# Magnon Spin-Momentum Locking: Various Spin Vortices and Dirac Magnons in Noncollinear Antiferromagnets

## TL;DR

This paper extends the concept of spin-momentum locking to magnonic systems, analyzing various antiferromagnets to reveal unique spin textures, vortices, and Dirac magnons, with implications for topological magnonics.

## Contribution

It introduces a generalized formula for magnon spin expectation values and explores novel spin vortices and Dirac magnons in noncollinear antiferromagnets.

## Key findings

- Magnon spin depends on momentum even with $z$-axis spin symmetry.
- Identified a spin vortex with winding number $Q=-2$ in kagome antiferromagnets.
- Discovered Dirac magnons with $Q=+1$ analogous to surface states.

## Abstract

We generalize the concept of the spin-momentum locking to magnonic systems and derive the formula to calculate the spin expectation value for one-magnon states of general two-body spin Hamiltonians. We give no-go conditions for magnon spin to be independent of momentum. As examples of the magnon spin-momentum locking, we analyze a one-dimensional antiferromagnet with the N\'eel order and two-dimensional kagome lattice antiferromagnets with the 120$^\circ$ structure. We find that the magnon spin depends on its momentum even when the Hamiltonian has the $z$-axis spin rotational symmetry, which can be explained in the context of a singular band point or a $U(1)$ symmetry breaking. A spin vortex in momentum space generated in a kagome lattice antiferromagnet has the winding number $Q=-2$, while the typical one observed in topological insulator surface states is characterized by $Q=+1$. A magnonic analogue of the surface states, the Dirac magnon with $Q=+1$, is found in another kagome lattice antiferromagnet. We also derive the sum rule for $Q$ by using the Poincar\'e-Hopf index theorem.