Integer, Fractional, and Sideband Injection Locking of a Spintronic Feedback Nano-Oscillator to a Microwave Signal

In this article we demonstrate the injection locking of recently demonstrated spintronic feedback nano oscillator to microwave magnetic fields at integers as well fractional multiples of its auto oscillation frequency. Feedback oscillators have delay as a new degree of freedom which is absent for spin-transfer torque based oscillators, which gives rise to side peaks along with a main peak. We show that it is also possible to lock the oscillator on its side band peaks, which opens a new avenue to phase locked oscillators with large frequency differences. We observe that for low driving fields, side band locking improves the quality factor of the main peak, whereas for higher driving fields the main peak is suppressed. Further, measurements at two field angles provide some insight into the role of symmetry of oscillation orbit in determining the fractional locking.