Non-Abelian Gauge Theory for Magnons in Topologically Textured Frustrated Magnets

TL;DR

This paper introduces a non-Abelian gauge theory for magnons in frustrated magnets with topological textures, revealing new topological magnetic fields and transport phenomena beyond previous Abelian models.

Contribution

It develops a non-Abelian gauge theory for magnons in frustrated magnets, extending the understanding of topological effects in magnon transport.

Findings

Topological solitons induce non-Abelian electromagnetic fields affecting magnons.

$4\\pi$-vortices and skyrmions generate Abelian and non-Abelian topological magnetic fields.

Topological Hall transport is demonstrated in textured frustrated magnets.

Abstract

We develop an effective gauge theory for three-flavored magnons in frustrated magnets hosting topological textures with the aid of the quaternion representation of the SO(3) order parameter. We find that the effect of topological solitons on magnons is captured generally by the non-Abelian emergent electromagnetic fields, distinct from the previously established gauge theory for magnons in collinear magnets where the gauge theory is often restricted to be Abelian. As concrete examples, $4\pi$-vortices in two-/three-dimensional magnets and Shankar skyrmions in three-dimensional magnets are discussed in detail, which are shown to induce, respectively, the Abelian and the non-Abelian topological magnetic field on magnons, and thereby engender the topological Hall transport in textured frustrated magnets. Our work is applicable to a broad class of magnetic materials whose low-energy manifold is described by the SO(3) order parameter. We envision that the discovery of the non-Abelian magnonic gauge theory will enrich the field of magnonics as well as prompt the study of magnon transport in textured frustrated magnets.