The low frequency dynamics of two coupled magnetic vortices oscillating in a pair of laterally patterned circular dots are calculated. The linearized Thiele equations of motion of the vortex core positions are applied to describe the dynamics. The main emphasis is put on the symmetry of the excited spin eigenmodes and the possibility to excite them by applying the variable driving magnetic fields in different directions. The importance of the high-order multipole terms in the interdot coupling integrals decomposition is underlined. Some recent experiments on the coupled magnetic vortex dynamics in patterned films are interpreted.
We investigate analytically and numerically nonlinear vortex spin torque oscillator dynamics in a circular magnetic nanodot induced by a spin-polarized current perpendicular to the dot plane. We use a generalized nonlinear Thiele equation including spin-torque term by Slonczewski for describing the nanosize vortex core transient and steady orbit motions and analyze nonlinear contributions to all forces in this equation. Blue shift of the nano-oscillator frequency increasing the current is explained by a combination of the exchange, magnetostatic, and Zeeman energy contributions to the frequency nonlinear coefficient. Applicability and limitations of the standard nonlinear nano-oscillator model are discussed.
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