Spin waves (SWs), the collective precessional motion of spins in a magnetic system, have been proposed as a promising alternative system with low-power consumption for encoding information. Spin Hall nano-oscillator (SHNO), a new-type spintronic nano-device, can electrically excite and control spin waves in both nanoscale magnetic metals and insulators with low damping by the spin current due to spin Hall effect. Here, we will review recent progress about spin-wave excitation and experimental parameters dependent spectrum in SHNOs. The nanogap SHNOs based on in-plane magnetization Py/Pt exhibits a nonlinear self-localized bullet soliton localized at the center of the gap between the electrodes and a secondary high-frequency mode which coexists with the primary bullet mode at higher currents. While in the nanogap SHNOs with strong perpendicular magnetic anisotropy (PMA), besides both nonlinear bullet soliton and propagating spin-wave mode are achieved and controlled by varying the external magnetic field and current, the magnetic bubble skyrmion mode also can be excited at a low in-plane magnetic field. These SW modes show thermal-induced mode hopping behavior at high temperature due to the coupling between modes mediated by thermal-magnon-mediated scattering. Moreover, thanks to PMA-induced effective field, a single coherent mode also can be achieved without applying an external magnetic field. The strong nonlinear effect of spin-waves makes SHNOs easy to achieve synchronization with external microwave signals or mutual synchronization between multiple oscillators with improving the coherence and power of oscillation modes significantly. Spin-waves in SHNOs with an external free magnetic layer have a wide range of applications from as a nanoscale signal source of low-power consumption magnonic devices to spin-based neuromorphic computing systems in the field of artificial intelligence.
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