From Stochasticity to Functionality: Harnessing Magnetic Domain Walls for Probabilistic and Neuromorphic Computing

Abstract

Domain walls (DWs) in magnetic nanowires are a topic of intense interest due to proposals to use them as data carriers in non-volatile logic and memory devices. However, despite their apparent technological potential such devices are challenging to realise, in part because DWs pinning and propagation is highly stochastic, making digital devices unreliable [1]. While materials engineering approaches can be used to supress stochasticity [2], it is also interesting to consider whether alternative computer paradigms could prove more resistant to, or even benefit from, stochasticity. In this talk we will present three examples of how embracing DW stochasticity as a functional, rather than technologically inhibiting feature can facilitate novel computational devices.Figure 1(a) presents results that illustrate typical stochastic DW behaviours in a 400 nm wide Ni80Fe20 nanowire device, as characterised by focused magneto-optic Kerr effect (FMOKE) magnetometry. DWs were injected from the pad to a patterned defect in the nanowire’s middle and the distributions of magnetic fields required to propagate them through the defect characterised. The depinning field histogram shows both fractional pinning probabilities and multimode depinning field distributions, both characteristic features of stochasticity induced by complex DW dynamics [3]. However, while individual reversals of such a device are highly stochastic, average properties are well-defined, and more importantly, highly tuneable. Figure 1(b) illustrates how applying modest magnetic fields orthogonal to a similar nanowire/defect combination allows DWs pinning probabilities to be tuned between 0 and 1. Thus, stochastic pinning can be used to create random bit-streams with tuneable average values.In our first example of the utility of these effects we use stochastic DW pinning to realise the stochastic computing paradigm in DW logic networks. In stochastic computing, floating point numbers are encoded in the average value of random binary bit-streams, and single conventional logic gates perform complex mathematical operations that would usually require extended logic networks to perform. For example, an AND gate performs a multiplication operation. Figure 2(a) presents the results of FMOKE magnetometry, illustrating how the output of a DW AND gate with stochastic input produces output bitstreams consistent with those expected.In our second example we use the stochastic pinning of DWs to facilitate two neuromorphic computing approaches: a feed-forward neural network and a Boltzman machine. In the feed-forward network, nanowires act as binary stochastic synapses, with the probability of DW propagation taking the role of a synaptic weight. Simulations of network behaviour allow us to demonstrate that such a device can perform machine learning tasks including written digit recognition. In the Boltzman machine, where stochasticity is used to sample a defined, or trained, probability distribution, the nanowires take the role of stochastic neurons. We apply this approach to an integer factorisation problem where network is defined so that the binary representation of the integer factors are the most probable states for the neurons.In our final example, we show how DWs driven by rotating magnetic fields within an interconnected nanoring array, can be used to perform reservoir computing [4]. We characterise a ring array’s behaviour using a combination of MOKE, polarised neutron reflectivity and photoemission electron microscopy, and show how emergent behaviour arises from stochastic interactions between DWs at the array’s junctions (Figure 2(b)). Using the magnitude of the rotating applied field as an input we then demonstrate how this allows the array to be used as a reservoir and perform a range of time series analysis tasks including speech recognition and chaotic series prediction. **