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We experimentally study the auto-oscillating spin-wave modes inNiFe/$\beta-$W constriction-based spin Hall nano-oscillators as a function ofbias current, in-plane applied field strength, and azimuthal field angle, inthe low-field range of 40-80 mT. We observe two different spin-wave modes: i) alinear-like mode confined to the minima of the internal field near the edges ofthe nanoconstriction, with weak frequency dependencies on the bias current andthe applied field angle, and ii) a second, lower frequency mode that hassignificantly higher threshold current and stronger frequency dependencies onboth bias current and the external field angle. Our micromagnetic modelingqualitatively reproduces the experimental data and reveals that the second modeis a spin-wave bullet and that the SHNO mode hops between the two modes,resulting in a substantial increase in linewidths. In contrast to thelinear-like mode, the bullet is localized in the middle of the constriction andshrinks with increasing bias current. Utilizing intrinsic frequency doubling atzero field angle we can reach frequencies above 9 GHz in fields as low as 40mT, which is important for the development of low-field spintronic oscillatorswith applications in microwave signal generation and neuromorphic computing.

Mapping out the spin-wave modes of constriction-based spin Hall nano-oscillators in weak in-plane fields