Chiral magnetism: a geometric perspective

TL;DR

This paper presents a geometric framework for understanding chiral ferromagnetism, linking the Dzyaloshinski-Moriya interaction to gauge fields and providing exact solutions and variational states in a 2D model.

Contribution

It introduces a geometric perspective on chiral magnetism, connecting gauge theory to magnetic interactions and constructing explicit solutions and states.

Findings

Exact solutions to the Bogomolny equation at specific magnetic fields.

Construction of a skyrmion crystal as a variational ground state.

Monte Carlo simulations confirming the skyrmion state's viability.

Abstract

We discuss a geometric perspective on chiral ferromagnetism. Much like gravity becomes the effect of spacetime curvature in theory of relativity, the Dzyaloshinski-Moriya interaction arises in a Heisenberg model with nontrivial spin parallel transport. The Dzyaloshinskii-Moriya vectors serve as a background SO(3) gauge field. In 2 spatial dimensions, the model is partly solvable when an applied magnetic field matches the gauge curvature. At this special point, solutions to the Bogomolny equation are exact excited states of the model. We construct a variational ground state in the form of a skyrmion crystal and confirm its viability by Monte Carlo simulations. The geometric perspective offers insights into important problems in magnetism, e.g., conservation of spin current in the presence of chiral interactions.