Magnetic vortex dynamics in a 2D easy plane ferromagnet
  In this thesis, we consider the dynamics of vortices in the easy plane insulating ferromagnet in two dimensions. In addition to the quasiparticle excitations, here spin waves or magnons, this magnetic system admits a family of vortex solutions carrying two topological invariants, the winding number or vorticity, and the polarization. A vortex is approximately described as a particle moving about the system, endowed with an effective mass and acted upon by a variety of forces. Classically, the vortex has an inter-vortex potential energy giving a Coulomb-like force (attractive or repulsive depending on the relative vortex vorticity), and a gyrotropic force, behaving as a self-induced Lorentz force, whose direction depends on both topological indices. Expanding semiclassically about a many-vortex solution, the vortices are quantized by considering the scattered magnon states, giving a zero point energy correction and a many-vortex mass tensor. The vortices cannot be described as independent particles--that is, there are off-diagonal mass terms, such as 1/2 Mij vi vj, that are non-negligible. This thesis examines the full vortex dynamics in further detail by evaluating the Feynman-Vernon influence functional, which describes the evolution of the vortex density matrix after the magnon modes have been traced out. In addition to the set of forces already known, we find new damping forces acting both longitudinally and transversely to the vortex motion. The vortex motion within a collective cannot be entirely separated: there are damping forces acting on one vortex due to the motion of another. The effective damping forces have memory effects: they depend not only on the current motion of the vortex collection but also on the motion history. 
Lara Thompson