DYNAMICS OF INTERACTING MAGNETIC VORTICES IN A MODEL LANDAU-LIFSHITZ EQUATION

Magnetic bubbles are modeled within a strictly two-dimensional Landau- Lifshitz equation in which the bubble radius is stabilized by a Skyrme -like term together with a suitable uniaxial anisotropy and the nonloc al magnetostatic field is replaced by a local one. The model admits an exact static solution with unit winding number which will be referred to as the fundamental magnetic vortex. We then study numerically the dynamics of a system of two fundamental vortices and show that they or bit around each other on trajectories that exhibit roughly a triangula r pattern. In contrast, a vortex-antivortex pair is shown to move in a direction perpendicular to the line connecting the vortex and the ant ivortex. A very useful guide for understanding our numerical results i s provided by the unambiguous conservation laws of the Landau-Lifshitz equation constructed recently.