Reaction diffusion dynamics and the Schryer-Walker solution for domain walls of the Landau-Lifshitz-Gilbert equation

TL;DR

This paper analyzes the reaction diffusion dynamics of domain walls in the Landau-Lifshitz-Gilbert equation, providing analytic expressions for domain wall speed and conditions for the Schryer-Walker solution's applicability.

Contribution

It offers new analytic formulas for domain wall speed and identifies regimes where the Schryer-Walker solution is not selected, advancing understanding of magnetic domain dynamics.

Findings

Derived analytic expressions for domain wall speed.

Identified conditions where the Schryer-Walker solution is not selected.

Clarified the role of anisotropy ratios in domain wall dynamics.

Abstract

We study the dynamics of the equation obtained by Schryer and Walker for the motion of domain walls. The reduced equation is a reaction diffusion equation for the angle between the applied field and the magnetization vector. If the hard axis anisotropy $K_d$ is much larger than the easy axis anisotropy $K_u$, there is a range of applied fields where the dynamics does not select the Schryer-Walker solution. We give analytic expressions for the speed of the domain wall in this regime and the conditions for its existence.