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

In superparamagnetic tunnel junctions (SMTJ), the energy barriers that separate the parallel and the antiparallel magnetization configurations are sufficiently small that the thermal noise causes stochastic magnetization fluctuations between the two states. Through magnetoresistance effects, those stochastic fluctuations give rise to telegraphic noise signals with two voltage levels (see Fig.1) [1, 2]. The relative average time spent in each of the two configurations can be controlled by an applied dc current via the spin-transfer torque. Due to their inherent stochastic nature, SMTJs are promising candidates for truly random number generator applications [3, 4], brain-inspired and probabilistic computing [5-10]. However, an external bias magnetic field was always required to fully operate the SMTJ’s with current, which represents a drawback to their integration with the required microelectronic circuits. In this work, we report for the first time, SMTJs that are fully controlled by DC current at zero applied magnetic field using perpendicular magnetic tunnel junctions (pMTJ). Stable pMTJs are used in densely magnetic memories [11], nevertheless their thermal stability can be strongly reduced by tuning their free layer thickness, leading to a superparamagnetic state. Here, we use pMTJ’s with a free layer thickness of t=1.6 nm, and with diameters ranging from 150 nm to 80 nm. By applying a DC current in one direction (sign), without any external bias field, we observe stochastic fluctuations in the resistance for dc currents between -0.3 mA and -0.27 mA. As shown in Fig. 2, the average probability in being in high and low resistance state is well controlled by the applied current. In order to obtain good statistics on the extracted probability, we record to stochastic transitions. We extracted the dwell time distribution, which follows an exponential distribution with a mean dwell time that is in agreement with the modified Néel-Brown model. The authors acknowledge partial funding from ERC MAGICAL No 669204, and the Nanoscience Foundation (Grenoble, France).

![](https://assets.underline.io/uploads/markdown_image/1/image/032d011551d8698e3dc1b74244af9c81.jpg)

Figure 1 : Experimental voltage time trace of the SMTJ.

![](https://assets.underline.io/uploads/markdown_image/1/image/f8c0fe8daabe77b0c738c5d388eadce3.jpg)

Figure 2 : The probability of occupancy of the high resistance state versus current.

Current controlled perpendicular superparamagnetic tunnel junctions operating at zero applied magnetic field

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

https://1worldcontent.com/ess/9226.pdf

**Abstract:**

Spin-Transfer Torque Magnetic Tunnel Junctions (STT-MTJ) are devices featuring stochastic properties. They are promising candidates for non-volatile memory or true random number generators. To design reliable hybrid CMOS circuits including STT-MTJs, one needs to use a compact model accounting for its stochasticity in the circuit simulations. This paper proposes a compact model that accurately mimics the MTJ stochastic switching behavior and meets the needs of fast execution time. The relevance of such a model together with its fast execution velocity are illustrated with a bitstream generator.

Fast Behavioral VerilogA Compact Model for Stochastic MTJ

Magnetic tunnel junctions offer significant and near-term improvements to new computer chips, most immediately from non-volatile memory applications [1]. These devices consist of two magnetic layers whose relative alignment – parallel or antiparallel – determine the device's two-terminal resistance. When the energy barrier between these two states is sufficiently small, thermal fluctuations can cause the device to exhibit random telegraph noise in its resistive state. In this case, the device is called a superparamagnetic tunnel junction [2]. Computing with random telegraph noise can offer favorable properties such as noise-tolerance, massive parallelism, and – for certain operations – low power and area footprints. The field of stochastic computing addresses questions of engineering such systems but has mostly been restricted to the use of low-quality pseudorandom number generators. The low periodicity and high cross-correlations between these devices have restricted traditional stochastic computing by forcing frequent regeneration of stochastic bitstreams. Crossing in and out of the stochastic domain can incur significant energy penalties [3]. In our work [4], we introduce a low-energy circuit for extracting programmable randomness from superparamagnetic tunnel junctions. The required probability is determined via a digital input signal, rather than an analog current, so ohmic losses are minimized (Figure 1). Using detailed analog circuit simulation, we find that our device requires only half the energy of the traditional all-CMOS solution, while also offering infinite-period truly random bitstreams. To demonstrate the value of truly random bitstreams, we designed a deep neural network modeled after LeNet5 [5], a famous convolutional neural network used for handwriting recognition. Traditional neural networks multiply neuron outputs by a synaptic weight, add these products together at the input of another neuron, and then apply a nonlinear operation to that input sum. In our implementation, the values passed between neurons are encoded in the expected value of the voltage on any given wire. To multiply two signals together, we need only use a Boolean AND gate to construct the joint distribution of the wires. Feeding many wires into a Boolean OR gate generates a polynomial function which looks like linear addition near the origin, but acquires high-order nonlinear corrections when the inputs are strong. However, the OR gate only functions in this way because the inputs can be regarded as statistically independent, which would be impossible with pseudorandom number generators absent an unacceptable increase in energy consumption. We implement LeNet5 using superparamagnetic tunnel junctions together with these simple logic gates and train a simulation of this deep neural network. We are able to achieve 97 % accuracy on handwritten digit recognition using only 150 nJ per inference. This energy efficiency represents a factor of 1.4 to 7.7 improvement over comparable proposals that do not use tunnel junctions. However, after systematic optimization, the best CMOS-only solution is able to achieve 99.1 % accuracy [6]. Questions about the best way to train OR-gate neurons for optimal performance is a question for future research. Nevertheless, our demonstration shows that taking a digital approach to utilizing SMTJ fluctuations can unlock extremely energy-efficient circuit designs with the potential for offering stochastic neural networks computing in near-term application specific integrated circuits.

**References:**

[1] Apalkov, Dieny, and Slaughter, Proc. IEEE 104, 1796 (2016) [2] Camsari, Faria, Sutton, and Datta, Phys. Rev. X 7, 031014 (2017) [3] Manohar, IEEE Comp. Arch. Lett. 14, 119 (2015) [4] Daniels, Madhavan, Talatchian, et al., Phys. Rev. App. 13, 034016 (2020) [5] LeCun, Bottou, Bengio, et al., Proc. IEEE 86, 2278 (1998) [6] Li, Ji, Ren, et al., IEEE Trans. Comp. Aid. Des. Int. Circ. Sys. 38, 1543 (2019)

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/a7dfe1770e892cca4d62d45c58f83e71.jpg)
Neurons in the brain have analog outputs in analog time; superparamagnetic tunnel junctions have digital states in analog time. To use digital circuitry to discretize the time variable, removing the need for steady state currents and the associated ohmic losses.

 Running Deep Neural Networks on Superparamagnetic Fluctuations

Magnetic tunnel junctions consist of two ferromagnetic layers separated by a thin insulating layer. The relative orientation of the two layers' magnetization has two stable configurations: parallel or antiparallel (P or AP). For use as a binary non-volatile memory in magnetic random access memory (MRAM), the retention time in each of the two configurations needs to be on the order of several years. This corresponds to energy barriers larger than 40 kT (k is the Boltzmann constant, and T=300 K is room temperature). If the energy barrier becomes smaller than 12 kT, thermal fluctuations induce random switching of the magnetization between the P and the AP states with a mean timescale between 10 µs and 1 ms. Such fluctuating, low-energy-barrier tunnel junctions are referred to as superparamagnetic tunnel junctions [1]. Recently, superparamagnetic tunnel junctions have become attractive as compact and energy-efficient devices for applications that require truly random variables [2,3], including innovative computing schemes [4,5,6,7,8]. Through adapted circuit co-design approaches, we previously showed that those devices are promising for implementing artificial neural networks with reduced energy consumption [9]. In cognitive computing, these superparamagnetic tunnel junctions can be used to emulate biological neurons [10, 11]. Here, we investigate simple ways of coupling these devices to extend these innovative computing schemes. To mimic neuron-like interconnections, it is important to develop simple schemes to couple such devices. Significant work has been done to develop coupling strategies for magnetic systems such as harmonic spin-torque nano-oscillators, which are useful for cognitive computing [12,13,14,15], but there is no equivalent scheme for superparamagnetic tunnel junctions. In this work, we experimentally demonstrate a simple electrical coupling method between two superparamagnetic tunnel junctions. We couple two stochastic magnetic junctions by placing them in parallel in a simple electrical circuit. We use the fact that their switching rate can be controlled deterministically by the applied current. They couple because their stochastic electrical transitions change the current flowing through the other device, changing its switching rate. In our circuit, the total applied current in each nanojunction is shared and depends on the joint resistance states of the nanojunctions. Depending on the current state of the system, transitions to certain joint states are favored while others are less probable. This coupling mechanism leads to non-zero cross-correlation between the stochastic switching events of the two fluctuating tunnel junctions, demonstrating their mutual coupling. We show experimentally that the cross-correlation becomes large when the switching time scales of the two superparamagnetic tunnel junctions are such that they both have roughly a 50 % probability to be in the parallel or antiparallel state. We also demonstrate that the cross-correlation increases when the total current applied to the system increases. We reach 18 % for the largest Pearson correlation value measured in the system. We find good agreements between numerical simulations of a comparable four-state Markov state process and our experiments. As we do not use sophisticated circuits for the coupling purpose, our approach opens new paths to compact and energy-efficient implementations of scaled-up arrays of coupled superparamagnetic tunnel junctions for new cognitive computing schemes.

**References:**

[1] W. H. Rippard et. al. PRB, Vol 84, 064439 (2011). [2] B. Parks et. al. AIP Advances, Vol 8, 055903 (2018). [3] D. Vodenicarevic et. al. Phys. Rev. Appl, Vol 8, 054045 (2020). [4] A. Mizrahi et. al. Nature Communications, Vol 9, 1533 (2018). [5] K. Camsari et. al. Appl. Phys. Rev, Vol 6, 011305 (2019). [6] K. Camsari et. al. Phys. Rev. X, Vol 7, 031014 (2017). [7] A. Sengupta et. al. IEEE Trans. on Electron Devices, Vol 63, 2963 (2016). [8] W. A. Borders et. al. Nature, Vol 573, 390 (2019). [9] M. W. Daniels, et al. Phys. Rev. Appl, Vol 13, 034016 (2020). [10] W. Gerstner et. al. Neuronal Dynamics, Cambridge Univ. Press (2014). [11] J. Grollier et. al. Nature Electronics, Vol 3, 360 (2020). [12] W. H. Rippard et. al. PRL, Vol 95, 067203 (2005). [13] S. Kaka et. al. Nature, Vol 437, 389 (2005). [14] A. A. Awad, Nat. Phys, Vol 13, 292 (2017). [15] M. Romera†, P. Talatchian† et al. Nature, Vol 563, 230-234 (2018).

**Images:**

 Mutually coupled superparamagnetic tunnel junctions

Spin torque nano-oscillators (STNO) generate high frequency output voltage signals upon injection of a spin polarized DC current into a magnetic tunnel junction. For their applications in wireless communications or neuromorphic computing schemes, a central aspect is the control of their phase dynamics via injection locking to an external rf signal [1, 2]. Many interesting, non-linear effects may arise at higher excitation levels that manifest themselves in the Arnold tongue [3, 4]. For the in-plane magnetized STNO (in-plane magnetized polarizer and free layer) [2], we provide here analytical expressions for (i) the asymmetric Arnold tongue boundaries, arising from the dependence of the forcing on the STNO power; (ii) the Takens-Bogdanov bifurcation threshold [4] which leads to a reduced locking range and (iii) the hysteresis boundaries [3,4]. These effects are discussed within a common model for ‘pure’ rf signals arising from either a spin polarized current or a magnetic field. ‘Pure’ refers to a well-defined direction ui (i=x,y,z ; ux the STNO easy axis) of the spin polarization or a magnetic field [2]. In a further study we also investigate synchronization at harmonic order n=1 (rf signal frequency close to the STNO frequency) for mixed spin polarization with x- and y- components. The important and unexpected finding here is that the STNO phase does not follow an arcsine (Adler-type) behavior [5] within the locking range, but shows a discrete jump that can be as large as Pi/2. Our analysis shows that the phase jump results from a competition between locking to the ux- and uy-components of the rf signal, where locking to the ux-component at n=1 is enabled through the fact that the free running oscillation power is non-constant with frequency components at f. This demonstrates that, for mixed rf signals, injection locking can be more complex, and that the results can be of interest for applications such as the phase jump for phase shift keying concepts [6]. MIG was supported by the French Space Agency (CNES) and the CEA NUMERICS program, which has received funding from the European Union's Horizon 2020 program (No 800945). Partial support was provided by the French National Research Agency (ANR-20-CE24-0002).

Arnold tongue of injection locked spin torque nano-oscillators under high and mixed driving signals

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DPA: Spintronic Devices for Memory and Computing

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GOL - MRAM, Magnetic Logic and Related Devices II

technical paper

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ESSCIRC ESSDERC 2021

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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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GA: Spintronics for Probabilistic Computing

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GB: Neuromorphic Computing

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Philippe Talatchian

6

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Presentations

Spiking dynamics with dual free layer MTJ

Current controlled perpendicular superparamagnetic tunnel junctions operating at zero applied magnetic field

Fast Behavioral VerilogA Compact Model for Stochastic MTJ

Running Deep Neural Networks on Superparamagnetic Fluctuations

Mutually coupled superparamagnetic tunnel junctions

Arnold tongue of injection locked spin torque nano-oscillators under high and mixed driving signals

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