Interaction energy of domain walls in a nonlocal Ginzburg-Landau type model from micromagnetics

TL;DR

This paper analyzes a nonlocal Ginzburg-Landau model from micromagnetics, revealing how Neel walls interact through core and tail effects, showing attraction or repulsion depending on their signs.

Contribution

It introduces a renormalized energy for Neel walls in a nonlocal Ginzburg-Landau model, highlighting novel tail-tail and core-tail interactions.

Findings

Neel walls have a core and logarithmically decaying tails.

Interactions depend on the signs of the Neel walls, with attraction or repulsion.

The model reveals new interaction features not present in standard Ginzburg-Landau vortices.

Abstract

We study a variational model from micromagnetics involving a nonlocal Ginzburg-Landau type energy for S^1-valued vector fields. These vector fields form domain walls, called Neel walls, that correspond to one-dimensional transitions between two directions within the unit circle S^1. Due to the nonlocality of the energy, a Neel wall is a two length scale object, comprising a core and two logarithmically decaying tails. Our aim is to determine the energy differences leading to repulsion or attraction between Neel walls. In contrast to the usual Ginzburg-Landau vortices, we obtain a renormalised energy for Neel walls that shows both a tail-tail interaction and a core-tail interaction. This is a novel feature for Ginzburg-Landau type energies that entails attraction between Neel walls of the same sign and repulsion between Neel walls of opposite signs.