Spin-Space Groups and Magnon Band Topology

TL;DR

This paper explores how spin-space symmetries influence magnon band topology, revealing new topological features and constraints in magnetic materials through the application of advanced symmetry group theory.

Contribution

It introduces the use of spin-space groups to analyze magnon band topology, providing a detailed theoretical framework for symmetry-enforced topological features in magnetic systems.

Findings

Magnon bands exhibit symmetry-enforced nodal points, lines, and planes.

Spin-space groups are essential for understanding magnetic band topology.

Hierarchy of magnetic symmetries depends on lattice and couplings.

Abstract

Band topology is both constrained and enriched by the presence of symmetry. The importance of anti-unitary symmetries such as time reversal was recognized early on leading to the classification of topological band structures based on the ten-fold way. Since then, lattice point group and non-symmorphic symmetries have been seen to lead to a vast range of possible topologically nontrivial band structures many of which are realized in materials. In this paper we show that band topology is further enriched in many physically realizable instances where magnetic and lattice degrees of freedom are wholly or partially decoupled. The appropriate symmetry groups to describe general magnetic systems are the spin-space groups. Here we describe cases where spin-space groups are essential to understand the band topology in magnetic materials. We then focus on magnon band topology where the theory of spin-space groups has its simplest realization. We consider magnetic Hamiltonians with various types of coupling including Heisenberg and Kitaev couplings revealing a hierarchy of enhanced magnetic symmetry groups depending on the nature of the lattice and the couplings. We describe, in detail, the associated representation theory and compatibility relations thus characterizing symmetry-enforced constraints on the magnon bands revealing a proliferation of nodal points, lines, planes and volumes.