A proposal for leaky integrate-and-fire neurons by domain walls in antiferromagnetic insulators

Abstract

Brain-inspired neuromorphic computing is a promising path towards next generation analogue computers that are fundamentally different compared to the conventional von Neumann architecture. One model for neuromorphic computing that can mimic the human brain behavior are spiking neural networks (SNNs), of which one of the most successful is the leaky integrate-and-fire (LIF) model. Since conventional complementary metal-oxide-semiconductor (CMOS) devices are not meant for modelling neural networks and are energy inefficient in network applications, recently the focus shifted towards spintronic-based neural networks. In this work, using the advantage of antiferromagnetic insulators, we propose a non-volatile magnonic neuron that could be the building block of a LIF spiking neuronal network. In our proposal, an antiferromagnetic domain wall in the presence of a magnetic anisotropy gradient mimics a biological neuron with leaky, integrating, and firing properties. This single neuron is controlled by polarized antiferromagnetic magnons, activated by either a magnetic field pulse or a spin transfer torque mechanism, and has properties similar to biological neurons, namely latency, refraction, bursting and inhibition. We argue that this proposed single neuron, based on antiferromagnetic domain walls, is faster and has more functionalities compared to previously proposed neurons based on ferromagnetic systems.

Figure 1

Schematic of a spiking neural network. A LIF neuron $\mathrm{\Xi }$ receives input spikes from several presynaptic neurons. In the present work, we model $\mathrm{\Xi }$ by an AFM DW. The spike trains are multiplied by weights $w_i$ and merged before they get sent into $\mathrm{\Xi }$. A non-linear function determines whether the neuron should fire as a consequence of stimuli from its synapses.

Figure 2

Leaky integrate-and-fire circuit. A capacitor, C, and a resistor, R, are connected in parallel. The voltage over the capacitor u(t) integrates the current input, while it leaks to ground. When u(t) reaches a threshold value, a switch controlling the input wire is flipped, stopping new currents into the system for a refractory period. During the refractory period charge is completely depleted from the capacitor.

Figure 3

Schematic setup of the AFM-based single neuron proposal in the IP geometry. There are two domains in the AFM stripe, represented by the Néel vectors in blue and red. The two domains are connected by a DW texture in turquoise. On top of the AFM stripe, an injector is placed at the left side as a source of magnons and two detectors are placed right and left of the equilibrium position of the DW, the latter shown by ${\mathcal{X}}_0$.

Figure 4

Snapshots of all-magnonic DW motion through an AFM-based neuron in the IP configuration with magnetic field pulse excitation. In (a), the DW is at equilibrium position ${\mathcal{X}}_{\mathit{DW}}={\mathcal{X}}_0$, set by the magnetic anisotropy profile. Once a left-handed magnetic field pulse with strength $H_0$ is turned on, left-handed AFM magnons are excited at the injector. As a result, the DW moves towards the magnon source, panels (b) and (c). After switching the magnetic field off, the DW relaxes back to its equilibrium position, panels (d) and (e). The illustrated movement corresponds to the first excitation stage followed by the first relaxation stage in our protocol. We set $D=150\mathrm{\mu }\text{J}{\text{m}}^{-2}$ in this case.

Figure 5

DMI-dependent all-magnonic AFM DW movement. Left- and right-handed AFM magnons are excited with polarized magnetic field pulses, see the orange area. In the IP geometry (a) the direction and amplitude of the DW motion can be tuned by DMI strength and the chirality of the excited magnons. However, the direction of AFM DW motion in the OOP geometry (b) is independent of the magnon chirality. The strength of DMI is encoded by colors, from lowest $D=0$ in blue to highest in yellow, see the insets. In the insets, the maximal displacements of AFM DWs, ${\mathcal{X}}_{\text{DW}}^{\text{max}}$, are shown for each excitation stage (crosses for the first and points for the second excitation stage).

Figure 6

Leaky integrate-and-fire behavior of the all-magnonic AFM DW motion in the IP geometry with a DMI strength of $D=150\mathrm{\mu }\text{J}{\text{m}}^{-2}$. (a) The integration of three separate pulses, denoted by orange areas, provides enough energy to pull the DW away from its equilibrium position, denoted by the gray dashed line, to the detector, denoted by the blue area. This is the realization of the integrate-and-fire characteristic of the LIF model. During the inter-pulse intervals, the DW undergoes relaxation towards its equilibrium position, thereby exhibiting the leaky property. After the last pulse, the AFM DW relaxes back to the equilibrium position. (b) An impulse-like signal is fired when the DW passes the detector at t=25 ps. This spike, generated when the synaptic inputs to the neuron reach a certain threshold value, represents the neuron action potential.

Figure 7

Electrical control of the AFM DW motion in the IP geometry. The orange areas depict the injector region that excites magnons via spin transfer torque pulses with two opposite spin torques, indicated by the arrow directions, at a finite temperature. Each trajectory is computed from an ensemble average over 60 realizations, and the uncertainty environment represents the standard deviation of the ensemble average. The equilibrium position of DW at ${\mathcal{X}}_0$ is denoted by a horizontal gray dashed line.

Figure 8

Bursting behavior in the IP geometry with a DMI strength of $D=150\mathrm{\mu }\text{J}{\text{m}}^{-2}$. (a) A longer magnon excitation, here by a magnetic field, provides enough energy to pull the AFM-DW away from its equilibrium position, denoted by the gray dashed line, and passes the detector, denoted by the blue area. (b) An impulse-like signal with opposite polarity is fired each time the AFM-DW passes the detector in opposite directions.

Figure 9

Demonstration of inhibition in the IP geometry: Integration over excitation pulses with different helicities demonstrates the possibility of modelling inhibition. Compare to Fig. 6a where pulses with same chirality are integrated and lead to a spiking event.