Control of vortices by homogeneous fields in asymmetric ferroelectric and ferromagnetic rings

Effective Hamiltonians have been used (i) to demonstrate that the shape asymmetry of ferromagnetic rings is essential to the recently discovered switching of the chirality of their vortices by homogeneous magnetic fields, via a transition into onion states; (ii) to reveal that an electric vortex can also be controlled by a homogeneous electric field in asymmetric ferroelectric nanorings, via the formation of antiferrotoroidic pair states rather than onion states; and (iii) to provide the fundamental reason that allows such control, namely, two new interaction energies involving a vector characterizing the asymmetry, the applied field, and the toroidal moment.