# Spin eigen-excitations of an antiferromagnetic skyrmion

## TL;DR

This paper theoretically predicts and classifies localized eigenmodes of antiferromagnetic skyrmions, revealing two energy branches with distinct properties and identifying high-energy modes without ferromagnetic equivalents.

## Contribution

It introduces a classification of skyrmion eigenmodes in antiferromagnets, including novel high-energy localized modes and their dependence on skyrmion size and magnetic field.

## Key findings

- Low-energy mode frequency scales as R_0^{-2} for large skyrmions.
- Identifies high-energy localized eigenmodes with no ferromagnetic counterpart.
- Most modes are doubly degenerate without magnetic field, splitting otherwise.

## Abstract

We theoretically predict and classify the localized modes of a skyrmion in a collinear uniaxial antiferromagnet and discuss how they can be excited. As a central result, we find two branches of skyrmion eigenmodes with distinct physical properties characterized by being low or high energy excitations. The frequency dependence of the low-energy modes scales as $R_0^{-2}$ for skyrmions with large radius $R_0$. Furthermore, we predict localized high-energy eigenmodes, which have no direct ferromagnetic counterpart. Except for the breathing mode, we find that all localized antiferromagnet skyrmion modes, both in the low and high-energy branch, are doubly degenerated in the absence of a magnetic field and split otherwise. We explain our numerical results for the low-energy modes within a string model representing the skyrmion boundary.