Jaehak Yang, Hyeon-Kyu Park, Gyuyoung Park, Claas Abert, Dieter Suess, Sang-Koog Kim

We explored the variations of the topological magnetic textures of vortices, skyrmions, and skyrmioniums in magnetic elements of hemispherical-shell shape with respect to surface-normal uniaxial magnetic anisotropy constant ${K}_{u}$, Dzyaloshinskii-Moriya interaction (DMI) constant ${D}_{\mathrm{int}}$, and shell diameter $2R$. For given values of $2R$, the combination of ${K}_{u}$ and ${D}_{\mathrm{int}}$ plays a crucial role in the stabilization of those different spin textures. With decreasing $2R$, the geometrical confinement of hemispherical shells more significantly affects the stabilization of skyrmions owing to curvature-induced DM-like interaction. This effect is contrastingly dependent on the sign of ${D}_{\mathrm{int}}$: skyrmion formation is more favorable for positive ${D}_{\mathrm{int}}$ values, whereas it is less favorable for negative ones. A quite promising feature is that skyrmions can be stabilized even in the absence of intrinsic DMI for $2R<25\phantom{\rule{0.16em}{0ex}}\mathrm{nm}$. We also explored characteristic dynamic properties of skyrmions excited by in-plane and out-of-plane oscillating magnetic fields. Similarly to the fundamental dynamic modes found in planar dots, in-plane gyration and azimuthal spin-wave modes as well as out-of-plane breathing modes were found, but additional higher-frequency hybrid modes also appeared due to coupling between radially quantized and azimuthal spin-wave modes. Finally, we found a switching behavior of skyrmion polarity through a transient skyrmionium state using very-low-strength AC magnetic fields. This work provides further physical insight into the static and dynamic properties of skyrmions in curved-geometry nanodots and suggests potential applications to low-power-consumption and ultra-high-density information-storage devices.