A simple formula of the magnetic potential and of the stray field energy induced by a given magnetization

TL;DR

This paper derives a simple, general formula for stray field energy in micromagnetics using Arar-Boulmezaoud functions, enabling fast and efficient energy computations even for complex magnetizations and geometries.

Contribution

It introduces a new, tractable formula for stray field energy applicable to non-uniform magnetizations and unbounded samples, with a proven fast summation technique.

Findings

The formula remains valid for non-constant magnetizations.

The summation technique converges and is computationally efficient.

Numerical experiments confirm the method's effectiveness.

Abstract

The primary aim of this paper is the derivation and the proof of a simple and tractable formula for the stray field energy in micromagnetic problems. The formula is based on an expansion in terms of Arar-Boulmezaoud functions. It remains valid even if the magnetization is not of constant magnitude or if the sample is not geometrically bounded. The paper continuous with a direct and important application which consists in a fast summation technique of the stray field energy. The convergence of this technique is established and its efficiency is proved by various numerical experiences.