Spin Hall nano oscillator (SHNO), a new type spintronic nano-device, can generate microwave signal
and excite coherent spin waves due to spin current-driven magnetization precession and have
strong potential for applications from data storage,rf communication, microwave generation to
neuromorphic computing. In this review, we focus on the complex nonlinear dynamic characteristics
of spin-wave modes generated by SHNOs in the various ferromagnetic/nonmagnetic (FM/NM)
bilayer systems with an extended free layer. Based on the abundantly previous experimental results
obtained by combining microwave spectroscopy and micro-focused Brillouin light scattering
techniques, as well as micromagnetic simulation, we detailedly describe and summarize the experimental
parameters dependent magnetic dynamics of SHNOs with different device configurations
and magnetic materials, such as in-plane nanogap-type, nanoconstriction-type, nanowire-type,
vertical nanocontact-type SHNOs with in-plane or out-of-plane magnetization. Finally, we also
discuss mutual synchronization of SHNO arrays and the potential applications in magnon-based
logic devices with ultralow energy consumption and spin-based artificial neural network for neuromorphic
computing in the field of artificial intelligence.