Two-dimensional topological solitons: Canonical Hamilton dynamics and semiclassical description

The dynamics of two-dimensional topological magnetic solitons is discussed and compared with that of other topological solitons known in two-dimensional Josephson junctions. The origins of the soliton effective mass are analyzed for various magnetic models. For the general equations governing the coordinates of these magnetic solitons, with the inertial term added to the standard purely gyroscopic Thiele equation, canonical pairs of Hamiltonian variables are constructed, providing a straightforward way for the semiclassical quantization of this dynamics. One pair of these variables corresponds exactly to the guiding-center coordinates of the soliton; this motion is expected to be slow. For free soliton motion, the dynamics of the second pair resemble the standard Larmor precession of a charged particle. The effects of the mutual influence of these two degrees of freedom are estimated for a general form of the potential forces acting on the soliton. Within a simple approximation based on the Thiele equation, inertial effects in the soliton motion in long magnetic strips and the appearance of a Hofstadter butterfly-type fractal structure in the soliton spectrum of real spin-lattice systems are found.