Helical edge modes in a triangular Heisenberg antiferromagnet

TL;DR

This paper demonstrates the theoretical and computational emergence of helical edge modes in a triangular Heisenberg antiferromagnet, revealing a topological mechanism that enables magnonic edge states without Dzyaloshinskii-Moriya interactions.

Contribution

It introduces a topological field-theoretic framework for helical edge modes in antiferromagnets, verified through a realistic lattice model, expanding potential for magnonic edge state realization.

Findings

Helical edge modes arise from a topological term in the spin-wave energy.

Edge modes propagate with opposite polarizations in opposite directions.

The topological term's strength depends on superexchange path disparity.

Abstract

We investigate the emergence of helical edge modes in a Heisenberg antiferromagnet on a triangular lattice, driven by a topological mechanism similar to that proposed by Dong et al. [Phys. Rev. Lett. 130, 206701 (2023)] for chiral spin waves in ferromagnets. The spin-frame field theory of a three-sublattice antiferromagnet allows for a topological term in the energy that modifies the boundary conditions for certain polarizations of spin waves and gives rise to edge modes. These edge modes are helical: modes with left and right circular polarizations propagate in opposite directions along the boundary in a way reminiscent of the electron edge modes in two-dimensional topological insulators. The field-theoretic arguments are verified in a realistic lattice model of a Heisenberg antiferromagnet with superexchange interactions that exhibits helical edge modes. The strength of the topological term is proportional to the disparity between two inequivalent superexchange paths. These findings suggest potential avenues for realizing magnonic edge states in frustrated antiferromagnets without requiring Dzyaloshinskii-Moriya interactions or nontrivial magnon band topology.