Robust formation of skyrmion and skyrmionium in magnetic hemispherical shells and their dynamic switching

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.