Magnon modes and magnon-vortex scattering in two-dimensional easy-plane   ferromagnets
  We calculate the magnon modes in the presence of a vortex in a circular system, combining analytical calculations in the continuum limit with a numerical diagonalization of the discrete system. The magnon modes are expressed by the S-matrix for magnon-vortex scattering, as a function of the parameters and the size of the system and for different boundary conditions. Certain quasi-local translational modes are identified with the frequencies which appear in the trajectory X(t) of the vortex center in recent Molecular Dynamics simulations of the full many-spin model. Using these quasi-local modes we calculate the two parameters of a 3rd-order quation of motion for X(t). This equation was recently derived by a collective variable theory and describes very well the trajectories observed in the simulations. Both parameters, the vortex mass and a factor on the third time derivative of X(t), depend strongly on the boundary conditions. 
B. A. Ivanov (1), H. J. Schnitzer (2), F. G. Mertens(2), G. M.   Wysin(3) ((1)Ukraine Academy of Sciences, (2)University of ...