Field-tuned spin excitation spectrum of kπ skyrmion

We study spin wave excitation modes of kπ skyrmion (k = 1,2,3) in a magnetic nanodot under an external magnetic field along z-direction using micromagnetic simulations based on Landau-Lifshitz-Gilbert equation. We find that a transition of kπ skyrmion to other skyrmion-like structures appears under some critical external fields, the corresponding spin wave excitations are simulated for each state under magnetic field. For skyrmion, the frequencies of excitation modes increases and then decreases with the low frequency mode splitting at a critical magnetic field. In addition to the well-known two in-plane rotation modes and an out-of-plane breathing mode of skyrmion, more excitation modes are found with a higher k (k = 2, 3). The excitation modes vary as a function of magnetic field, and the excitation frequencies for different modes exhibit a rapid or slight change depending on the field-induced change of magnetization profile. Our study indicates the rich spin wave excitations for kπ skyrmion and opens a possibility in theoretical or experimental investigation of magnonics application.