Gyration eigenfrequencies of vertically coupled vortices in layered magnetic disks

The dynamic properties of vertically coupled vortices in two magnetic nanodisks were studied using numerical simulations and analytical calculations. If the core polarizations of the two vortices are parallel, there exist two distinct normal modes with two distinct eigenfrequencies corresponding to the apparent complex motions of two vortices. Conversely, only a degenerate mode with a single eigenfrequency exists when the cores have opposite polarization. We show that the gyration eigenfrequencies can be tuned by changing the coupling strength, i.e., the separation between the disks. The dependence of the normal modes and the eigenfrequencies on the relative vortex-state configuration can be well understood based on the analytic model.