Dynamic modes of kπ skyrmions excited by spin waves

The dynamic modes of the kπ skyrmions excited by spin waves are investigated. Firstly, formations of kπ skyrmions are investigated. Secondly, breathing modes of kπ skyrmions excited by spin waves are studied, and it is found that spin waves can effectively excite breathing modes. The breathing frequencies excited by spin waves are identical to the intrinsic frequencies for 1π skyrmions, while the breathing frequencies excited by spin waves are larger than the intrinsic frequencies for 2π skyrmions and 3π skyrmions. Thirdly, gyration modes of kπ skyrmions excited by spin waves are studied, and it is found that spin waves can effectively excite gyration modes. In particular, the ranges of the trajectories driven by spin waves with intrinsic gyration frequencies are larger than the ranges of the trajectories driven by spin waves with other frequencies. This work promotes the understanding of kπ skyrmion dynamics under spin-wave excitation and provides a platform for developing spin-wave-based microwave devices utilizing kπ skyrmions.