  Super-harmonic injection locking of single nano-contact (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 magneto-electronic measurements. The
large frequency tunability of the STVO with respect to $f_{0}$ allowed the
device to be locked to multiple sub-harmonics of the microwave frequency
$f_{RF}$, or to the same sub-harmonic over a wide range of $f_{RF}$ 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 non-linear 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
core trajectories within the same device. Super-harmonic 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
synchronisation to be achieved in multi-oscillator networks by tuning the
spatial character of the dynamics within shared magnetic layers.
