  Injection of a radio frequency (RF) current was used to phase lock the SHNO
to the TRSKM. The out of plane magnetization was detected by means of the polar
magneto optical Kerr effect (MOKE). However, longitudinal MOKE images were
dominated by an artifact arising from the edges of the Au NCs. Time resolved
imaging revealed the simultaneous excitation of a non-linear `bullet' mode at
the centre of the device, once the DC current exceeded a threshold value, and
ferromagnetic resonance (FMR) induced by the RF current. However, the FMR
response observed for sub-critical DC current values exhibits an amplitude
minimum at the centre, which is attributed to spreading of the RF spin current
due to the reactance of the device structure. This FMR response can be
subtracted to yield images of the bullet mode. As the DC current is increased
above threshold, the bullet mode appears to increase in size, suggesting
increased translational motion. The reduced spatial overlap of the bullet and
FMR modes, and this putative translational motion, may impede the injection
locking and contribute to the reduced locking range observed within NC-SHNO
devices. This illustrates a more general need to control the geometry of an
injection-locked oscillator so that the autonomous dynamics of the oscillator
exhibit strong spatial overlap with those resulting from the injected signal.
