Including sample shape in micromagnetics with 3D periodic boundary conditions

TL;DR

This paper introduces a new, efficient method for including sample shape effects in micromagnetic simulations with periodic boundary conditions, addressing computational challenges of traditional approaches.

Contribution

The authors provide a formal proof that only average magnetization influences shape effects in large samples and develop a simple modification to existing PBC methods.

Findings

Shape effects are dominated by average magnetization in large samples.

The proposed method efficiently incorporates shape effects into PBC micromagnetic simulations.

The approach reduces computational complexity compared to traditional macrogeometry methods.

Abstract

Periodic boundary conditions (PBCs) for computing magnetic fields in repeating magnetic structures, e.g. in micromagnetic simulations, are typically imposed using the quasi periodic macrogeometry approach, where many copies of the simulated domain are introduced. This can be computationally problematic, especially if the simulated domain is incommensurate with the desired sample shape. In this work, we present a formal proof that for sufficiently large magnetic samples, only the average magnetisation gives non-negligible shape effects. Using this insight, we develop a simple, computationally efficient modification of existing implementations which incorporates shape effects in PBC methods.