Beyond the dipole approximation: A compact operator form to describe magnetizable many-body systems

TL;DR

This paper introduces a compact operator-based method to accurately model many-body magnetic interactions, surpassing traditional dipole approximations in efficiency and precision.

Contribution

It develops an analytic approximation scheme based on the full 2-body solution, providing a simple, efficient operator form for many-body magnetic interactions.

Findings

The new operator accurately describes cluster formation in magnetic fields.

The method is computationally efficient and easy to implement.

It outperforms classical dipole models near particle contact.

Abstract

To describe the interactions in magnetically soft particle systems either numerical full-field methods or dipole models are used. Whereas the former are computationally challenging, simple dipole interactions are largely underestimating the actual forces when particles get closer. Based on the full 2-body solution, an analytic approximation scheme for many-body full-field interactions is developed. The concept is formulated in terms of an improved operator that is equivalent to the classical dipole form. The full interaction operator allows to describe cluster formation and dispersion among particles in applied magnetic fields very compactly and highly efficient. In view of its simple 'dipole-like' form, the implementation is straightforward in many areas where magnetically soft objects are used.