# Non-Hermitian topology of spontaneous magnon decay

## TL;DR

This paper explores how interactions induce non-Hermitian topological features in magnon spectra, revealing exceptional points and lines near Dirac or Weyl points, with potential experimental detection in magnetic materials.

## Contribution

It introduces an effective non-Hermitian Hamiltonian framework for magnons affected by spontaneous decay, linking topological magnon band structures to non-Hermitian physics.

## Key findings

- Spectral functions show anisotropy near Dirac/Weyl points due to exceptional features.
- Effective non-Hermitian models accurately describe magnon splitting at Dirac points.
- Topological magnon bands provide a platform for studying non-Hermitian phenomena.

## Abstract

Spontaneous magnon decay is a generic feature of the magnetic excitations of anisotropic magnets and isotropic magnets with non-collinear order. In this paper, we argue that the effect of interactions on one-magnon states can, under many circumstances, be treated in terms of an effective, energy independent, non-Hermitian Hamiltonian for the magnons. In the vicinity of Dirac or Weyl touching points, we show that the spectral function has a characteristic anisotropy arising from topologically protected exceptional points or lines in the non-Hermitian spectrum. Such features can, in principle, be detected using inelastic neutron scattering or other spectroscopic probes. We illustrate this physics through a concrete example: a honeycomb ferromagnet with Dzyaloshinskii-Moriya exchange. We perform interacting spin wave calculations of the structure factor and spectral function of this model, showing good agreement with results from a simple effective non-Hermitian model for the splitting of the Dirac point. Finally, we argue that the zoo of known topological protected magnon band structures may serve as a nearly ideal platform for realizing and exploring non-Hermitian physics in solid-state systems.