Ampere-Oersted field splitting of the nonlinear spin-torque vortex oscillator dynamics

We investigate the impact of the DC current-induced Ampère-Oersted field on the dynamics of a vortex based spin-torque nano-oscillator. In this study we compare micromagnetic simulations performed using mumax[Formula: see text] and our analytical model based on the Thiele equation approach. The latter is improved by adding two important corrections to the Thiele equation approach. The first is related to the magneto-static contribution and depends on the aspect ratio of the magnetic dot. The second is a full analytical description of the Ampère-Oersted field contribution. The model describes quantitatively the simulation results in the resonant regime as well as the impact of the Ampère-Oersted field. Depending on the relative orientation between the vortex in-plane curling magnetisation (chirality) and the Ampère-Oersted field a strong splitting phenomenon appears in the fundamental properties (frequency and vortex core position) of the nano-oscillator. Thus, we show that the Ampère-Oersted field should not be neglected as it has a high impact on the spin-torque vortex oscillator dynamics.