THE EQUATION-OF-MOTION FOR A SPIN VORTEX AND GEOMETRIC FORCE

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.