Convolutional neural networks (CNN) are state of the art algorithms for image processing. Despite a small number of synaptic weights, the CNNs remain computationally costly to train in software due to the necessity to exchange huge data flows between memory and processing units. Unconventional hardware is suited to address this limitation. In neuromorphic spintronics, it has been previously demonstrated that the spin diode effect can be used to apply a synaptic weight on a radiofrequency signal [1][2]. Here we go a step beyond, to show an experimental implementation of a convolutional layer employing chains of spin-diodes. We design a compact architecture of 3 chains with 3 spin-diodes connected in series, that performs a padded convolution with a filter of 3 pixels on 5 input pixels multiplexed in frequency in one RF signal (See Figure 1). The synaptic weights corresponding to the filter are encoded by a small frequency detuning between the inputs and the spin-diodes resonance and are controlled in parallel using currents in 3 strip lines. This architecture exploits the intrinsic weight redundancy of convolutions (all filters share the same weights) to enhance the compacity of the hardware and greatly simplify the process of updating a weight, only requiring updating a the current in one strip line. We will also present processed experimental results highlighting the scalability of the proposed architecture. An error on the performed convolution as low as 0.28% was achieved (See Figure 2). The proposed architecture enables us to both reduce the size of this hardware implementation while, at the same time, performing the convolution in one timestep contrary to previous time-multiplexed implementations. According to a previous study [3] we can achieve to decrease by one order of magnitude the energy consumption compared to current GPUs and two orders of magnitude in operating latency. This proof of concept of spintronic CNN, opens the path to spintronic neural networks that can exploit the power of convolutional layers in a fully parallel, compact, and energy efficient way.

Fully Parallel Convolution with Chains of Spin

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 nano-oscillators can provide energy efficient solution to realize neuromorphic applications. They have been shown to emulate biological neurons and perform
machine learning tasks with an accuracy similar to that of state-of-the-art neural networks [1]. Moreover, they can serve as synapses when operated as a spin diode [2]. In this context,
systems with compensated anisotropy could offer key advantages. For instance, an easy plane geometry achieved by compensating the anisotropy can produce spikes as an output, a
phenomenon, recently demonstrated via micromagnetic simulations for a spin Hall nano-oscillator (SHNO) geometry [3]. Moreover, an SHNO with a compensated or near zero effective
magnetization would require low operating current and exhibit extremely low phase noise, making it suitable to realize large chain of synchronized neurons [4]. A synapse or a spin diode
with a compensated anisotropy would also resonate at a relatively fixed frequency, which is an essential requirement for frequency multiplexing and transmitting data from the SHNO
based neurons. This motivates us to study spin Hall systems with compensated anisotropy. Here, Pt/CoFeB based thin films are used as the spin Hall system. The anisotropy has been tuned
by varying the thickness of the magnetic layer. The thin films have been fabricated into micro-strip waveguides and nano-constrictions to study the magnetization dynamics in these
systems which emulate the behaviour of an SHNO. Spin-torque ferromagnetic resonance (ST-FMR) technique is employed to evaluate the effective magnetization of the fabricated devices.
The measurements indicate the fabricated devices achieve compensation when the starting thin films have perpendicular anisotropy, implying the effects of post-fabrication anisotropy
reduction and shape anisotropy. Different nano-constriction geometries have been studied to evaluate the effect of shape on the compensation point. We also demonstrate frequency
tunability of the nano-synapses and thereby its weights by anisotropy modification. We then propose a non-volatile method to control the synaptic weights via electric fields which would
enable realization of compact and energy efficient neuromorphic chips. 
**References** [1] J. Torrejon et al., “Neuromorphic computing with nanoscale spintronic oscillators”, Nature 547, 428 (2017).
[2] N. Leroux et al., “Radio-Frequency Multiply-and-Accumulate Operations with Spintronic Synapses”, Phys. Rev. Appl. 15, 034067 (2021).
[3] D. Markovic et al., “Easy-plane spin Hall nano-oscillators as spiking neurons for neuromorphic computing”, Phys. Rev. B 105, 014411 (2022).
[4] A.A. Awad et al., “Long-range mutual synchronization of spin Hall nano-oscillators”, Nat. Phys. 13, 292 (2017).

Compensation of anisotropy in spin Hall systems for realizing neuromorphic applications

Spiking neural networks have attracted a lot of interest in the past decade as they meet the need of energy efficiency in deep neural network computing (1). Using spikes instead of continuous signals enables low power operation, event-based computations and fast response time, which is better adapted to spatial-temporal data. Combined with unsupervised and local learning rules such as the spike-timing-dependant plasticity rule (2), SNN with magnetic tunnel junction (MTJ) based neurons provide interesting solutions for embedded technologies with better back-end-of-line compatibility (3) compared to other technologies.
For the spike generation, we propose an MTJ-based neuron composed of two magnetized layers (M1 and M2), with low thermal stabilities, separated by an oxide tunnel barrier. Under applied current, the spin-transfer torque (STT) enables an alternating switching of both magnetic layers leading to a so-called “windmill motion” (see Fig1.a-c) previously predicted by simulation for in-plane and out-of-plane magnetized MTJs (4,5). Here we designed, fabricated and characterized such type of structure and were able to achieve steady alternating magnetization reversal of both layers generating a characteristic spike-like resistive response.
MTJ stacks of FeCoB/MgO/FeCoB, with varying FeCoB thicknesses, were deposited by magnetron sputtering and patterned into nano-pillars with diameters ranging from 50 to 200 nm. The electrical characterization of the nano-pillars reveals essential changes of the magnetization dynamics depending on the pillar diameters, layer thicknesses, voltage, applied magnetic field and temperature of the junction. As predicted by the simulation, the frequency of the oscillations and the width of the spikes evolve with the voltage amplitude and the applied field. Important similarities confirm the parameter dependence with temperature and bias voltage. Controlling the spiking rates at low voltages is a critical requirement to build an efficient spiking neural network.
References Acknowledgements:
This work was supported by ANR via grant SpinSpike Projet-ANR-20-CE24-0002. 

**References:** 
(1) A. Tavanaei, M. Ghodrati and S.R. Kheradpisheh, Neural networks, 111, 47-63 (2019). 
(2) T. Iakymchuk, A. Rosado-Muñoz and J.F. Guerrero-Martínez, EURASIP Journal on Image and Video Processing 2015, 1-11 (2015). 
(3) D. Shum, D. Houssameddine and S.T. Woo, 2017 Symposium on VLSI Technology. IEEE pp. T208-T209 (2017). 
(4) R. Matsumoto, S. Lequeux, and J. Grollier, Physical Review Applied, 11(4), 044093 (2019) 
(5) G. Gupta, Z. Zhu and G. Liang, arXiv preprint arXiv, 1611.05169 (2016). 

![](https://s3.eu-west-1.amazonaws.com/underline.prod/uploads/markdown_image/1/image/8611b8d23f4be4ece5ea2d8e459a4a2f.png)

Spiking dynamics with dual free layer MTJ

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

DOC: Neuromorphic Computing

technical paper

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SF: Computing with Spintronic Oscillators

GOE: Magnetization Dynamics V

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**Session Co-Chairs:** Shouzhong Peng, *Beihang University* and Luding Wang, *Eindhoven University of Technology*

DPA: Spintronic Devices for Memory and Computing

poster

**Session chairs:** Riccardo Tomasello, Politecnico di Bari and Mario Carpentieri, Politecnico of Bari



Symposium SB: Spintronic Diodes: Challenges and New Directions

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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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Julie Grollier

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Fully Parallel Convolution with Chains of Spin

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

Compensation of anisotropy in spin Hall systems for realizing neuromorphic applications

Spiking dynamics with dual free layer MTJ

Radio-Frequency Spintronic Neural Networks

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