wall motion in ferromagnets, considering effects like non-adiabaticity, the $eta$-term, and extrinsic pinning, revealing four distinct regimes.

Contribution

It introduces a comprehensive theoretical model that incorporates non-adiabaticity and the $eta$-term into domain wall motion, identifying four regimes based on various physical parameters.

Findings

Four different regimes with unique threshold current dependencies

Effect of extrinsic pinning on domain wall motion elucidated

Role of non-adiabaticity and $eta$-term clarified

Abstract

Threshold current of domain wall motion under spin-polarized electric current in ferromagnets is theoretically studied based on the equation of motion of a wall in terms of collective coordinates. Effects of non-adiabaticity and a so-called $\beta$-term in Landau-Lifshitz equation, which are described by the same term in the equation of motion of a wall, are taken into account as well as extrinsic pinning. It is demonstrated that there are four different regimes characterized by different dependence of threshold on extrinsic pinning, hard-axis magnetic anisotropy, non-adiabaticity and $\beta$.