Gauge theory applied to magnetic lattices

TL;DR

This paper develops a unified gauge and graph theory framework to derive micromagnetic models that incorporate crystal symmetries and spin-orbit effects, accurately predicting Dzyaloshinskii-Moriya interactions across all crystal point groups.

Contribution

It introduces a novel approach combining gauge and graph theories to derive comprehensive micromagnetic models considering all symmetry constraints.

Findings

Predicts the form of DMI in all 32 point groups

Accounts for higher-order exchange interactions

Integrates crystal symmetry and spin-orbit effects

Abstract

Micromagnetic exchange is usually derived by performing the continuum limit of the Heisenberg model on a cubic lattice, where the exchange integrals are assumed to be identical for all nearest neighbors. This limitation normally imposes the use of a microscopic theory to explain the appearance of higher order magnetic interactions such as the Dzyaloshinskii-Moriya interaction (DMI). In this paper we combine graph- and gauge field- theory to simultaneously account for the symmetries of the crystal, the effect of spin-orbit coupling and their interplay on a micromagnetic level. We obtain a micromagnetic theory accounting for the crystal symmetry constraints at all orders in exchange and show how to successfully predict the form of micromagnetic DMI in all 32 point groups.