Spin wave modes of skyrmioniums in the presence of Dzyaloshinskii-Moriya interaction

A skyrmionium or 2π skyrmion is an exotic magnetic configuration that can be stabilized in ferromagnetic nanostructures, e.g., nanodisks. Differently from the standard (or π) skyrmion, it can move without suffering deflections due to the skyrmion Hall effect (SkHE), a property that is desirable for potential applications in spintronics. In this work, using micromagnetic simulations, it is investigated the influence of the Dzyaloshinskii-Moriya interaction on the azimuthal and radial spin wave spectra of the skyrmionium. First, the ground state of the ferromagnetic disk is obtained for several values of Dzyaloshinskii-Moriya exchange constant D_int and a fixed value of perpendicular anisotropy constant K_z. The spin wave modes of the skyrmionium were obtained using in-plane and out-of-plane magnetic pulses. The results show that the values of the frequencies of the spin wave modes depend on the values of D_int. Additionally, it is shown that it is possible to create a skyrmionium using in-plane rotating magnetic fields, by tuning parameters such as the intensity of the applied perpendicular magnetic fields, and their duration.