Title: Reconfigurable neural spiking in bias field-free spin Hall nano oscillator

Abstract: In this study, we theoretically investigate neuron-like spiking dynamics in an elliptic ferromagnet/heavy metal bilayer-based spin Hall nano oscillator (SHNO) in bias field-free condition, much suitable for practical realization of brain inspired computing schemes. We demonstrate regular periodic spiking with tunable frequency as well as the leaky-integrate-and-fire (LIF) behavior in a single SHNO by manipulating the pulse features of input current. The frequency of regular periodic spiking is tunable in a range of 0.5 GHz to 0.96 GHz (460 MHz bandwidth) through adjusting the magnitude of constant input dc current density. We further demonstrate the reconfigurability of spiking dynamics in response to a time varying input accomplished by continuously increasing the input current density as a linear function of time. Macrospin theory and micromagnetic simulation provide insights into the origin of bias field-free auto-oscillation and the spiking phenomena in our SHNO. In addition, we discuss how the shape anisotropy of the elliptic ferromagnet influence the bias field-free auto oscillation characteristics, including threshold current, frequency and transition from in-plane to out-of-plane precession. The SHNO operates below $10^{12} A/m^2$ input current density and exhibits a large auto-oscillation amplitude, ensuring high output power. We show that the threshold current density can be reduced by decreasing the ellipticity of the ferromagnet layer as well as enhancing the perpendicular magnetic anisotropy. These findings highlight the potential of bias field-free elliptic SHNO in designing power-efficient spiking neuron-based neuromorphic hardware.