# Kelvin modes of a skyrmion line in chiral magnets and the associated magnon transport

## TL;DR

This paper investigates Kelvin modes of skyrmion lines in chiral magnets, revealing symmetric low-energy modes and asymmetric higher modes, suggesting skyrmion lines can act as one-way magnon waveguides.

## Contribution

It provides the first detailed analysis of Kelvin mode dispersion in skyrmion lines, highlighting symmetry properties and potential for unidirectional magnon transport.

## Key findings

- Lowest Kelvin mode is symmetric at low energy despite inversion symmetry breaking.
- Higher Kelvin modes are asymmetric and mostly have positive group velocity.
- Skyrmion lines can serve as one-way waveguides for magnons.

## Abstract

Magnetic skyrmions in bulk crystals are line-like topologically protected spin textures. They allow for the propagation of magnons along the skyrmion line but are localized inside the skyrmion line. Analogous to the vortex line, these propagating modes are the Kelvin modes of a skyrmion line. In crystals without an inversion center, it is known that the magnon dispersion in the ferromagnetic state is asymmetric in the wavevector. It is natural to expect that the dispersion of the Kelvin modes is also asymmetric with respect to the wavevector. We study the Kelvin modes of a skyrmion line in the ferromagnetic background. In contrast, we find that the lowest Kelvin mode is symmetric in the wavevector in the low energy region despite the inversion symmetry breaking. Other Kelvin modes below the magnon continuum are asymmetric, and most of them have a positive group velocity. Our results suggest that a skyrmion line can function as a one-way waveguide for magnons.