H. Kuratsuji et H. Yabu, THE EQUATION-OF-MOTION FOR A SPIN VORTEX AND GEOMETRIC FORCE, Journal of physics. A, mathematical and general, 29(20), 1996, pp. 6505-6513
The Hamiltonian equation of motion is studied for a vortex occurring i
n a two-dimensional Heisenberg ferromagnet of anisotropic type by star
ting with the effective action for the spin field formulated by the Bl
och (or spin) coherent state. The resultant equation shows the existen
ce of a geometric force that is analogous to the so-called Magnus forc
e in superfluids. This specific force plays a significant role in the
quantum dynamics of a single vortex, for example the determination of
the bound state of the vortex trapped by a pinning force arising from
the interaction of the vortex with an impurity.