# Breathing Mode of a Skyrmion on a Lattice

## TL;DR

This paper investigates the breathing mode of skyrmions on a lattice, analyzing how their oscillation frequency depends on magnetic field and developing an analytical model to explain the numerical results.

## Contribution

It introduces a numerical study of skyrmion breathing modes and presents an analytical model that explains the field dependence of oscillation frequencies.

## Key findings

- Oscillation frequency is linear at small fields.
- Frequency peaks and then drops to zero near collapse threshold.
- Large-amplitude breathing is damped and leads to collapse.

## Abstract

The breathing mode of a skyrmion, corresponding to coupled oscillations of its size and chirality angle is studied numerically for a conservative classical-spin system on a $500\times500$ lattice. The dependence of the oscillation frequency on the magnetic field is computed. It is linear at small fields, reaches maximum on increasing the field, then sharply tends to zero as the field approaches the threshold above which the skyrmion loses stability and collapses. Physically transparent analytical model is developed that explains the results qualitatively and provides the field dependence of the oscillation frequency that is close to the one computed numerically. It is shown that a large-amplitude breathing motion in which the skyrmion chirality angle $\gamma$ is rotating in one direction is strongly damped and quickly ends by the skyrmion collapse. To the contrary, smaller-amplitude breathing motion in which $\gamma$ oscillates is undamped.