Reaching the full potential of spintronics requires modeling to predict the results of spintronic experiments, optimize structures, and design systems. Currently, the gold standard for modeling spintronic structures is micromagnetic simulations. Unfortunately, these simulations can be extremely slow and struggle with modeling accurately the imperfections
and noise inherent to experimental devices. In this work, we introduce an alternative approach: design models for spintronic devices by letting an artificial intelligence automatically
generate a model based on examples of the device behavior. For this, we make use of the recently-proposed formalism of Neural Ordinary Differential Equations (Neural ODE) [1], which
we adapt to the specificities of spintronics [2]. An appropriately-trained Neural ODE can simulate a skyrmion-based device 200 times faster than micromagnetic simulations while being
highly accurate, even in complex situations and for multiple values of materials parameters (magnetic anisotropy, DMI). We also train a Neural ODE based on five milliseconds of
experimental measurements of vortex-based spin-transfer nano oscillators. The Neural ODE could then predict weeks of experimental measurements. We show how to adapt the Neural
ODE, an originally deterministic formalism, to incorporate noise and show that the predictions of the Neural ODE match the experiments very precisely. All these results highlight the
potential of Neural Ordinary Differential Equations for developing spintronic applications. 
**References** 
[1] R. T. Chen, Y. Rubanova, J. Bettencourt, and D. K. Duvenaud, "Neural Ordinary Differential Equations", Advances in Neural Information Processing Systems, 6571–6583
(2018).
[2] X. Chen, F. A. Araujo, M. Riou, J. Torrejon, D. Ravelosona, W. Kang, W. Zhao, J. Grollier, D. Querlioz, "Forecasting the outcome of spintronic experiments with Neural Ordinary
Differential Equations", Nature Communications 13, 1016 (2022).

Forecasting the Outcome of Spintronic Experiments with Neural Ordinary Differential Equations

The domain wall (DW) magnetic tunnel junction (MTJ) is a promising component of next-generation neuromorphic, in-memory, and logical computing hardware due to features including non-volatility, multiple analog resistive states, low power, and ultrafast read-write operation [1-3]. Predicting the DW motion along a magnetic track involves complicated and time-consuming micromagnetic simulations, which greatly impede the development of computing systems designed with interconnected DW-MTJ devices [4]. The neural ordinary differential equations (ODE) is a recently conceptualized deep learning framework that can predict the behavior of dynamic systems [5]. In this approach, the ODE that defines the time derivative of the system output is expressed as a deep neural network; when provided with initial conditions, an ODE solver determines the system response at future times. Chen et al. [6] extended this approach by expressing hidden variables that are difficult to probe with higher-order derivatives of the output, which are then replaced with mathematically equivalent time-delayed versions. External inputs can be applied to the network in a similar time-delayed fashion. In this work, DW motion by spin-transfer torque excitation is modeled utilizing the neural ODE framework. Temporal DW position data along a magnetic track excited by a set of random sinusoidal current inputs are generated by mumax3 [7] and are used to train a neural ODE in a supervised fashion through backpropagation. For a different set of random sinusoidal current inputs, the DW position forecasted by the trained network matches with the results generated by mumax3 with very high accuracy (Fig. 2) while reducing the simulation time by a factor greater than 200x, thereby opening the path to efficiently design integrated systems interconnecting a large number of DWMTJs. 

**References** [1] M. Alamdar, T. Leonard, C. Cui et al., Appl. Phys. Lett., vol. 118, no. 11, p. 112401 (2021).
[2] N. Hassan, X. Hu, L. Jiang-Wei et al., Jour. Appl. Phys., vol. 124, no. 15, p. 152127 (2018).
[3] W. H. Brigner, N. Hassan, L. Jiang-Wei et al., IEEE Trans. Electron Devices, vol. 66, no. 11, pp. 4970-4975 (2019).
[4] X. Hu, A. Timm, W. H. Brigner et al., IEEE Trans. Electron Devices, vol. 66, no. 6, pp. 2817-2821 (2019).
[5] R. T. Q. Chen, Y. Rubanova, J. Bettencourtet al., Proceedings of NeurIPS, 31 (2018).
[6] X. Chen, F. A. Araujo, M. Riou et al, Nat. Comm., vol. 12, no. 1016 (2022).
[7] A. Vansteenkiste, J. Leliaert, M. Dvornik et al., AIP Advances, vol. 4, no. 10, p. 107133 (2014). 

![](https://s3.eu-west-1.amazonaws.com/underline.prod/uploads/markdown_image/1/image/01364715490ab753cd3ac85dcf7e5cc1.png) 
Up (blue) and down (red) polarized magnetic domains along a track separated by a DW (yellow). Current inputs control the position of the DW by applying spin-transfer torque. 

![](https://s3.eu-west-1.amazonaws.com/underline.prod/uploads/markdown_image/1/image/9e4b8c52f3c00844a1d6aa3d22edfa85.png) 

DW position forecasted by a trained neural ODE in comparison with mumax3 simulation.

Modeling Magnetic Domain Wall Motion with Neural Ordinary Differential Equations

The combination of the two key effects of spintronics, magnetization dynamics and magneto-resistive effects, allows the realization of nano-neurons and nano-synapses with high computational capabilities. However, multilayer spintronic neural networks have never been realized with these nanodevices because there is no way to connect them that can work on a large scale. I will show that it is possible to exploit the two key effects of spintronics to connect together magnetic tunnel junctions that implement both neurons and synapses of a multilayer network. The magnetic tunnel junctions perform neural operations on DC signals and output the result as RF, operate synaptic operations on RF signals and output the result as DC thus giving rise to multilayer networks based on successive, clean, and fast conversions from RF to DC and from DC to RF. I will give a proof of concept with a two-layer neural network composed of nine interconnected magnetic tunnel junctions functioning as both synapses and neurons and experimentally demonstrate its ability to solve non-linear tasks with high performance. I will show that with junctions downscaled to 20 nm, such a network would consume 10fJ per synaptic operation and 100fJ per neuronal operation, several orders of magnitude less than current software neural network implementations. Finally, I will show through physical simulations that these networks, which can process DC data, can also natively classify RF inputs, achieving state-of-the-art drone identification from their RF transmissions. This study lays the foundation for deep spintronic neural networks at the nanoscale.

Series of synaptic and neuronal operations in a multilayer magnetic tunnel junction network through RF to

Neuromorphic computing is a particularly exciting application of spintronics, able to exploit its rich physics to achieve low-power-consumption computation inspired by the brain. Designing neuromorphic systems requires simulating the response of spintronic devices to multiple types of inputs over long time periods. Currently, the dominant approach to predicting the complex behavior of spintronic devices is micromagnetic simulation. This technique, however, requires very long simulation times, easily reaching weeks in time-dependent experiments or in micrometer-scale devices. In this work, we take an alternative road by adopting a deep learning technique, Neural Ordinary Differential Equations (ODEs), to model spintronic devices and develop spintronic systems. We show that Neural ODEs, trained on a minimal amount of data, can predict the behavior of spintronic devices with high accuracy and an extremely efficient simulation time, compared to micromagnetic simulations. For this purpose, we re-frame the formalism of Neural Ordinary Differential Equations (ODEs) [1] to the constraints of spintronics: few measured outputs, multiple inputs and internal parameters (Fig. 1). We demonstrate with Neural ODEs an acceleration factor over 200 compared to micromagnetic simulations for a neuromorphic system -- a reservoir computer made of magnetic skyrmions (20 minutes compared to three days). We also demonstrate that this state-of-the-art deep learning technique for time series modeling can be applied to model an experimental neuromorphic experiment [2], in which spin-torque nano-oscillators are used as reservoir computers to achieve a spoken digit recognition task (Fig. 2). Neural ODEs can therefore constitute a disruptive tool for developing spintronic applications in complement to micromagnetic simulations, which are time-consuming and cannot fit experiments when noise or imperfections are present [3].

Building spintronics neuromorphic systems with Neural Ordinary Differential Equations

Spintronic devices are promising for neuromorphic computing due to their greater energy efficiency, high endurance compared to phase change memory and resistive random-access memory [1]. Popular spintronic memristors involve movement of a domain wall (DW) in a perpendicularly anisotropic (PMA) racetrack to achieve variable conductance to implement synaptic weights for deep neural networks (DNNs). However, energy efficient voltage controlled DW devices driven by spin orbit torque with Neel DW stabilized by Dzyaloshinskii-Moriya interaction show stochastic behavior and therefore provide limited states (see Fig.1 [2]). This is modelled rigorously with micromagnetics. To work with these DW devices and achieve high testing accuracy, the DNNs need to be trained with specific algorithms. In this study, we propose both in-situ and ex-situ training algorithms of DNN based on 2-, 3- and 5-state DW synaptic devices. For in-situ training, a mixed precision framework [3] is adopted where low precision synaptic conductances are tuned based on the quantized value of high precision gradients. With our quantized training, the learning is able to tolerate large conductance variation without any considerable accuracy loss as the synaptic state changes only few times during the entire training due to large inter-state interval. Thus, high programming noise intrinsic to DW devices is accommodated in the training which reduces the required number of programming pulses and the energy to train a DNN. The programming energy required for a DNN with 5-state DW synapse is found to be 1.25 pJ/image for MNIST digit classification with ~96.7% accuracy shown in Fig.2. Ex-situ training algorithm is also proposed where the DW devices are characterized based on statistics and then the devices characteristic is inputted to the quantized training algorithm as constraints which shows ~95% accuracy for 5-state synapses for large conductance variation. This work will pave the way to implement high accuracy intelligent future battery powered IoT edge devices using DW devices. Acknowledgement: NSF grant ECCS: #1954589

![](https://assets.underline.io/uploads/markdown_image/1/image/31364699a8a16e0f648f76850d498230.jpg)

Fig. 1: Stochastic nature of DW devices for voltage control of PMA (Ku) [2]

![](https://assets.underline.io/uploads/markdown_image/1/image/17758a182c49845d7959075dda8cb138.jpg)

Fig. 2: Testing accuracy comparison with proposed training

Neuromorphic Learning of a Deep Neural Network with Low Precision and Stochastic Domain Wall Based Memristor

A key challenge of neuromorphic computing is to build hardware neural networks with dense connectivity between nanoscale synapses and neurons, approaching the brain’s thousands of synapses per neuron (1). In this talk, I will show that spin diodes are microwave nano-synapses that naturally and densely interface with neurons made of spin-torque nano-oscillators (2). I will describe the principle of these novel synapses and explain how their microwave features can be harnessed to achieve the multiply-and-accumulate operations at the core of neural networks, with over 500 synapses/neuron. I will show that they implement all-to-all connections as well as convolutional operations in a fully parallel way with high density and speed. I will describe our experiments highlighting these functionalities (3), and show that they open the path to radio-frequency deep learning.

Radio-Frequency Spintronic Neural Networks

**Please read the paper on the following link:**

https://1worldcontent.com/ess/9196.pdf

**Abstract:**

By alleviating the multiply operation with simple XNOR, Binary Neural Networks seem an appealing solution to overcome the von Neumann bottleneck. In this context, we demonstrate experimentally the robustness of XNOR operation, in memory, based on resistive bridge (2T2R cell), with complementary coding of weights and input neuronal activations. Based on these measurements, we validate, through an extensive set of Monte Carlo simulations, that this approach is suitable for large neurons with very low error rate. Based on circuit results, Neural network simulations shows a very limited accuracy degradation on the MNIST task (0.07%) and CIFAR-10 task (0.35%).

Low-Overhead Implementation of Binarized Neural Networks Employing Robust 2T2R Resistive RAM Bridges

The emergence of novel memories such as memristors or resistive memory (RRAM) opens the way to highly energy-efficient computation, near- or in-memory. However, this type of computation has to deal with the severe unreliability of emerging memories. To address this issue, inspired by the architecture of animal brains, we present a manufactured differential hybrid CMOS/RRAM memory architecture suitable for neural network implementation that functions without formal error correction. We also highlight that using highly error-prone programming conditions only slightly reduces network accuracy while bringing important benefits in energy efficiency. Then, we present a second approach where the probabilistic nature of RRAM, instead of being mitigated, can be fully exploited to implement a type of probabilistic learning. We show that the inherent variability in hafnium oxide RRAM can naturally implement the sampling step in the Metropolis-Hastings Markov Chain Monte Carlo algorithm and train experimentally an array of 16,384 RRAM cells to recognize images of cancerous tissues using this technique. These results highlight the interest in fully embracing the unreliable nature of emerging devices in neuromorphic designs.

Using Imperfect Nanodevices to Achieve Energy-Efficient Artificial Intelligence

HOC: New Approaches in Computational Magnetism

technical paper

#### Welcome to the 67th Annual Conference on Magnetism and Magnetic Materials, MMM 2022!

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MMM 2022

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SF: Computing with Spintronic Oscillators

DOC: Neuromorphic Computing

**Session chair:** Daniele Pinna, Forschungszentrum Jülich


HOG - New Computation Schemes

The 15th Joint MMM-INTERMAG Conference (2022 Joint) is sponsored jointly by AIP Publishing and the IEEE Magnetics Society. Members of the international scientific and engineering communities interested in recent developments in fundamental and applied magnetism are invited to attend and contribute to the technical sessions. The technical program will include invited and contributed papers in oral and poster sessions, invited symposia, a plenary session, and an evening session, with about 1500 presentations overall. This Conference provides an outstanding opportunity for worldwide participants to meet their colleagues and collaborators and discuss developments in all areas of magnetism research.

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2022 Joint MMM-INTERMAG

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Symposium SB: Spintronic Diodes: Challenges and New Directions

symposium

**Session Chairs:** Manuel Le Gallo, IBM Zurich; Thomas Mikolajick, Namlab gGmbH and Technische Universität Dresden

B2L-1: Machine Learning & In-Memory-Computing with Emerging Technologies

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ESSCIRC ESSDERC 2021

The aim of ESSCIRC and ESSDERC is to provide an annual European forum for the presentation and discussion of recent advances in solid-state devices and circuits.
The level of integration for system-on-chip design is rapidly increasing.

This is made available by advances in semiconductor technology. Therefore, more than ever before, a deeper interaction among technologists, device experts, IC designers, and system designers is necessary. ESSCIRC and ESSDERC are governed by a common Steering Committee and share Plenary Keynote Presentations and Joint Sessions bridging both device and circuit communities.





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SYM I - Nano-Devices for IoT and AI/Spin Texture and Resonance

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MATERIALS FOR HUMANITY (MH 21)

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Presentations

Forecasting the Outcome of Spintronic Experiments with Neural Ordinary Differential Equations

Modeling Magnetic Domain Wall Motion with Neural Ordinary Differential Equations

Series of synaptic and neuronal operations in a multilayer magnetic tunnel junction network through RF to

Building spintronics neuromorphic systems with Neural Ordinary Differential Equations

Neuromorphic Learning of a Deep Neural Network with Low Precision and Stochastic Domain Wall Based Memristor

Radio-Frequency Spintronic Neural Networks

Low-Overhead Implementation of Binarized Neural Networks Employing Robust 2T2R Resistive RAM Bridges

Using Imperfect Nanodevices to Achieve Energy-Efficient Artificial Intelligence

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