Antiferromagnet-Based Neuromorphics Using Dynamics of Topological Charges

We propose a spintronics-based hardware implementation of neuromorphic computing, specifically, the spiking neural network, using topological winding textures in one-dimensional antiferromagnets. The consistency of such a network is emphasized in light of the conservation of topological charges, and the natural spatiotemporal interconversions of magnetic winding. We discuss the realization of the leaky integrate-and-fire behavior of neurons and the spike-timing-dependent plasticity of synapses. Our proposal opens the possibility for an all-spin neuromorphic platform based on antiferromagnetic insulators.

Figure 1

Schematics of neurons and a synapse in an SNN based on dynamics of topological charges in biaxial antiferromagnets. (a) A neuron is a single-domain magnet with angular order parameter $\phi$. The neuron fires when $\phi$ rotates (counterclockwise) by $\pi$, creating a topological charge with $\zeta =+1$. An axon branches out into a feedback arm and a forward one, each further fans out into several telodendrons. Arrows indicate directions of signal flow. A synapse is a nanostrip holding a winding texture, a thermodynamic system (with temperature $T$ and chemical potential $\mu$) of interacting topological charges, their net density $w$ as the synaptic weight. An external source of winding with constant chemical potential ${\mu }_0$ is used to increase the synaptic weight $w$ upon causal firings. Sketches of $\cos \varphi (x)$ inside the synapse and the external source indicate the low and high density of topological charges. The order parameters ${\varphi }_1$ and ${\varphi }_2$ at the two ends of the synapse experience tilted washboard potentials. (b) A weak coupling between the neuron and the dendrite mediated by a metal spacer. A topological charge arrives from the dendrite and pumps a spin current $I_s$ into the normal metal, exerting torques of opposite signs on the two interfaces. (c) The learning function (the change in the synaptic weight $\mathrm{\Delta }w$ versus the relative arrival time $\mathrm{\Delta }t=t_{\mathrm{post}}-t_{\mathrm{pre}}$ of the post- and presynaptic signals) of a possible scheme of STDP of the synapse. Causal firings strengthen the synaptic connection.

Figure 2

Leaky integrate-and-fire functionality of the neuron. (a) The washboard potential. The angular order parameter $\phi$ of the neuron and its time derivative ${\partial }_t\phi$ are analogous to the position and speed of a particle. Inset: The tilted washboard potential where local minima become unstable. (b) The firing and nonfiring diagram depending on the input rate $\omega$ and amplitude ${\nu }_0$ of the incoming train of angular momentum kicks. Numerics are done with parameters ${\omega }_0=10\mathrm{GHz}$ and $\eta =5$. (c) The time evolution of the order parameter of the neuron $\phi (t)$ simulated for samples marked in the diagram. In each simulation, 20 pulses are sent to the neuron until it fires.

Figure 3

The nonlinear dependence of the chemical potential $\mu$ on the synaptic weight $w$, calculated for the metastable ground-state textures of the Hamiltonian (2), which are the solutions to the static sine-Gordon equation [52]. Inset: the magnetic textures and their $\cos \varphi (x)$ for two values of $w$. The texture becomes closer to a uniform spiral as $w$ approaches 1. The asymptote has the analytical expression $\mu =\sqrt{\mathcal{A}\mathcal{K}}{\pi }^{2}w$.