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.

Figure 1

Sketch of the measurement setup and a sample image of a nanopillar square element (obtained using scanning electron microscopy). The image is the same as the one shown in the inset of Fig. 1 of Ref. [19].

Figure 2

Dependence of the generation frequency (a) and the linewidth (b) of the first (fundamental) harmonic of the current-induced gyrotropic mode on the bias current.

Figure 3

Power spectrum of the gyrotropic auto-oscillations demonstrating seven frequency harmonics. Insets show closeup views of the generation spectrum in the vicinity of the first three harmonics of the fundamental auto-oscillation frequency. Solid red lines in the insets are Lorentzian fits to the experimental data.

Figure 4

Dependence of the harmonic linewidth $\Delta f_n$ on the harmonic number $n$. Dots, experimental data; solid line, fit using Eqs. (13) and (14).