Injection Locking of Linearlike and Soliton Spin-Wave Modes in Nanoconstriction Spin Hall Nano-oscillators

We study injection locking of two different spin wave (SW) modes (a field-localized linearlike interior mode and a self-localized SW bullet soliton) in a single nanoconstriction-based spin Hall nano-oscillator. Mode selection is achieved by varying the oblique magnetic field angle and magnitude. The two modes show dramatically different responses to injection locking, in terms of locking bandwidth and linewidth and output power in the locked state. Extracting the locking range graphically from the experimental data yields apparent thresholds for the required injected power, with the bullet mode showing a larger threshold than the linearlike mode. By instead fitting the full detuning behavior using a model including thermal noise, the apparent threshold vanishes, while the very different locking behavior of the two modes can instead be ascribed to the order of magnitude difference in their mode volumes.