COLLECTIVE-VARIABLE APPROACH TO THE DYNAMICS OF NONLINEAR MAGNETIC EXCITATIONS WITH APPLICATION TO VORTICES

We propose a collective-variable ansatz for a system of N extended, bu t finite, nonlinear excitations in magnetic systems. In contrast to ea rlier approaches, where the interactions between the different excitat ions have been treated only through an external force term, we explici tly consider a dependence of the microscopic spin field on all the coo rdinates and velocities of the localized objects. This leads to N coup led equations of motion with parameters (mass and gyro tensors) which explicitly depend on the mutual distances of the excitations. We apply this ansatz to vortices in two-dimensional Heisenberg ferromagnets wi th weak easy-plane anisotropy. For vortex pairs we find either rotatio nal or translational motion, with an additional cyclotronlike oscillat ion on top of the main trajectories. Due to the interactions between t he two vortices we obtain two different eigenvalues of the mass and gy ro tensors with values depending on the distance between the vortices; their vorticities, and the sign of their out-of-plane structures. In contrast to the single-vortex mass, which depends logarithmically on t he system size L, we find two-vortex masses, which are independent of L, but depend on their mutual distance. These predictions are in good qualitative agreement with numerical simulations of the complete spin systems. However, since these simulations are performed at zero temper ature, where the vortex pairs extend throughout the whole system, we o bserve a strong influence of the boundaries on the absolute values of the masses.