Point-gap topology of damped magnon excitations in skyrmion strings

TL;DR

This paper explores the non-Hermitian topological properties of damped magnons in skyrmion strings, revealing conditions for the non-Hermitian skin effect and its impact on spin-wave dynamics.

Contribution

It analytically evaluates the spectral winding number for point gaps in magnon spectra, linking damping effects to non-Hermitian topology in skyrmion systems.

Findings

Non-Hermitian skin effect can occur without nonlocal damping.

Winding number depends on the sign of wave number at band minimum.

Propagation direction of spin waves varies with damping and band structure.

Abstract

We theoretically study the non-Hermitian topology of magnons with finite lifetimes due to Gilbert damping. By incorporating the spin-wave theory and perturbation theory for the Landau-Lifshitz-Gilbert equation including nonlocal damping terms, we analytically evaluate the spectral winding number for point gaps, which indicates the existence of the non-Hermitian skin effect (NHSE). We find that the NHSE can occur even in the absence of nonlocal damping. In the presence of nonlocal damping along one direction, we show that the winding number for an energy band with a unique minimum is determined from the sign of the wave number at the band minimum. We demonstrate these results using a model that hosts a skyrmion-string lattice as a steady state. We further investigate spin-wave propagation dynamics excited by a magnetic-field pulse and show that the propagation direction changes drastically from band to band depending on the presence of local and nonlocal damping, consistent with the nontrivial winding numbers.