Analytical solution of the equation of motion for a rigid domain wall in a magnetic material with perpendicular anisotropy

TL;DR

This paper derives an analytical solution for the motion of a magnetic domain wall with high anisotropy, matching experimental velocities and elucidating conditions for uniform wall motion.

Contribution

It provides the first analytical expression for domain wall dynamics in high-anisotropy materials based on the Landau-Lifschitz-Gilbert equation.

Findings

Analytical expression for domain wall position over time.

Good agreement between calculated and experimental wall velocities.

High field uniform wall motion occurs under high rigidity assumptions.

Abstract

This paper reports the solution of the equation of motion for a domain wall in a magnetic material which exhibits high magneto-crystalline anisotropy. Starting from the Landau-Lifschitz-Gilbert equation for field-induced motion, we solve the equation to give an analytical expression, which specifies the domain wall position as a function of time. Taking parameters from a Co/Pt multilayer system, we find good quantitative agreement between calculated and experimentally determined wall velocities, and show that high field uniform wall motion occurs when wall rigidity is assumed.