Elliptical kπ skyrmions in the presence of the anisotropic Dzyaloshinskii–Moriya interaction

In this work, using micromagnetic simulations, we studied the stabilization of kπ skyrmions (k =1, …, 5), in the presence of the anisotropic Dzyaloshinskii–Moriya interaction (DMI), in a ferromagnetic dot. Our results show that the shape and size of the kπ skyrmions depend on the values of D_x and D_y (area unit energy densities along the x and y axes). A rich phase diagram was obtained as a function of D_x and D_y. Also, power spectra and the spatial profile of the spin wave modes of the kπ skyrmions were obtained as a function of D_x and D_y. These results show that the distribution of the maximum amplitudes of oscillation of the spin wave modes are distributed in circular or elliptical ring in the ferromagnetic dot, according to values of D_x and D_y.