A Nanoscale Room-Temperature Multilayer Skyrmionic Synapse for Deep Spiking Neural Networks
Runze Chen, Chen Li, Yu Li, James J. Miles, Giacomo Indiveri, Steve Furber, Vasilis F. Pavlidis, Christoforos Moutafis
AA Nanoscale Room-Temperature Multilayer Skyrmionic Synapsefor Deep Spiking Neural Networks
Runze Chen, ∗ Chen Li, ∗ Yu Li, James J. Miles, Giacomo Indiveri, Steve Furber, Vasilis F. Pavlidis, and Christoforos Moutafis † Nano Engineering and Spintronic Technologies (NEST) Group,Department of Computer Science, School of Engineering,the University of Manchester, Manchester M13 9PL, United Kingdom Advanced Processor Technologies (APT) Group,Department of Computer Science, School of Engineering,the University of Manchester, Manchester M13 9PL, United Kingdom Institute of Neuroinformatics, University of Zurich and ETH Zurich, 8057 Zurich, Switzerland (Dated: October 1, 2020)Magnetic skyrmions have attracted considerable interest, especially after their recent experimentaldemonstration at room temperature in multilayers. The robustness, nanoscale size and non-volatilityof skyrmions have triggered a substantial amount of research on skyrmion-based low-power, ultra-dense nanocomputing and neuromorphic systems such as artificial synapses. Room-temperatureoperation is required to integrate skyrmionic synapses in practical future devices. Here, we nu-merically propose a nanoscale skyrmionic synapse composed of magnetic multilayers that enablesroom-temperature device operation tailored for optimal synaptic resolution. We demonstrate thatwhen embedding such multilayer skyrmionic synapses in a simple spiking neural network (SNN)with unsupervised learning via the spike-timing-dependent plasticity rule, we can achieve only a ∼
78% classification accuracy in the MNIST handwritten data set under realistic conditions. Wepropose that this performance can be significantly improved to ∼ .
61% by using a deep SNN withsupervised learning. Our results illustrate that the proposed skyrmionic synapse can be a potentialcandidate for future energy-efficient neuromorphic edge computing.
I. INTRODUCTION
Neuromorphic computing draws inspiration from howthe human brain performs extremely energy-efficientcomputations [1, 2]. Building ultra-low power cognitivecomputing systems by mimicking neuro-biological archi-tectures is a promising way to achieve such efficiency.One of the candidate technologies is spintronics [3–5].Recently, skyrmion-electronics (‘skyrmionics’), a branchof spintronics, has been proposed as a promising build-ing block for next-generation data storage and processingapplications [6, 7].Magnetic skyrmions [Fig. 1(a, b)] are topologicallyprotected spin textures exhibiting particle-like prop-erties [6]. Skyrmions were recently demonstrated inboth bulk non-centrosymmetric chiral magnets and mag-netic multilayer (MML) thin films with the existenceof Dzyaloshinskii-Moriya interaction (DMI) originatingfrom strong spin-orbit coupling (SOC) and broken inver-sion symmetry [9]. Skyrmion-based computational andstorage devices can be envisaged as hybrid solutions withtraditional Complementary Metal Oxide Semiconductor(CMOS) technologies that enhance functionality due totheir robustness, nanoscale size, and non-volatility [6].Magnetic skyrmions have recently been demonstrated ex-perimentally at room temperature (RT) for the first time ∗ These authors contributed equally to this work † christoforos.moutafi[email protected] in tailored technologically relevant MMLs [10, 11] witha diameter of individual skyrmions in the sub-100 nmrange [12], which opens the way for their use in futurenanocomputing applications. Magnetic skyrmions can benucleated, manipulated and deleted via various externalstimuli [13, 14], such as spin-polarised current [6, 7, 12],magnetic field gradient [15] and localized heating withlaser irradiation [16, 17].The enhanced stability and robustness of skyrmionsresults from their topology [6] and energy contributions[18]. Skyrmionic spin textures can be described by thetopological charge or skyrmion number [19], which countshow many times the vector field configuration wrapsaround a unit sphere and which is therefore an integer.This is defined as: N = 14 π (cid:90) m · ( ∂ x m × ∂ y m ) dxdy , (1)where N = ± N in chiral magnets [20] as well as topologically trivialstates with N = 0 [7, 19].Magnetic skyrmions have attracted considerable inter-est as information carriers in nanodevices that can emu-late biological synapses due to their unique physical char-acteristics [8, 21]. Micromagnetic simulations of suchdevices suggest that these devices consume far less en-ergy than conventional chips and other non von Neumannarchitectures [8, 21]. Meanwhile, a multi-bit skyrmion-based non-volatile storage device has been proposed and a r X i v : . [ phy s i c s . a pp - ph ] S e p FIG. 1. The proposed skyrmionic synaptic device. Illustrations of (a) a N´eel skyrmion (used in this device) and (b) a Blochskyrmion spin texture. (c) Schematic of biological neurons connected with a synapse. (d) The proposed nanoscale multilayerskyrmionic synapse device based on skyrmion flow between a pre-synapse and a post-synapse region [8]. The multilayer structurehere enables room-temperature operations. numerically simulated, where the synaptic states of thedevice are modulated by electric pulses shifting the posi-tion of skyrmions within the device [22]. More recently, aconsiderably larger, micrometer-scale, room-temperatureferrimagnetic artificial synapse has been recently exper-imentally demonstrated [23]. Further possibilities havebeen proposed to utilize magnetic skyrmions in Artifi-cial Neural Networks (ANNs), Spiking Neural Networks(SNNs) and reservoir computing [24, 25].Although skyrmion-based devices have been pro-posed to perform pattern recognition in ANNs [23, 26],skyrmionic synapses can potentially form more effi-cient neuromorphic hardware for SNNs. State-of-the-artANNs require convolutions which lead to massive matrix-vector multiplications. Therefore, specialized hardwarefor ANNs focuses on making matrix operations faster andmore power-efficient by using matrix acceleration units,e.g. Graphics Processing Unit (GPU) and Tensor Pro-cessing Unit (TPU). In contrast, SNNs feature a massiveconnection of synapses and sparse activation of neurons.Typically, the hardware implementations for SNNs en-tail the mapping of spiking neurons and their synapsesinto digital systems [27, 28], analog electronic circuits [2],and hybrid neuromorphic systems [29] to achieve energyefficiency through event-driven computing. Skyrmion-based neuromorphic hardware can be a promising candi-date due to its potential for i ) storing the informationin a non-volatile manner via the corresponding statesof skyrmions, and ii ) energy-efficient device program-ming, due to their non-volatility and the promise of low current densities needed for manipulating the movementof skyrmions [6, 7]. Experiments in B20 systems haveshown current densities as low as 10 − MA/cm [30–32].More recent work on technologically relevant multilay-ers showed that high-speed ( ∼
100 m/s) manipulation ofskyrmions in multilayer thin films required higher currentdensities ( ∼
10 MA/cm ) [33–35].Hitherto, all of the published numerical works onnanoscale skyrmion-based neuromorphic components, in-cluding skyrmion-based synapses [8, 22] and skyrmion-based leaky-integrate-fire (LIF) neurons [36] were per-formed in ideal simulation conditions (0 K). However,integrated systems, including SNNs, normally operate atroom temperature (RT) which significantly deviates fromthe assumed (ideal) conditions of the previous works. Us-ing a zero temperature simulation of skyrmionic devicesintegrated into hybrid skyrmion-CMOS systems, includ-ing neuromorphic systems, can therefore be potentiallymisleading. This paper aims to fill this important gapby investigating skyrmion-based neuromorphic comput-ing components for stable RT operation with realisticparameters and device structures.We propose a RT skyrmionic synapse and investigateit systematically via micromagnetic simulations. Insteadof utilizing a simple structure of ferromagnetic metal(FM) / heavy metal (HM) [8, 22], we numerically de-sign and evaluate a skyrmionic synapse with a tailoredMML structure composed of repetitive [HM / FM / HM ]sandwiched tri-layers inspired by [10, 11]. Micromagneticsimulations show that the operational stability of our pro- FIG. 2. The characteristic conductance modulation curves of the skyrmionic synapse. Micromagnetic simulations of askyrmionic synapse device at (a) T = 0 K, and (b) T = 300 K. The length of the device is l = 800 nm and the width is w = 220 nm. The patterned area indicates a rounded rectangle barrier with a size of 145 nm ×
60 nm. The color code(red-blue) is the same for (a) and (b). The evolution of conductance (in units of G ) (left y -axis) and the number of skyrmions(right y -axis) within the post-synapse region during the whole LTP/LTD process at (c) T = 0K and (d) T = 300K. Notethat we apply 10 electric current pulses in + x direction and then 10 electric current pulses in − x direction, respectively. Theerror-bars represent the standard deviation of each data point, obtained by 100 distinct calculations of conductance of the samedevice (post-synapse region) at each state (defined by the intra-pulse period). posed skyrmionic MML synapse is improved at RT (300K). The stability and robustness of the device can befurther enhanced by modifying the number of repeatedMML stacks and the structure of the device. To improvethe synaptic resolution of the skyrmionic synapse we usea stacked MMLs device structure with 4 repeated MMLs.This synapse can embed six discrete synaptic states withan estimated energy consumption of ∼
300 fJ per con-ductance state update event.The proposed skyrmionic synapse is firstly inte-grated in an SNN framework and used for digit recog-nition exploiting the spike-timing-dependent plasticity(STDP) rule. Using this unsupervised learning ruleour skyrmionic SNN achieves ∼
78% classification ac-curacy on the MNIST handwritten digit data set, whichis around 10% lower than ideal synapses [37]. To fullyutilize the limited precision of synaptic weights and theintrinsic merits of skyrmionic synapses (non-volatilityand energy-efficient synaptic programming), we then in-tegrate the synapses into a deep SNN architecture - afeed-forward fully connected multilayer SNN - that hasbeen shown to achieve higher performance levels thanshallow SNNs [38, 39]. Specifically, we employ a biolog-ically inspired deep SNN according to Dale’s principle[40]. The classification accuracy improves significantly( ∼ . II. NANOSCALE ROOM-TEMPERATURESKYRMIONIC SYNAPSE IN MMLS
A synapse [Fig. 1(c)] in the mammalian neocortexrefers to a specialized junction that allows cell-to-cellcommunication. It is widely accepted that the synapseplays a role in the formation of memory in the membranebrain [40]. Like the biological synapse, the schematic of askyrmionic synapse is illustrated in Fig. 1(d), composedof a pre-synapse region, a post-synapse region, and a bar-rier located in between [8, 22]. The barrier is one of themost important parts of this proposed synapse. It can beachieved by locally tuning the anisotropy in the barrierarea. It is envisaged that this could be done by voltage-controlled magnetic anisotropy (VCMA) effect [41] orion irradiation [42]. Magnetic skyrmions can be nucle-ated in FM layers and driven in the track along the x -direction, as shown in Fig. 1. In such a synapse, synapticweights are represented by the conductance of the post-synapse region measured from the magnetic tunnel junc-tion (MTJ) reading device by applying an out-of-planeperpendicular reading current [43, 44]. With appropri-ate current pulses applied (typically MA / cm ) skyrmionscan be driven around the barrier. The skyrmions are thentrapped in the post-synapse region unless a current in thereverse direction is used. The motion of skyrmions canbe controlled by a current in-plane (CIP) flowing throughthe nanotrack or by a current perpendicular to the plane(CPP) [45]. When applying a CPP, a skyrmion receivesa larger Slonczewski in-plane torque than the field-likeout-of-plane torque generated by an equal CPP currentdensity. Skyrmions obtain higher velocities under CPPfor a given current density. Therefore, in this paper, weconsider the case of CPP.The measured conductance depends upon the numberof skyrmions in the post-synapse region underneath theMTJ reading device. A magnetoresistance change is ob-tained, which is directly proportional to the number andsize of skyrmions in the post-synapse area [44]. Here, theFM layers at the reading region serve as the “free layer”of the MTJ device, while the top layer of the MTJ de-vice (blue region in Fig. 1(d)) serves as the “fixed layer”.The conductance is denoted as G skr ( G ) with the pres-ence (absence) of magnetic skyrmions. The differenceof two conductance states ( G skr , G ) can be controlledby tunneling magnetoresistance ratio (TMR). In theory,the TMR ratio can be as large as 1 , G = 20 µ Sand the TMR ratio to be 280% as demonstrated experi-mentally [47]. Therefore, variation of the conductance ofskyrmionic synapses is programmable by current injec-tions, which is similar to biological synapses.Previous work on skyrmionic synapses utilized a sin-gle FM layer on an HM layer and investigated the longterm potentiation (LTP) and long term depression (LTD)behavior of the device via simulations [8, 22]. We firstlyapply this simple structure in the skyrmionic synapse andevaluate its functionality via the micromagnetic packagemumax [48]. In order to obtain the characteristic con-ductance modulation curve of the synapse device, 10 cur-rent pulses with a 2 ns duration between 5 ns intervals areinjected into the device, which will induce the increase ofthe conductance to form the LTP. Then, another 10 cur-rent pulses in the reverse direction are applied to reducethe number of skyrmions in the post-synapse region, re-sulting in the LTD. As shown in Figs. 2(a) and 2(c),the skyrmionic synapse performs well at 0K. With theforward and reverse direction of current, we received 11distinct synaptic states (including the background state G ), leading to a pattern recognition accuracy of ∼ ∼ (cid:126)B therm = (cid:126)η (step) (cid:115) αk B Tµ M sat γ LL V ∆ t , (2)where α is the damping parameter, k B the Boltzmannconstant, T the temperature, M sat the saturation magne-tization, γ LL the gyromagnetic ratio, V the cell volume, ∆ t the time step and (cid:126)η (step) a randomly oriented normalvector whose value is changed after each time step.From the results in Figs. 2(b) and 2(d), only two dis-tinct synaptic states can be roughly identified becauseof fluctuations of the shape of skyrmions. The function-ality of the skyrmionic synapse is catastrophically lostat T = 300K. In order to stabilize RT skyrmions andhave a working skyrmionic synapse that is technologicallyrelevant, we propose a tailored MML [Fig. 3(a)] struc-ture in the skyrmionic synapse inspired by experimentalobservations [10]. The basic unit of the structure is a[HM / FM / HM ] sandwiched tri-layer. The stabilizationof skyrmions is enabled by the enhanced DMI from theasymmetric interfaces [HM / FM] and [FM / HM ] [10], asshown in Fig. 3(b). Micromagnetic simulations with[HM / FM / HM ] n for n = 2 and n = 4 are shown inFigs. 3(c) and 3(d), respectively. Compared to the sim-ple FM / HM structure reported in previous work [22, 26],skyrmions in our proposed MML synapses exhibit en-hanced thermal stability, which enables us to recoverthe characteristic conductance modulation curve of theRT skyrmionic synapses. Figs. 3(e) and 3(f) depictthe resulting synaptic weights (calculated conductance)with respect to the injected current pulses. Skyrmionicsynapses with MML ( n = 4 repeats) exhibit a broaderrange of conductance as well as more distinct and discretesynaptic states than that with MML ( n = 2). Note thatfewer synaptic states can be distinguished in skyrmionicsynapses with MML ( n = 2) due to the overlap and am-biguity among different states arising from thermal in-stabilities of skyrmions.The improvement of performance metrics of the pro-posed MML skyrmionic synapse can be attributed to twoprimary reasons: i ) larger conductance ranges and ii )more synaptic states, arising from the enhanced thermalrobustness of the multilayer device. As explained pre-viously, the synaptic conductance variation range dur-ing the LTP/LTD process is calculated via the propor-tion of the “free layer” domain anti-parallel to the “fixedlayer” domain, determined by the cross-sectional areaand the number of skyrmions, so larger skyrmions en-able a larger conductance range and greater ability todiscriminate states. We numerically constructed a seriesof half skyrmionic synapses (post-synapse region) wherethe number of repeated MMLs varies between 2, 4, 6, and8, initially set to the background FM state. Skyrmionsare injected externally into the synapse one by one viacurrent pulses, as shown in Fig. 4(a). Subsequently, thefull capacity of the synapse and the stability of skyrmionsare evaluated in these systems. Due to the contributionof magnetostatic energy [50], as the number of MMLsincreases, skyrmions with larger radii are stabilized inthe system [Fig. 4(b)]. Note that the standard deviation(SD) of the calculated conductance decreases in synapseswith more repeated MMLs, indicating the better stabil-ity of skyrmions in the system and the thus the betterstability of the skyrmionic synapse. We calculated theconductance of each state and the results are shown in FIG. 3. The proposed skyrmionic synapses composed of the MML structure. (a) Cross-sectional view of the simulation volumefor a [HM / FM / HM ] multilayer device where skyrmions assemble. Arrows point in the direction of the magnetization m ,and m z is color-coded from blue ( −
1) to red (+1). (b) Illustration of the MML structure comprised of several repetitions ofthe tri-layers, where (FM, light blue) are sandwiched between two different heavy metals HM (blue, Pt in this paper) andHM (green, Ir in this paper) that induce a net enhanced DMI vector (where HM is the underlayer, and HM is the toplayer, respectively). Results of micromagnetic simulations of the proposed skyrmion-based synaptic devices with (c) MML ( n = 2) and (d) MML ( n = 4) in realistic RT conditions. The color code (red-blue) is the same for (c) and (d). Evolution ofconductance and number of skyrmions for the post-synapse region with (e) MML ( n = 2) and (f) MML ( n = 4). Fig. 4(c). Conductance ranges from 1 . G to 1 . G in 2 MMLs by 11 discrete states, 1 . G to 1 . G in 4MMLs by 14 discrete states (the last 4 states are notdistinguishable within the error bar), 1 . G to 1 . G in6 MMLs by 9 discrete states, and 1 . G to 1 . G in 8MMLs by 6 discrete states. The skyrmionic synapse with4 MMLs has both relatively large synaptic weight rangeand largest number of distinguishable states. Note thatthe results here (14 states) are different from Fig. 3(f) (6states), because in Fig. 3(f), two skyrmions are injectedsimultaneously by each programming pulse, while herewe artificially inject skyrmions one by one.Interestingly, we also observe that the conductancemodulation curves do not fully recover to the initial stateafter the first LTP/LTD process [Fig. 5(a, b)]. This sit-uation is due to a few skyrmions being constrained in thepre-synapse (post-synapse) region no matter how many current pulses in the + x ( − x ) direction are applied. Thenumber of remaining skyrmions increases with larger bar-riers, as shown in Figs. 5(a). However, if we take the firstLTP/LTD operation as a calibration process [Fig. 5(b)],the conductance range stays unchanged during subse-quent programming operation. Therefore, we define thevalid synaptic weight range of the RT skyrmionic synapseas the conductance range during the second LTP/LTDprocess. In order to explore further possibilities for tun-ing of the synaptic resolution, we carefully modified theinterspace between the barrier and edges from 0 . D skr to2 . D skr where D skr represents the diameter of a singleskyrmion in the synapse from Fig. 4(b). The calculatedsynaptic weight range with respect to the barrier inter-space is shown in Fig. 5(c). We find that the skyrmions inthe post-synapse region will cross the barrier back to thepre-synapse region during equilibration when the barrier FIG. 4. Improvement in the device behavior as the number of MML tri-layers is changed. (a) Micromagnetic simulations ofthe post-synapse region with 1 skyrmion and full capacity of skyrmions in 2, 4, 6 and 8 repeated MMLs at RT. J e denotes theelectric current applied within the HM layer in + x direction. (b) The radius of skyrmions and the standard deviation (SD) ofcalculated conductance with respect to the number of MML obtained from micromagnetic simulations. Inset: Schematics of asingle skyrmion within MML systems with n = 2, 3, 5, 9, and 15 repeats, respectively. (c) Conductance for the post-synapseregion of the simulated synapse devices with varying MML structure as a function of the number of skyrmions hosted. interspace is larger than 1 . D skr , resulting in the down-ward trend of the second half of the curve in Fig. 5(c).A peak value of the synaptic weight range of 0 . G atbarrier interspace of 1 . D skr is obtained from the Gaus-sian fitting of the discrete data points. Therefore, theskyrmionic synapses we mainly discuss in this paper arebased on the 4 MML structure and 1 . D skr barrier inter-space unless specified otherwise, including results of Figs.2 and 3. Thermal stability can be optimized by tuningthe multilayer stack, the original nucleated skyrmion den-sity, the device size and the driving current amplitude,to ensure that the device can operate without significantskyrmion collapse.The energy consumption per synaptic update event isgiven by [22]: E update = 2 ρtlwJ T pulse , (3)where ρ is the resistivity of Pt thin film [51], l , t and w arethe length, thickness and width of the top and bottomHM layers, J the amplitude of current density, and T pulse is the duration of the pulses applied on the device, so thetotal thickness is 2 t . The programming energy to updatethe synaptic state E update in the proposed synapse is es-timated ∼
300 fJ from Eq. (3) by using the simulationparameters in Appendix A.The proposed multilayer skyrmionic synaptic device isexperimentally feasible with industrially relevant mate- rial systems at lithographically accessible length scales.Furthermore, skyrmion-based devices can be technicallycompatible with CMOS circuits in hybrid spintronic-CMOS systems such as those proposed in [22, 52], whichmay enable further integration of skyrmionic synapses inneuromorphic hardware for pattern recognition and dy-namic signal analysis tasks.
III. SKYRMIONIC SNNS FOR PATTERNRECOGNITION
To validate the functionality of the proposed RTskyrmionic synapses, we simulate a 2-layer unsupervisedSNN. We then propose that skyrmion-based systems canalso be deployed within a supervised deep SNN in orderto achieve superior accuracy in pattern recognition tasks.The input synaptic resolution (six synaptic states) andthe synaptic range (0 . G ) of the nanoscale skyrmionicsynapse are derived from micromagnetic simulations atRT [Fig. 3(f)]. The detailed illustration of the simulationset-ups can be found in Figs. 6 and 7, and Appendix B.The proposed skyrmionic synapses can be embedded intoa crossbar array [53] to connect adjacent layers of neu-rons and to provide synaptic weights in SNNs. The LIFneurons can be implemented by analog circuits demon-strated in [2]. The crossbar hardware and LIF neurons FIG. 5. Tuning the size of the barrier to improve thecharacteristic conductance modulation curves of skyrmionicsynapses. (a) Micromagnetic simulations of the skyrmionicsynapse with the barrier interspace of 1 . D skr and 0 . D skr after the 10 th current pulse in the x direction. (b) Evolu-tion of conductance and number of skyrmions of the synap-tic device with the barrier interspace of 1 . D skr during twofull LTP/LTD programming operations. (c) Synaptic weightrange as a function of the interspace between the barrier andedges. could be implemented according to [53, 54], but that isbeyond the scope of the present work.We first simulate a fully-connected 2-layer SNN in-spired from [37], as shown in Fig. 6(a). The STDP rule,which states that the synaptic weights should increase(decrease) when the pre-neuron fires earlier (later) thanthe post-neuron [55, 56], trains the SNN on 60 ,
000 im-ages of the MNIST handwritten data set using BRIAN,a Python-based simulator for neuromorphic computing[57]. The MNIST data set consists of 10 classes (digits 0 →
9) on a grid of 28 ×
28 pixels, which is widely used as astandard benchmark. Note that the proposed skyrmionicSNNs will be mainly suitable for practical applicationscenarios that deal with dynamic signals, such as sensorysignal processing, brain-machine interfaces, robot con-trol, etc. The input-layer neurons encode these 28 × ×
28) of the connections from input to excitatory neu-rons in a 20 ×
20 grid. The visually displayed patternscorrespond to the response digit classes of 400 LIF neu-
FIG. 6. The 2-layer skyrmionic SNN for unsupervised learn-ing via STDP method. (a) SNN structure for pattern recog-nition. (b) Visual representation of the synaptic weights afterthe training process in SNNs of 400 neurons with six dis-crete synaptic states (corresponding to the synaptic resolutionachievable by the MML ( n = 4) skyrmionic synapse). Darkregions: higher weight values, indicating the pattern learnedby the corresponding LIF post-neuron. (c) Classification ac-curacy of SNN on the MNIST data set as a function of thenumber of distinct synaptic states. rons. Although there are only 10 classes of patterns inthe training set, larger number of excitatory LIF neuronswill correspond to higher network performance, becausemultiple neurons are assigned to each digit class aftertraining [37]. The classification accuracy of the proposedskyrmionic SNN after training is ∼
76% and convergesafter around 100 training time steps. The trained SNNis evaluated through 10 ,
000 MNIST images, where anaccuracy of ∼
78% is obtained, which is ∼
10% lowerthan ideal synapses illustrated in [37]. The result shownin Fig. 6(c) indicates that the large number of synapticstates is highly desirable for high classification accuracy.However, more skyrmionic synaptic states require largerdevices and more programming energy, which will coun-teract the advantages of our proposed RT synapse.To gain a better performance of the skyrmionic SNNs,we then design and evaluate a deep SNN with proposedRT skyrmionic synapses. Although high-precision synap-tic weights are essential to obtain converging results dur-ing the training process, neural networks are able to op-erate with limited-precision weights during the inferenceprocess with acceptable accuracy loss [58], which is com-
FIG. 7. The supervised skyrmionic deep SNN. (a) Schematicsof the proposed biologically inspired structure of the deepskyrmionic SNN utilizing Dale’s principle. (b) Comparison ofclassification accuracy between i) skyrmionic deep SNNs withdirectly converted weights and ii) skyrmionic deep SNNs withscaled weights and thresholds, for different number of synapticstates. patible with limited precision and low power hardwareplatforms as we proposed in this work.Here, we demonstrate a prototype and basic opera-tions of skyrmionic synapses in a simple deep SNN struc-ture, which can also be further upgraded to other state-of-the-art deep neural networks [59]. The deep SNN weinvestigate consists of an input layer, an output layer,and two hidden layers. The 784 input neurons, 2 hid-den layers with 2 ,
400 neurons per layer, and 10 outputneurons are fully connected in sequence. In order to de-ploy RT skyrmionic synapses in deep SNNs, we proposea biology-inspired structure of SNNs, according to Dale’sprinciple, by doubling the number of hidden layer neu-rons and splitting synaptic weights to positive W + andnegative value W − as shown in Fig. 7(a). At the sametime, the direct conversion of synaptic weights from fullto limited precision may cause significant accuracy drop FIG. 8. Introducing an initialization pulse to reboot theskyrmionic synapse after equilibration. Micromagnetic sim-ulations for the MML ( n = 4) skyrmionic synapse (a) afterthe 5 th pulse, and then (b) after the equilibration process.The skyrmionic synapse could be rebooted (c) through aninitialization pulse and then (d) programmed via program-ming pulses. (e) Evolution of conductance modulation curvesfor the post-synapse region of the skyrmionic synapse startingfrom different synaptic states with an initialization pulse. in SNNs [58, 60]. Therefore, we also propose a conversionmethod in R.T skyrmionic SNNs: introducing a scale fac-tor σ , which significantly increases the accuracy for SNNswith low-precision weights. More details for training andconversion of the skyrmionic deep SNNs are provided inAppendix B.We simulate the deep SNN with different precision ofweights by changing the number of synaptic states to1, 3, 5, 7, 9, 13, 17, 33, 65, and + ∞ . The numberof synaptic states is given by 2 X + 1, where X is thenumber of positive and of negative synaptic weights, andthere is one zero-weight state. The negative values canbe obtained by applying a reverse voltage in the cross-bar hardware implementations [53], and the zero-weightstate can be acquired by setting the same value of W + and W − in Fig. 7(a). For example, the number of 13synaptic states consists of 6 positive, 6 negative and azero-weight state. The classification accuracy for eachweight precision is illustrated in Fig. 7(b), where theheight difference between the light grey and dark greycolumns represents the improvement in accuracy of SNNswith directly converted synaptic weights to SNNs withscaled weights and thresholds. For SNNs with directlyconverted weights, the results show that the skyrmionicsynapse should have 33 synaptic states (16 skyrmionicstates) to achieve a <
1% accuracy loss compared tothe ideal full-precision synapses. In comparison, SNNswith scaled weights and thresholds show a much fasterincrease of classification accuracy when the number ofsynaptic states increases. The accuracy exceeds ∼ ∼ .
61% classification ac-curacy with 13 synaptic states (6 skyrmionic states ofRT skyrmionic synapse), which is merely ∼ .
06% lowerthan the SNNs with ideal full-precision synapses. Theresults here demonstrate the excellent potential for theuse of the proposed skyrmionic synapses in neuromorphiccomputing, especially when deployed in deep SNNs andensuring RT operation.
IV. DISCUSSION
In the micromagnetic simulations the motion ofskyrmions is induced by a series of CPP pulses witha fixed pulse duration. We observed that, over time,skyrmions encounter greater difficulty to cross the bar-rier. With the majority of skyrmions passing over thebarrier, fewer skyrmions are left in the pre-synapse re-gion. Consequently, skyrmion-skyrmion repulsion is lesslikely to enable the crossing of the barrier, also high-lighted in [22]. Once there is a long enough time intervalbetween adjacent programming operations, skyrmionsequilibrate into a uniform distribution, resulting in a la-tency and even failure for updating synaptic weights.In order to address this problem we propose a wayto operate the device from a “cold” start. We intro-duce a small-amplitude initialization pulse before anyprogramming pulses. In the simulations, we set a cur-rent pulse with a duration of 25 ns and an amplitude of5 MA / cm (1 /
10 of the programming pulses), as shownin Fig. 8. After the implementation of the initializationpulse, skyrmions in Fig. 8(c) form a similar ensembleas during the programming process in Fig. 8(a). Sim-ulations demonstrate that this method ensures the ro-bust operation of the skyrmionic synapse, as it can berebooted from a “cold” start to recover the modulationcurve from an arbitrary initial state, as shown in Fig.8(e).Compared to CMOS-modelled memristors [61] andfloating-gate memory cells [62], the proposed skyrmionicdevices utilize the evolution/propagation of the magneticexcitations as information carriers rather than the move-ment of electrons/holes themselves. This different natureof information processing offers opportunities for energy-efficient computing and storage by harnessing topologi-cal twists in the magnetic fabric. Moreover, skyrmionicsynapses have advantages of shorter update times and rel-atively smaller cycle-to-cycle and device-to-device vari-ability compared to existing transistor-free phase change memory (PCM) devices [63] and resistive random accessmemory (RRAM) [64]. Therefore, the skyrmionic devicesare promising for applications in low-power neuromor-phic computing and inference tasks in edge computingdevices [65] (see Appendix C for a proposed scheme).Moreover, further research should be undertaken to in-vestigate the high accuracy and low power in situ train-ing of skyrmionic SNNs utilizing the on-chip surrogategradient technique [66] and the Federated Learning (FL)for collaborative inter-device learning [67].
V. CONCLUSION
In order to enable the potential of skyrmionic devicesfor neuromorphic computing, we demonstrate the stabi-lization of magnetic skyrmions at RT in MMLs tailoredfor improving synaptic resolution. In this work, we pro-pose a nanoscale multilayer skyrmionic synapse for deepSNNs. Instead of the single FM / HM device structure uti-lized in existing work, we propose a tailored MML struc-ture with repeated sandwiched stack [HM / FM / HM ],which enhances the skyrmions’ stability in order to en-sure robust RT synaptic functionality and enable inte-gration in an SNN framework. We use the number ofMMLs repeats and the size of the barrier to tune thethermal stability of skyrmions and the desired synapticprofile and resolution. We then embed the skyrmionicsynapses into SNNs to demonstrate the pattern recogni-tion. Firstly a 2-layer skyrmionic SNN is established andtrained by the unsupervised STDP method. The func-tionality of the network is evaluated utilizing the MNISThandwritten digit data set. We obtain a classificationaccuracy of ∼
78% and approximately 10% drop of ac-curacy from ideal synapses with full-precision weights.To fully exploit the limited-precision weights and the in-trinsic merits of RT MML skyrmionic synapses, we inte-grate the skyrmionic synapse into a deep SNN. A highclassification accuracy of ∼ .
61% is achieved with sixskyrmionic synaptic states obtained from the proposedRT MML ( n = 4) skyrmionic synapses. The emulationof deep SNNs with our proposed RT skyrmionic synapsesenables wider possibilities for energy-efficient hardwareimplementations to perform neuromorphic computing. ACKNOWLEDGMENTS
RC and YL wish to acknowledge the China ScholarshipCouncil (CSC) and the University of Manchester for thefunding support.
Appendix A: MICROMAGNETIC SIMULATIONS
The micromagnetic simulations were performed us-ing the GPU-accelerated micromagnetic programme0 mumax . The time-dependent magnetization dynam-ics are described by the Landau-Lifshitz-Gilbert (LLG)equation. d m dt = −| γ LL | m × h eff + α m × d m dt + ut m × ( m p × m ) , (A1)where m = M /M s is the reduced magnetization, M s is the saturation magnetization, γ LL is the gyro-magnetic ratio, h eff = H eff /M s is the reduced ef-fective field, α is the damping parameter, t is thethickness of the FM layer, and m p is the polariza-tion direction. The energy density contains the ex-change energy term, the anisotropy energy term, theZeeman energy term, the magnetostatic energy termand the DMI energy term. We consider a tailoredsandwich structure of [HM / FM / HM ] n with perpen-dicular magnetic anisotropy and interfacial DMI. Theinput material parameters to perform the simulationsare chosen according to the reported experimental re-sults [10]. Damping parameter α = 0.1, DMI con-stant D ins = 1 . · m − , Gilbert gyromagnetic ratio γ LL = − . × mA − · s − , saturation magnetiza-tion M s = 956 kA · m − , the uniaxial out-of-plane mag-netic anisotropy K u = 717 kJ · m − , and the exchangestiffness A = 10 pJ · m − . The spin Hall polarizationΘ SH is chosen as 0.6 following Refs. [8, 22]. An exter-nal magnetic field of 80 mT in the out-of-plane direc-tion is applied. A higher magnetic anisotropy K u , high =860 kJ · m − is set for the barrier of the device. Thesize of the whole device is 800 nm ×
220 nm × n nm(where n denotes the number of repeated MML). In or-der to ensure the accuracy of calculation, the mesh sizeis set to 2 nm × × l ex = 2 (cid:112) A/ ( µ M s ) = 5 . l DMI = 2
A/D = 11 .
77 nm. In our multilayers,the intermediate HM and HM layers are thinner thanthe spin diffusion length. In this case the torques wouldbe efficient only in the external layers [68]. In this workthe spin orbit torque (SOT) created via CPP is appliedonly in the first bottom and the first top layers and theinjected spin polarization is uniform in these two layers.The injected current is then modeled as a fully polar-ized (along + y direction) vertical spin current of currentdensity J = 30 MA · cm − . Appendix B: SNN SIMULATIONS ON THEMNIST DATA SET
For the simulation of the unsupervised skyrmionicSNN, we utilized Python and the BRIAN simulator [57].For the MNIST pattern recognition, we simulated a 2-layer SNN (784 neurons as input layer and 400 neuronsas excitatory layers) on BRIAN inspired by [37]. Theproposed skyrmionic SNN updates synaptic weights by adiscrete STDP process adapted from [37], which meansthe weights are modified to the adjacent synaptic valuewithin the six synaptic states in Fig. 3(f) during training
FIG. 9. Conversion and training of skyrmionic deep SNNs.(a) Weight distributions for the full-precision weights in the4-layer ANN before and after training, and directly convertedlow-precision weights with 13 discrete states. (b) By usingDale’s principle, we re-scale and map the weights into thedeep SNN with six discrete synaptic states obtained at RTby the MML ( n = 4) skyrmionic synapse. The negative valuemarked as red columns in the left can be obtained by applyinga reverse voltage in the crossbar hardware implementations. iterations. The skyrmionic SNN is trained with 60 , ,
000 images.With respect to the simulation of the supervisedskyrmionic deep SNN, the proposed network is obtainedthrough the technique of ANN-to-SNN conversion, whichconsists of three steps: i ) We first train a 4-layer ANNwith full-precision weights. ii ) We then directly convertthe weights of the trained ANN to low-precision synapticweights with 13 states [Fig. 9(a)]. iii ) Finally, in orderto map the weights into six discrete synaptic states ob-tained at RT by the MML ( n = 4) skyrmionic synapse,we re-scale the synaptic weights via tuning the hyper-parameters of SNNs (e.g. neuron thresholds).We utilize the DeepLearn Toolbox on Matlab for thetraining of the ANN, where layers are fully connectedby the weight matrices W , W , and W , respectively[Fig. 7(a)]. The value of weight matrices is initializedrandomly between − . . W , W , and W which connect the four layers L , L , L , and L of the SNN in Fig. 7(a). The input is repre-sented as R and is fed into L to determine whether neu-rons fire or not. In the structure shown in the lower partof Fig. 7(a), the number of neurons in the input layer andtwo hidden layers is doubled, which forms the neurons L +1 , L − , L +2 , L − , L +3 , and L − . Meanwhile, the neuronsin the output layer keep unchanged as L . The inputs R + and R − are fed into L +1 and L − , respectively, with thesame value as R. The weight matrices W , W , and W are split to positive weight matrices W +21 , W +32 , and W +43 and negative weight matrices W − , W − , and W − withidentical size. The value of weights is within the range ofskyrmionic synaptic weights { [ − . , − . , [1 . , . } , asshown in Fig. 9(b).The proposed rescaling method [Fig. 9(b)] comes fromthe idea that the accuracy loss before and after conver-sion is due to the mismatch of synaptic weights. For ex-ample, most weighs are distributed in the range between − . . n = 4) skyrmionicsynapse range between − . .
6. This mismatchcould be eliminated by scaling the directly convertedlow-precision weights to a proper weight range, wherethe stored critical information could be adequately rep-resented in low-precision synapses. Therefore, a scaledfactor σ = 0 . / . σ and finding the value ofthe scaled factor achieving the highest accuracy. Notethat the dark grey columns in Fig. 7(b) show the clas-sification accuracy with the appropriate scaled factor σ applied on the thresholds of neurons in each layer. Appendix C: SKYRMIONIC DEEP SNN FOREDGE COMPUTING
The non-volatility, nanoscale footprint, energy-efficiency of the proposed skyrmionic synapse and theability to operate at RT make it suitable for intelligent edge devices that can perform low-power and accurateneural networks inference such as pattern recognition andspeech recognition. In edge devices, the power supply canbe limited. Therefore, only neural networks with highenergy-efficiency both on the programming and internetof things (IoT) inferring aspects can be supported.
FIG. 10. Skyrmionic deep SNNs for edge computing.Schematic shows a possible scenario of use. The proposedskyrmionic deep SNN can be integrated into a framework con-cept where training takes place in the cloud and updating atthe edge. The process is an iterative full-precision training tolow-precision conversion cycle: i ) full precision cloud-basedonline training and ii ) skyrmionic devices low-energy updat-ing with offloaded low-precision synaptic weights. Here we propose a scenario of possible use of theskyrmionic synapses in an intelligent edge terminal, e.g.a smart wrist band to monitor the body blood pressuredeployed in a deep SNN framework. The training is ac-complished using the standard SGD back-propagationmethod with full precision weights. 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