Work

Topological characterization of Hopfions in finite-element micromagnetics

Year: 2025

Type: article

Abstract: Topological magnetic structures, such as Hopfions, are central to three-dimensional magnetism, but their characterization in complex geometries remains challenging. We introduce a robust finite-element method for calculating the Hopf index in micromagnetic simulations of three-dimensional nanostructures. By employing the Biot–Savart form for the vector potential, our approach ensures gauge-invariant results, even in multiply connected geometries like tori. A novel variance-based correction scheme significantly reduces numerical errors in highly inhomogeneous textures, achieving accurate Hopf index values with fast mesh-dependent convergence. We validate the method using an analytically defined Hopfion structure and demonstrate its ability to detect topological transitions through a simulation of a Hopfion’s field-induced destruction into a toron, marked by an abrupt change in the Hopf index. This method enables precise quantification of topological features in complex three-dimensional magnetic textures forming in finite-element micromagnetic simulations, offering a powerful tool for advancing topological magnetism studies in general geometries.

Source: Journal of Applied Physics

DOI: 10.1063/5.0280041

Authors: Louis Gallard, Riccardo Hertel

Institutions: Centre National de la Recherche Scientifique, Institut de Physique et Chimie des Matériaux de Strasbourg, Université de Strasbourg

Language: English

Topic: Magnetic properties of thin films

Subfield: Atomic and Molecular Physics, and Optics

Field: Physics and Astronomy

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $3,500

Funders: Deutsche Forschungsgemeinschaft, Agence Nationale de la Recherche, Université de Strasbourg