Title: Observation of spin-Hall induced auto-oscillation in Pt/lithium aluminum ferrite bilayers via inverse spin-Hall effect.

Ferrimagnetic insulators with ultra-low damping are of great interest for their potential applications in efficient spin wave devices. This study demonstrates Pt nanowire spin-Hall current induced excitation of auto-oscillation states in unpatterned novel ultra-low damping ferrimagnetic insulator Li0.5Al0.5Fe2O4 (LFO) thin films. Auto-oscillations occur for only one current polarity, indicating that these states are not primarily induced by the spin Seebeck effect (i.e., temperature gradients). In contrast to previous approaches, the high-frequency (GHz) power spectral density (PSD) electrical signals are associated with the inverse spin-Hall effect at the Pt/LFO interface. A linear dependence of the PSD dispersion curves on the magnetic field is observed with a current onset threshold related to the intrinsic magnetic anisotropy of LFO. The threshold current, however, is higher than expected from the damping of LFO, which may be related to the spin-pumping-induced additional dissipation. In addition, ferromagnetic resonance (FMR) and spin-torque FMR are conducted on LFO thin films and nano-oscillators to determine their characteristics. Micromagnetic modeling shows good agreement with the PSD dispersion curves, showing only one dominant mode. This behavior in contrast with the two modes observed in transition metal nanowire-type spin-Hall nano-oscillators. The continuous thin film ferrimagnetic insulator layer thus provides a means of coupling neighboring oscillators of interest for a variety of applications, including neuromorphic computing.