Gyrotropic Modes of Ferromagnetic Resonance in System of Two Exchange-Coupled Magnetic Vortices

We report the results of micromagnetic simulations of low-frequency resonances associated with gyrotropic motion of exchange-coupled magnetic vortices in a system of two overlapping ferromagnetic disks. The dependences of the resonance frequencies on the method of excitation, the mutual direction of the vortex cores and on the external magnetizing magnetic field are analyzed. The modeling demonstrates that the most effective influence on the change in the resonance frequency is realized when the system is magnetized in the sample plane in the direction perpendicular to the line connecting the disks centers, opposite to the direction of magnetization in the area of disks overlapping. It is shown that for the state with opposite core polarity there are two resonant modes in which the cores and consequently the in-plane dipole moments induced in vortex shells are rotated in the opposite directions. On the contrary, in the resonant mode of the state with the same core polarity, the cores are rotated in the same directions and induced dipole moments are rotated in phase. The possibilities of using the overlapping disks system for the synchronization of vortex nano-oscillators are discussed.