# Dirac and nodal line magnons in three-dimensional antiferromagnets

## TL;DR

This paper explores the topological features of magnon excitations in three-dimensional antiferromagnets with $PT$-symmetry, revealing Dirac points and nodal lines, and demonstrates their realization in a specific material with topologically nontrivial nodal lines.

## Contribution

It establishes the generic presence of Dirac points and nodal lines in $PT$-symmetric antiferromagnets and predicts a new type of topologically charged nodal lines in real materials.

## Key findings

- Dirac points and nodal lines are common in $PT$-symmetric antiferromagnets.
- In Cu$_3$TeO$_6$, magnon Dirac points are observed under collinear magnetic order.
- Dzyaloshinsky-Moriya interactions induce topologically nontrivial nodal lines with $Z_2$ charge.

## Abstract

We study the topological properties of magnon excitations in three-dimensional antiferromagnets, where the ground state configuration is invariant under time-reversal followed by space-inversion ($PT$-symmetry). We prove that Dirac points and nodal lines, the former being the limiting case of the latter, are the generic forms of symmetry-protected band crossings between magnon branches. As a concrete example, we study a Heisenberg spin model for a "spin-web" compound, Cu$_3$TeO$_6$, and show the presence of the magnon Dirac points assuming a collinear magnetic structure. Upon turning on symmetry-allowed Dzyaloshinsky-Moriya interactions, which introduce a small non-collinearity in the ground state configuration, we find that the Dirac points expand into nodal lines with nontrivial $Z_2$-topological charge, a new type of nodal lines unpredicted in any materials so far.