  Magnetic skyrmions are nano-scale magnetic whirls that can be driven by
currents via spin torques. They are promising candidates for spintronic devices
such as the racetrack memory, where a motion along the uniform current is
typically desired. However, for spin torque nano-oscillators in Corbino disks,
the goal is to achieve a circular motion, perpendicular to the radially applied
current. As we show, based on analytical calculations and micromagnetic
simulations, Bloch skyrmions engage in a circular motion with frequencies in
the MHz range when driven by spin-orbit torques. In contrast, N\'eel skyrmions
get stuck at the edges of the disk. Our analysis reveals that the antagonistic
dynamics between Bloch- and N\'eel-type magnetic textures arise from their
helicity. Furthermore, we find that skyrmioniums, which are topologically
trivial variations of skyrmions, move even faster and allow an increase in the
current density without being pushed toward the edges of the disk. When driven
by spin-transfer torques instead, Bloch and N\'eel skyrmions no longer exhibit
different dynamics. Instead, they move along a circular trajectory due to the
skyrmion Hall effect caused by their topological charge. Consequently, the
topologically trivial skyrmioniums inevitably become trapped at the disk edge
in this scenario. To provide a comprehensive understanding, our study also
examines currents applied tangentially, further enriching our insights into
skyrmion dynamics and appropriate current injection methods for skyrmion-based
devices.
