Semiclassical dynamics of vortices in 2D easy-plane ferromagnets

Semiclassical dynamics of magnetic vortices in 2D lattice models of easy-plane ferromagnets is investigated. It is shown that the low-energy part of the spectrum of vortices treated as quantum excitations of the system exhibits a nontrivial structure. The simplest spectrum is observed for standard magnetic vortices, in which magnetization at long distances from the center of a vortex is parallel to the basal plane. In this case, the spectrum has a band structure consisting of several nonintersecting bands, whose number is determined only by the value of atomic spin S and lattice symmetry. For purely 2D magnets with a single spin per unit cell, the number of bands is S or 2S for integral and half-integral values of spin S, respectively. For a lattice with the basis with an even number 2n of spins per unit cell, the number of bands is 2nS for any spins. The situation radically changes for vortices in the cone state as compared to standard vortices, for which the magnetization at a long distance from the center of a vortex rotates in the easy plane of the magnet. Vortices in the cone state are formed under the action of a constant external field perpendicular to the easy plane of the magnet. As a rule, the spectrum for such vortices is not a standard band spectrum and forms a set such that a forbidden energy value can be found in any small neighborhood of an allowed value, and vice versa. The possibility of an oscillatory motion of a vortex under the action of a constant external force is indicated (analog of Bloch oscillations of electrons in crystals). Possible realization of these effects in other ordered media with vortices is considered.