Superharmonic injection locking of nanocontact spin-torque vortex oscillators

Superharmonic injection locking of single nanocontact (NC) spin-torque vortex oscillators (STVOs) subject to a small microwave current has been explored. Frequency locking was observed up to the fourth harmonic of the STVO fundamental frequency ${f}₀$ in microwave magnetoelectronic measurements. The large frequency tunability of the STVO with respect to ${f}₀$ allowed the device to be locked to multiple subharmonics of the microwave frequency ${f}_{\mathrm{RF}}$, or to the same subharmonic over a wide range of ${f}_{\mathrm{RF}}$ by tuning the dc current. In general, analysis of the locking range, linewidth, and amplitude showed that the locking efficiency decreased as the harmonic number increased, as expected for harmonic synchronization of a nonlinear oscillator. Time-resolved scanning Kerr microscopy (TRSKM) revealed significant differences in the spatial character of the magnetization dynamics of states locked to the fundamental and harmonic frequencies, suggesting significant differences in the vortex core trajectories within the same device. Superharmonic injection locking of a NC-STVO may open up possibilities for devices such as nanoscale frequency dividers, while differences in the core trajectory may allow mutual synchronization to be achieved in multioscillator networks by tuning the spatial character of the dynamics within shared magnetic layers.