Breathing mode of a skyrmion on a lattice

The breathing modes of a skyrmion, corresponding to coupled oscillations of its size and chirality angle, are studied numerically for a conservative classical-spin system on a 500×500 lattice. The dependence of the oscillation frequency on the magnetic field is computed for a model with Dzyaloshinskii-Moriya interaction. In accordance with previous works, 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. Dissipation of a breathing motion in which the skyrmion chirality angle γ is rotating in one direction depends on the initial amplitude. Below a certain threshold the mode is stable, while above that threshold it becomes strongly damped by the reservoir of spin waves and quickly ends with the skyrmion collapse. To the contrary, smaller-amplitude breathing motion in which γ oscillates is undamped in the absence of other interactions. Adding perpendicular anisotropy and removing the applied field makes the breathing mode of any amplitude very slow and undamped.