Artificial neural networks (ANNs) are powerful tools for data intensive classification and regression, but the memory wall in von Neumann architectures prevents efficient processing [1]. Though there are many candidates for devices and architectures to realize ANNs, there are no comprehensive solutions to implement hardware Bayesian NNs (BNNs). BNNs are much less susceptible to overfitting when available data is sparse or unreliable, accomplished by representing and learning the weights of the network as distributions instead of deterministic values [2]. We propose a novel spintronic synaptic cell design that can implement tunable distributions by taking advantage of the intrinsic stochasticity of magnetic materials. The design of the cell is composed of a noise and weight encoding element respectively (see Fig. 1). The noisy element is a circular in-plane magnetic tunnel junction (MTJ) that relies on thermal activation to output a random conductance within the range of its TMR. This TMR can then be controlled through several methods such as voltage-controlled magnetic anisotropy (VCMA) [3] or magneto-ionics [4]. Combined with a weight encoding conductance element like a domain wall-magnetic tunnel junction (DW-MTJ) artificial synapse [5,6], we propose a novel cell design that can represent the distributions necessary for inference in a hardware BNN. We demonstrate device functionality through Landau-Lifshitz-Gilbert and micromagnetics [7] models, model analog Bayesian inference in CrossSim [8] for regression (see Fig. 2) and classification to detect out-of-distribution data, and compare the systemâ€™s energy efficiency to CMOS implementations. These results propose a novel synapse implementation for accurate and efficient Bayesian inference, a foundational step toward hardware BNN accelerators. SNL is managed and operated by NTESS under DOE NNSA contract DE-NA0003525.

Hardware Aware Bayesian Variational Inference Using Magnetic Tunnel Junction Noise Distributions in Artificial Synapse Arrays

The processing of artificial neural networks (ANNs) is limited by the memory wall in von Neumann architectures, driving the need for hardware ANNs realized by neuromorphic devices [1]. Previously proposed multi-weight synaptic devices often suffer from a nonlinear and asymmetric update response, limiting their viability for supervised learning [2]. Domain wall-magnetic tunnel junction (DW-MTJ) devices driven by spin transfer torque (STT) and spin orbit torque (SOT) have shown promise in neuromorphic applications, realizing leaky integrate-and-fire neurons in simulation [3-8]. Simulations also show that DW-MTJs can implement synaptic spike-timing dependent plasticity [9]. A type of DW-MTJ with multiple MTJs was demonstrated experimentally [10], and we have recent results on experimental DW-MTJ synapses that are submitted separately for consideration in the conference. Most prior work on DW-MTJ synapses in ANNs do not consider thermal effects and process variation. We evaluate notched DW-MTJ designs shown in Fig. 1a and account for these effects using MuMax3 for device simulation and CrossSim for network simulation [11-13]. Figure 1b shows that excellent linearity, high symmetry, and low thermal noise are maintained at 300 K. High training accuracy was obtained on the Fashion-MNIST task, shown in Fig. 2 [14]. Notably, the greater stochasticity of SOT-driven synapses counters the discretizing effect of notches, boosting accuracy to near ideal. We also implemented short term potentiation for network pruning using shape anisotropy. These results propose a magnetic synapse with tunable plasticity, superior backpropagation performance, and fast updates, a foundational step toward ANNs with fully spintronic matrix operations. SNL is managed and operated by NTESS under DOE NNSA contract DE-NA0003525

![](https://assets.underline.io/uploads/markdown_image/1/image/a44eed1961abbd5be85c2b76d154f44f.jpg)

a) Device diagram b) Conductance G vs dG statistics of a DW-MTJ at 300 K for STT and SOT propagation. Heatmaps are generated from micromagnetic simulations. The CDF represents the probability that a given conductance update is less than the average dG.

![](https://assets.underline.io/uploads/markdown_image/1/image/8b8eb9cbd24d31e6dd1da9e5c0cf1410.jpg)

Validation accuracy of a two-layer perceptron of STT and SOT DW-MTJ synapses at 300 K assuming (a) continuous levels and (b) 32 notches and periodic carry.

Multifunctional Design of Domain Wall-Magnetic Tunnel Junction Artificial Synapses for Accurate Training of Neural Networks

Emulation of neurobiological information processing by artificial neural networks enables new frontiers in efficiency when performing data-intensive and real-time artificial intelligence tasks1,2. In this work, we experimentally demonstrate a multi-weight (MW) artificial synapse using a domain wall-magnetic tunnel junction (DW-MTJ) with a straight, notched geometry, depicted in Fig. 1(a). While previous simulations show that DW-MTJ synapses have the necessary characteristics for neuromorphic computing, experimental work has focused on binary DW-MTJs3, and no experimental works have closely studied the behavior of the MW-DW-MTJ synapse, in contrast with works studying multi-MTJ devices4. The heavy metal/ferromagnet/oxide trilayer stack3 is patterned into a DW track with a single, long output MTJ centered on top of the track. To achieve MW synaptic switching, five notches are fabricated on the track (n1-5). Fig. 1(b) shows the MTJ resistance (RMTJ) vs. out-of-plane magnetic field for a synapse with DW track width w = 350 nm, showing the maximum and minimum RMTJ. To study synaptic switching behaviors, voltage V is applied between the IN and CLK terminals (50 ns pulses of increasing amplitude, with step size 0.1 V) to move the DW from notch to notch via current driven via spin orbit torque. Fig. 2(a) shows RMTJ vs. V for 10 cycles, showing five resistances each corresponding to the DW in one of the notches. From the spacing dimensions of the notches, we estimate RMTJ when the DW is pinned at each notch, as shown in Fig. 2(b), which are close to the resistances observed in Fig. 2(a). We will show that repeated single-amplitude V pulses also move the DW notch to notch but ramping up the amplitude allows us to observe all switches without tuning the amplitude precisely. We will show how the cycle-to-cycle stochasticity may aid certain online learning tasks when V can be applied repeatably over time to set the synapse weight, allowing for stochastic outer product updates. This work informs essential design parameters using DW-based synapses for future neuromorphic computing.

![](https://assets.underline.io/uploads/markdown_image/1/image/0326a4371e8db824bf485edae008119b.jpg)

Fig. 1. (a) DW-MTJ synapse. (b) Field loop.

![](https://assets.underline.io/uploads/markdown_image/1/image/25feb81acfb52d72151ddba93b51f603.jpg)

Fig. 2. (a) MW switching for 10 cycles. (b) Expected vs measured RMTJ when the DW is pinned at each notch.

Multi-Weight Artificial Synapses with Straight Notched Geometry for Neuromorphic Computing

The development of efficient processing of unstructured information necessitates research into neuromorphic computing. In this work, we report domain wall-magnetic tunnel junction (DW-MTJ) artificial synaptic devices with a trapezoidal geometry that are uniquely suited for neuromorphic computation. DW-MTJ devices are nonvolatile memory-in-logic elements that can be integrated into an artificial neural network1. The bottom ferromagnetic layer of the MTJ is a DW track, and the magnetization of that layer is determined by the position of the DW within the track. The device can act as a programmable resistor based on the location of the DW. Simulations have shown that this high level of resistance state control and stability could allow for advanced functionalities for neuromorphic computing1,2,3. However, experimental work has focused on binary DW-MTJs4, and almost no experimental work has been done to understand the behavior of the multi-weight (MW) DW-MTJ synapse, with one paper showing results on a multi-MTJ device5. Here, we present a DW-MTJ based MW synapse that is directional, has stable and repeatable resistance states, and uses a single MTJ. The MTJ was lengthened and pinning notches were fabricated along the DW track. This way the DW could rest under the MTJ, opening more resistance states. A trapezoidal DW track was patterned for directional switching, shown in Fig. 1. As the DW is moved from IN to CLK using spin orbit torque switching, the voltage amplitude required to propagate the DW increases as the track widens, which results in MW switching. Going CLK to IN does not exhibit MW switching since depinning from the right-most notch requires the maximum voltage, shown in Fig. 2. We will show how this asymmetry in writing and reset is useful for offline learning to bring the synapse to a resistance state using a particular voltage, and then to reset the device efficiently. We will compare the behavior of the trapezoidal DW-MTJ synapse to the straight DW-MTJ synapse presented separately.

![](https://assets.underline.io/uploads/markdown_image/1/image/d8758b10df5900a61b218c67399668ce.jpg)

Fig. 1: Trapezoidal Synapse. Left) SEM image. Right) Schematic with DW track in blue, MTJ in red, electrodes in green.

![](https://assets.underline.io/uploads/markdown_image/1/image/00ff215da248f99f97ffb70a113e6586.jpg)

Fig. 2: Three consecutive directional write then reset cycles

Multi-Weight Directional Artificial Synapses with Trapezoidal Geometry for Neuromorphic Computing

DOC: Neuromorphic Computing

technical paper

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GOK - MRAM, Magnetic Logic and Related Devices I

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Samuel Liu

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Hardware Aware Bayesian Variational Inference Using Magnetic Tunnel Junction Noise Distributions in Artificial Synapse Arrays

Multifunctional Design of Domain Wall-Magnetic Tunnel Junction Artificial Synapses for Accurate Training of Neural Networks

Multi-Weight Artificial Synapses with Straight Notched Geometry for Neuromorphic Computing

Multi-Weight Directional Artificial Synapses with Trapezoidal Geometry for Neuromorphic Computing

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