# Topological Magnetoelastic Excitations in Non-Collinear Antiferromagnets

## TL;DR

This paper investigates topological properties of magnetoelastic excitations in non-collinear antiferromagnets, revealing that magnon-polaron bands can carry non-trivial Chern numbers due to magnon-phonon hybridization under magnetic fields.

## Contribution

It introduces a simple algorithm to compute Berry curvature and Chern numbers of magnon-polarons without diagonalizing the phonon Hamiltonian, advancing topological analysis methods.

## Key findings

- Magnon-polaron bands can have non-zero Chern numbers.
- Hybridization induces large Berry curvature affecting thermal Hall conductivity.
- The proposed algorithm simplifies topological calculations in magnetoelastic systems.

## Abstract

We study the topological property of the magnetoelastic excitation in non-collinear antiferromagnets. As a toy model, we consider the magnon-phonon coupling in a triangular antiferromagnet with a $120^\circ$ N\`eel order. We find that in the presence of out-of-plane external magnetic field, the magnon-polaron bands, which arise from hybridization of magnons and phonons, can carry Chern number, even though the individual magnon and phonon bands are topologically trivial. Large Berry curvature is induced from the anti-crossing regions between the magnon and phonon bands, which renormalizes the thermal Hall conductivity of phonon bands. To compute the Berry curvature and Chern number of magnon-polarons, we give a simple algorithm to diagonalize magnetoelastic Hamiltonian without diagonalizing the phonon Hamiltonian, by mapping the problem to the diagonalization of bosonic Bogoliubov-de-Gennes (BdG) Hamiltonian. This is necessary because the contribution to the Berry curvature from phonon cannot be properly captured if we compute the Berry curvature from magnetoelastic Hamiltonian whose phonon sector has been already diagonalized.