  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. We perform
micromagnetic simulations of such oscillators realized in the nano-constriction
geometry and show that the easy-plane spiking dynamics is preserved in an
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.
