Current-driven gyrotropic mode of a magnetic vortex as a nonisochronous auto-oscillator

It is shown that a stable gyrotropic motion of a vortex core in a vortex-state free layer of a magnetic nanopillar driven by a spin-polarized current can be quantitatively described in the framework of a standard model of a nonisochronous auto-oscillator. The nonisochronous parameters of a vortex auto-oscillator, determining its nonautonomous dynamics and synchronization properties, can be found from the experimentally measured linewidths of higher harmonics of the generated microwave signal. The presented results demonstrate that vortex spin-torque nano-oscillators, having low generation linewidth and relatively high output power, can be strongly nonisochronous, and, therefore, could be prospective candidates for mutual synchronization in large oscillator arrays. At the same time, the optimization of their working parameters can be done using the traditional auto-oscillator theory.