On the dispersion relation of kink-type solitons in one-dimensional ferromagnets

Abstract

The nonlinear classical and quantum dynamics of topological solitons (kinks) in a spin chain with appreciable biaxial anisotropy is investigated. Analytical calculations and numerical simulations are carried out for a discrete model with classical spins, and the results are used for analysis of the quantum properties of a kink in the semiclassical approximation. The analysis is based primarily on the lattice pinning potential. The pinning potential is largely determined by the microscopic source of the anisotropy: it is absent for purely exchange anisotropy, and it can be appreciable only for purely single-ion anisotropy. It is shown that under the influence of an external driving magnetic field a kink undergoes Bloch oscillations. The quantum spectrum of the kink consists of a finite number of nonoverlapping bands, equal to S for integer atomic spin S and to 2S for half-integer spin. Various quantum tunneling effects are investigated, including the tunneling transition from one position in the lattice to another and the tunneling change of the topological charge of the kink.