Weihao Li(李伟浩) Xiukai Lan(兰修凯) Xionghua Liu(刘雄华)Enze Zhang(张恩泽) Yongcheng Deng(邓永城) and Kaiyou Wang(王开友)

1State Key Laboratory for Superlattices and Microstructures,Institute of Semiconductors,Chinese Academy of Sciences,Beijing 100083,China

2Center of Materials Science and Optoelectronics Engineering,University of Chinese Academy of Sciences,Beijing 100049,China

3Beijing Academy of Quantum Information Sciences,Beijing 100193,China

4Center for Excellence in Topological Quantum Computation,University of Chinese Academy of Sciences,Beijing 100049,China

Current-induced multilevel magnetization switching in ferrimagnetic spintronic devices is highly pursued for the application in neuromorphic computing. In this work, we demonstrate the switching plasticity in Co/Gd ferrimagnetic multilayers where the binary states magnetization switching induced by spin–orbit toque can be tuned into a multistate one as decreasing the domain nucleation barrier. Therefore, the switching plasticity can be tuned by the perpendicular magnetic anisotropy of the multilayers and the in-plane magnetic field. Moreover, we used the switching plasticity of Co/Gd multilayers for demonstrating spike timing-dependent plasticity and sigmoid-like activation behavior. This work gives useful guidance to design multilevel spintronic devices which could be applied in high-performance neuromorphic computing.

Keywords: switching plasticity,compensated ferrimagnet,spin–orbit torque,spike timing-dependent plasticity,sigmoidal neuron,handwritten digits recognition,neuromorphic computing

1. Introduction

Neuromorphic computing inspired by biological brain is getting increased attention attributing to ultralow-power compared to the traditional computers.[1–3]The nonvolatile neurons and synapses can process datain situ, which avoids the unnecessary energy cost of the data movement between different modules.[4]Besides, neuromorphic computing not only aims to achieve significant energy saving but also attempts to improve the efficiency during performing complex tasks including cognition, control, movement, and decision making.[5,6]Although various artificial neural networks algorithms have been developed in recent years, the lack of dedicated hardware still limits the application of neuromorphic computing.[7]Recently,spintronic devices have exhibited great potential in neuromorphic computing,[8–19]since they can simulate the functions of neurons and synapses, such as nonlinearity,[9]stochasticity[8,20]and nonvolatility.[1,21]Moreover, the fast dynamics[22,23]and virtually unlimited endurance make them stand out from other competitors including phase-change,[24,25]floating gated[26]and resistive memory[6]devices.

Compensated ferrimagnets offer the combined advantages of both ferromagnets and antiferromagnets,namely,the rich methods of manipulation and/or detection of their magnetization,ultrafast and energy-efficient spin–orbit torque(SOT)switching.[22,27–29]These advantages make them promising candidates for neuromorphic computing devices. In spintronic-based neuromorphic computing, the multilevel spintronic devices based on domain-wall (DW) motion generated multi-resistance states have been used to emulate biological synapses.[30–32]However, the stochastic nature of the DW pinning and depinning relying on the defects may limit the performance of the devices. Thus, searching for wellcontrolled methods to allow a binary ferrimagnet to realize tunable current-induced multilevel magnetization switching behavior is one of the vital issues. Recently,the tunable multilevel SOT-induced magnetization switching by adjusting the magnitude of in-plane magnetic field or current pulse with a built-in in-plane magnetic field has been observed in a ferromagnet system which suggests the plasticity of switching behavior.[18,33]However, as far as we know, few works on the switching plasticity in ferrimagnets have been reported,[23]which is certainly an urgent topic to promote the application process for spintronic-based neuromorphic computing.

In this work, we perform experiments with perpendicular magnetic anisotropy(PMA)Co/Gd ferrimagnetic multilayers under various AlOxthickness. Both the Co and Gd layers are atomically thin, and their moments are coupled antiferromagnetically to form an artificial compensated ferrimagnetic structure. We demonstrate the switching plasticity in the Co/Gd compensated ferrimagnetic multilayers,that is,the binary switching characteristic can be tuned into a multi-state one as the domain nucleation plays a more dominating role during the magnetization switching. The magnitude of the domain nucleation barrier is dependent on the PMA of the multilayers and the external in-plane magnetic field. The excellent switching plasticity gives the ferrimagnets great potential for various neuromorphic computing applications. On the one hand, we demonstrate the spike timing-dependent plasticity(STDP)using the multilevel switching of the Co/Gd compensated ferrimagnetic multilayers.On the other hand,we demonstrate that a three-layers neural network using ferrimagnetic neurons can well recognize patterns in Modified National Institute of Standards and Technology (MNIST) database with accuracy more than 97%. Our work could provide useful information for designing future high-performance spintronicbased neuromorphic computing devices.

2. Method

The schematic stack structures,as shown in Fig.1(a),Ta(1)/Pt(5)/[Co(0.36)/Gd(0.34)]6/Pt(1)/AlOx(t)(thickness in nm)witht=0,0.5,1,1.5,and 2.0 were sputtered on Si/SiO2substrates by direct and alternating voltage sources at room temperature. The base pressure of the chamber was less than 1×10-8Torr, and the argon pressure was set as 2 mTorr for AlOxand 0.8 mTorr for other targets during deposition. Subsequently, the samples were patterned into Hall bars devices with channel widths of 10 μm by standard photolithography and Ar-ion etching.

3. Results and discussion

Firstly,we measured the anomalous Hall effect resistance(Rhall)under an out-of-plane magnetic field(Hz),as shown in Fig.1(b). A small current of 0.1 mA was used to measure the magnetic state of the device.It is worth noting that all samples with different AlOxthicknesses(t)exhibit square-shaped magnetic hysteresis loop, indicating that the magnetization easy axis is along thezdirection. The hysteresis loops show a positiveRhallpolarity,which reflects that the magnetization in the films is Co-riched since the anomalous Hall effect resistance is dominated by Co in the Co–Gd system.[34]Notably,the magnetic hysteresis loops show a gradual switching behavior with increasing the thicknesses of the AlOxlayer to 2 nm,indicating the switching plasticity in the Co/Gd multilayers.

Subsequently,the switching plasticity in the Co/Gd multilayers under various in-plane and PMA field was systematically investigated in Fig.2. The pulsed current of width 10 ms was applied and then we measured theRhallafter each pulse at a low current of 0.1 mA.Figure 2(a)shows the magnetization switching driven by SOT under different in-plane fields(Hx)for the device with AlOxthickness of 1 nm. The squareness and switching ratio(ΔRRatio)of magnetization switching loops decrease with the increase ofHx,and the number of intermediate states increases. Here,ΔRRatiois defined as the ratio of current-induced maximum change in Hall resistance to field-induced maximum change in Hall resistance. This phenomenon is also observed in other samples. Moreover,we set the magnitude ofHx=800 Oe in all samples to check the impact of the AlOxthickness,as presented in Fig.2(b).

Fig.1.(a)The schematic Hall device with stack structures of Ta(1)/Pt(5)/[Co(0.36)/Gd (0.34)]6/Pt (1)/AlOx (t). (b) Anomalous Hall resistance Rhall as a function of perpendicular magnetic field Hz for various AlOx thickness.

Similarly, the samples with thicker AlOxare inclined to obtain multilevel magnetization switching behavior with a lower ΔRRatiounder the same in-plane field. The increasing AlOxthickness would reduce the effective PMA field of the device, which is because the strong interfacial 3d–5d hybridization in Co/Pt is weakened by the Pt/AlOxinterdiffusion.[35,36]Then, we determine the effective PMA field (Hk) of Ta(1)/Pt(5)/[Co(0.36)/Gd(0.34)]6/Pt(1)/AlOx(t)by fitting the in-plane field dependence of the in-phase first harmonic Hall voltage. In addition,the damping-like effective field of Ta(1)/Pt(5)/[Co/Gd]6/Pt(1) is estimated by harmonic Hall voltage analysis, and the SOT efficiency is calculated to be 25 Oe/(1×107A·cm-2)(see the supporting information for details). TheHkas a function of the AlOxthickness is summarized in Fig.2(f),which clearly shows the magnitude ofHkdecreases with increasing the AlOxthickness. The magnetic moment of the samples with higher ratio of|Hx|/Hkwould tilt away from thezdirection corresponding to a larger angle(θM),leading to a lower switching ratio in Figs.2(a)and 2(b). Besides,a fatter switching curve is obtained accompanying with a lower ΔRRatio(corresponding to a greater tilting angleθM).Thus,the relationship between the switching behavior and the tilting angleθM(∝|Hx|/Hk)needs to be further explored.

Then, we fixed the value ofHx/Hk≈0.5 to check the impact ofHkon current-induced magnetization switching behavior, as presented in Fig. 2(c). The intermediate sates increase with increasing the thickness of AlOx(corresponding to a lowerHk). However,the switching ratio is roughly the same for all samples. Then we use ΔIto qualitatively evaluate the number of the intermediate magnetization states,which corresponds to the current range covering full ΔRhall,as functions ofHxand AlOxthickness.As clearly shown in Figs.2(d)–2(f),ΔIincreases nonlinearly with higherHxand thicker AlOx,which also indicates the switching behavior can be tuned by the inplane magnetic field and/or effective anisotropy field. The broader current range accompanied by more multi-resistance states is useful for neuromorphic computing applications. Besides,the linearity of ΔIregulated byHxandHkis summarized in the supporting information.

In this section,we will go deep into the experimental phenomena and explain the switching plasticity which first shows sharp switching characteristic(binary state)then tunes to gradual switching one(multilevel)under increasing in-plane field.In general, magnetization switching takes place through DW propagation and domain nucleation.[37–39]It was verified experimentally that magnetic stripes with N´eel-type chiral domain walls show sharp switching characteristics.[40]Compared to domain wall propagation, the nucleation switching induced by SOT is prone to provide gradual switching behavior, since they naturally form the basis of intermediate states.[17,33]The domain nucleation can be understood from an energy perspective. The probability of nucleation is proportional to e-Eb/kBT,[33]whereEb,kB, andTare the nucleation energy barrier,Boltzmann constant,and the temperature,respectively.Ebhas a spatial distribution across the sample which follows the normal distribution statistically. A higherHkbrings a higher energy barrier for domain nucleation while the in-plane fieldHxcan reduce the barrier.[33,41]Thus, the switching behavior depends on the magnitudes ofHkandHx,as presented in Fig.2. Moreover,the switching plasticity can also be explained by comparing the DW propagation field and nucleation field(see the supporting information for details).

After systematically studying the dependence of switching plasticity on the in-plane and PMA field, we then investigate how to use the plasticity of the magnetization switching for neuromorphic computing. Artificial neural networks(ANNs) and spiking neural networks (SNNs) are two important and complementary branches in neuromorphic computing with different advantages in dealing with practical tasks.[42]In the following section, the multi-level switching devices with excellent switching plasticity are exploited for both SNNs and ANNs.

Fig. 2. (a) Pulsed current-driven Rhall–I SOT switching loops under various Hx in Ta/Pt/[Co/Gd]6/Pt/AlOx (1). Rhall–I SOT switching loops with different AlOx thickness for Hx =800 Oe (b) and Hx/Hk ≈0.5 (c) respectively. Tunable current range (ΔI) versus in-plane field Hx (d) and AlOx thickness for Hx=800 Oe(e). (f)AlOx thickness dependence of the current range ΔI and PMA field Hk for Hx/Hk ≈0.5. The inset in(d)presents the current range ΔI we defined.

A synapse in SNNs builds the connection between the pre-neuron and post-neuron and its weights are updated when spikes and/or action potentials from the pre-neuron propagate to the post-neuron through the synapses. Moreover, the synaptic weight update rule depends on the delays between the spikes arriving from the pre-and post-neuron,which is known as STDP found in real biological synapses.[43]Figure 3(c)shows the dependence of the weight (Rhall) with the amplitude of current pulses in our CoGd-based artificial synapse.The existence of well-defined current thresholds beyond which switching between low and highRhallstates occurs making it possible to implement STDP in our device. Based on the current pulseIdependence on theRhall, spikes as shown in Fig. 3(b) are designed for realizing the STDP in our device.Before the application of each single spike,a sequence of current pulses with decreasing amplitudes and alternating polarities was applied (e.g., +28 mA→-27.5 mA→+27 mA→···→-1.5 mA→+1 mA→-0.5 mA)to achieve a zeroRhallstate. When pre-and post-neuron spikes reach the CoGd multilayers with a delay Δt, their superposition produces the waveforms (Ipre-Ipost) displayed in the inset of Fig. 3(d)(waveforms with various Δtcould be found in the supporting information). We measure the change ofRhallproduced by pairs of spike 1 and 2 with the time delay from-12 ms to 12 ms. Finally,the STDP window based on ferrimagnet artificial synapse is obtained where the weight(|ΔRhall|)decreases with increasing|Δt|,as shown in Fig.3(d). It obviously shows that the form of STDP can be tuned by the shape of spikes.We note that the symmetry of the STDP form is invariable under differentHxandHkas shown in Fig.2,hence the symmetry of the spike synapse is also retained.Notably,the performance of a certain learning procedure is highly dependent on the form of STDP in a spike neural network. Therefore,the form of STDP can be used to emulate various types of pre-and post-neuron activities.[44,45]

On the other hand, the nonlinear switching behavior of the ferrimagnetic multilayers makes it possible to construct a sigmoid neuron for an artificial neural network. Figure 4(a) shows the evolution of minor switching loops for Ta/Pt/[Co/Gd]6/Pt/AlOx(2) underHx=-500 Oe by limiting the maximum pulsed current, and the presence of the minor loops indicates the intermediate magnetization states are nonvolatility. Then we select one of theRhall–Icurves (from-5 mA to 30 mA) in Fig. 4(a) to construct an artificial sigmoid neuron as an activation function for neural networks,as shown in Fig.4(b). The inputXis transformed to a currentIapplied into the devices,thenRhallis measured to represent the outputY. It is worth noting that a single SET pulse is required if a subsequent current pulse is higher than the previous one(I ＞I0), however, an additional RESET pulse before the set pulse is needed to avoid the minor switching loops,as shown in Fig. 4(a). A modified sigmoid function is used to fit the experimental dates:Y=1/[1+e-(X-X0)/K],whereKandX0represent the slope and the rising point of the function,respectively.

Fig.3. (a)The illustration of CoGd-based artificial synapse. Spikes(blue)propagate between the neurons via synapses. (b)Two engineered spikes with different shapes named as spike 1 and spike 2,arriving from the pre-neuron and post-neuron.(c)Single-pulse Rhall–I SOT switching loop displays clear current threshold(Ith)for Ta/Pt/[Co/Gd]6/Pt/AlOx(2)under Hx=-500 Oe. (d)Measurement of STDP generated with spike 1 and spike 2. The device was demagnetized before each spike applied.

Fig. 4. (a) Minor switching loops (Rhall vs. I) with different maximum pulsed current (Imax) under Hx =-500 Oe. The current range is sweeping from -30 mA to Imax. (b) The normalized Rhall (output Y) as a function of pulsed current I (input X). (c) Three layers of neural network structure for handwritten digits recognition task. (d)Pattern recognition accuracy and(e)loss as a function of training iteration for an ideal sigmoid function(simulation)and experiment dates(live).

In order to evaluate the performance of the inference using the sigmoidal compensated ferrimagnetic neural,we construct a feed forward neural network based on gradient descent algorithm,[17,19]as presented in Fig.4(c). It consists of three layers: an input layer of 784 neurons, a hidden layer of 100 neurons and an output layer of 10 neurons. Here,the MNIST handwritten pattern dataset consisting of labeled 60000 training examples and 10000 labeled testing samples is utilized as the written digit dataset. Figure 4(d)shows the recognition accuracy as a function of training iteration for experimental dates and ideal sigmoid function shown in Fig.4(b). It is worth noting that our neural network based on Co/Gd multilayers neurons can achieve a high recognition accuracy of 97.7%,which is very close to the ideal software simulation (97.8%). The respective values of loss decrease quickly toward saturation,as shown in Fig. 4(e). Besides, the recognition accuracy is roughly independent of the in-plane field (see the supporting information for details). These training results prove the validity of our spintronic artificial sigmoidal neuron.

4. Conclusion

In summary,we have unambiguously tuned the switching behavior between binary state and multistate in Co/Gd multilayer. We find that the switching plasticity can be controlled by the nucleation energy barrier. Lowering the PMA and/or applying an in-plane field can lower the nucleation energy barrier, it thus can result in multilevel magnetization switching. We further used the switching plasticity for demonstrating neuromorphic computing. We demonstrate that the multilevel magnetization states in Co/Gd multilayer can not only act as a synapse to achieve spike timing-dependent plasticity,but also can as a neuron with sigmoid-like activation behavior.We have simulated an ANN to perform the pattern recognition tasks with an accuracy rate over 97%. Thus, the switching plasticity in compensated ferrimagnets not only provides useful guidance to design multistate spintronic devices, but also opens the prospective door for future high-performance neuromorphic computing.

Acknowledgements

This work was supported by Beijing Natural Science Foundation Key Program (Grant No. Z190007), Beijing Natural Science Foundation (Grant No. 2212048), the National Natural Science Foundation of China (Grant Nos. 11474272,61774144, and 12004212), and the Chinese Academy of Sciences(Grant Nos.QYZDY-SSW-JSC020,XDB28000000,and XDB44000000).