H. Kuratsuji et H. Yabu, FORCE ON A VORTEX IN FERROMAGNET MODEL AND THE PROPERTIES OF VORTEX CONFIGURATIONS, Journal of physics. A, mathematical and general, 31(2), 1998, pp. 61-65
The general form is given for a force acting on a vortex in the ferrom
agnet model without any assumption for the profile of the vortex. The
strength of the force is shown to be written in terms of the Mermin-Ho
topological invariant for the vortex in superfluid He3-A. The discuss
ions are given on the point of how the resulting formula can be interp
reted as the mapping degree for the vortex configuration. These result
s are extended to the system described by the generalized spin.