Harnessing Stochastic Domain Wall Pinning for Machine Learning

Abstract

Magnetic materials are already widely used for long-term data storage, but ongoing work seeks to use them as both working memory and computing architectures. Particularly, devices based on magnetic domain walls (DWs) can perform logic operations and can readily store information [1]. However, the stochasticity of DW pinning limits the feasibility of creating technologically viable devices. Here, we demonstrate how stochasticity can be changed from a technologically inhibitive behaviour into an integral property of machine learning algorithms for specialised neuromorphic devices. We first present experimental measurements that demonstrate the tunability of stochastic processes by applying external stimuli. Focused magneto-optic Kerr effect measurements were used to probe the pinning of DWs at notch-shaped defect sites in 400 nm wide Permalloy nanowires (Fig. 1). DWs were injected into the nanowires and propagated to the defect sites using a field parallel to the nanowire (Hx). The probability of the DWs being pinned at the defect sites was found to depend sigmoidally on the magnitude of a field transverse to the nanowires (Hy). The stochastic behaviour of the nanowire were then integrated into machine learning models. We have developed feedforward neural networks with the nanowires acted as binary stochastic synapses (BSS) that can be sampled by repeating the network. It is found that for a single cycle of the network it can be trained to recognise handwritten digits with an error rate of 19%. Repeated sampling of the network decreases the error rate to 9% for 128 cycles - close to mean field performance (Fig. 2). Adding a hidden layer improves performance with extra pathways for the stochastic behaviour to be averaged over. Our work illustrates how the stochasticity of DW devices can be harnessed to provide tunable bespoke hardware for machine learning tasks.