Dynamics of coupled vortices in layered magnetic nanodots

The spin dynamics are calculated for a model system consisting of two ferromagnetic (F) cylindrical dots, each with a magnetic vortex ground state, are separated by a nonmagnetic spacer (N). The effects of interlayer magnetostatic interactions on the vortex dynamics were explored by applying the equations of motion for the vortex core positions. For trilayer F∕N∕F dots with opposite chiralities and the same core polarizations two eigenmodes are predicted. One mode is in the sub-GHz range for submicron dot diameters and corresponds to quasicircular rotation of the cores about the dot center. A second mode in the MHz range corresponds to a small amplitude rotation of the mean core position.