Recent reports on spin structures produced in nanomaterials due to confinement of spins imposed by geometrical restrictions are at the center of rising scientific interest. Topological curling magnetic structures (vortices) exhibit unique properties, regarding the energy profile, good colloidal stability in suspensions, manipulation under a low-frequency magnetic field, and torque exertion. The last property provides the potential to mechanically eradicate cancer cells via magnetomechanical actuation using remote ac magnetic fields. Here, we study, theoretically and by micromagnetic simulations, the magnetic energy evolutions for vortex nanosystems, i.e., Fe3O4 nanodisks (NDs) and nanorings (NRs). The obtained results for magnetic energy, magnetic susceptibility, and magnetization reversal confirm that the vortex-domain structure in NRs exhibits better stability and avoids agglomeration in solution, owing to the presence of a central hole, whereas the presence of a vortex core in NDs induces magnetic remanence. Although NDs are found to exert slightly higher torques than NRs, this weakness can be compensated for by a small increase (i.e., approximately equals 20%) in the amplitude of the applied field. Our results provide evidence of the magnetic stability of the curling ground states in NRs and open the possibility of applying these systems to magnetomechanical actuation on single cells for therapeutics in biomedicine, such as cancer-cell destruction by low-frequency torque transduction.