Easy-plane spin Hall nano-oscillators as spiking neurons for neuromorphic computing

We show analytically using a macrospin approximation that easy-plane spin Hall nano-oscillators excited by a spin current polarized perpendicularly to the easy plane have phase dynamics analogous to that of Josephson junctions. Similarly to Josephson junctions, they can reproduce the spiking behavior of biological neurons that is appropriate for neuromorphic computing. To take advantage of typical spin-orbit torques, we use a nanoconstriction geometry, in which the magnetostatic interaction and magnetocrystalline anisotropy are tuned to create an easy plane that includes the interface normal direction. We perform micromagnetic simulations of such oscillators realized in this geometry and show that the easy-plane spiking dynamics is preserved in this experimentally feasible architecture. Finally we simulate two elementary neural network blocks that implement operations essential for neuromorphic computing. First, we show that output spikes energies from two neurons can be summed and injected into a following layer neuron and second, we demonstrate that outputs can be multiplied by synaptic weights implemented by locally modifying the anisotropy.