Dynamics of coupled magnetic vortices in trilayer conducting nanocylinder

Solving numerically the generalized Landau–Lifshitz equation, we have carried out the micromagnetic investigation of the dynamics of two dipole-coupled magnetic vortices in a trilayer nanocolumn under the action of the external magnetic field directed perpendicular to the sample plane and spin-polarized electric field. The possible existence of different regimes of vortex motion, depending on the polarized current, is demonstrated. The current dependence of the oscillation frequency for the case of stationary dynamics of coupled vortices with the same frequency has been established. The possibility of controlling the frequency of the stationary vortex motion and tuning the control current amplitude by the external magnetic field is shown. Using the analytical method for simplified description of the dynamics of coupled vortices, the current and magnetic-field dependences of the frequency have been obtained, which are qualitatively consistent with the numerical data.