Multilayer Ferromagnetic Spintronic Devices for Neuromorphic Computing Applications

Spintronics has gone through substantial progress due to its applications in energy-efficient memory, logic and unconventional computing paradigms. Multilayer ferromagnetic thin films are extensively studied for understanding the domain wall and skyrmion dynamics. However, most of these studies are confined to the materials and domain wall/skyrmion physics. In this paper, we present the experimental and micromagnetic realization of a multilayer ferromagnetic spintronic device for neuromorphic computing applications. The device exhibits multilevel resistance states and the number of resistance states increases with lowering temperature. This is supported by the multilevel magnetization behavior observed in the micromagnetic simulations. Furthermore, the evolution of resistance states with spin-orbit torque is also explored in experiments and simulations. Using the multi-level resistance states of the device, we propose its applications as a synaptic device in hardware neural networks and study the linearity performance of the synaptic devices. The neural network based on these devices is trained and tested on the MNIST dataset using a supervised learning algorithm. The devices at the chip level achieve 90\% accuracy. Thus, proving its applications in neuromorphic computing. Furthermore, we lastly discuss the possible application of the device in cryogenic memory electronics for quantum computers.


Introduction
2][3][4][5] In particular, owing to the different operating behaviours such as binary-deterministic, 6-8 stochastic [9][10][11][12] and analog resistance, 13,14 these devices are proving to be quite promising for neuromorphic computing applications.8][29] But to the best of our knowledge, not much effort has been made in employing these systems for neuromorphic computing.Considering the interesting physical phenomenon in these systems thus, the associated emerging device characteristics.In this paper, we present the experimental and micromagnetic realization of a spintronic device exhibiting discrete resistance states.The discreteness of the device behavior increases as we lower the temperature and for 100K temperature, 15 resistance states are observed.We attribute this discrete resistance behaviour to the magnetic domain wall pinning/depinning and gradual switching of different magnetic layers at low temperatures.The discrete resistance behavior is also observed in the micromagnetic simulations of similar crossbars of different widths.Furthermore, the evolution of resistance states with current pulses providing spin transfer and spin-orbit torque is also explored in experiments and simulations.Using the multi-level resistance state of the device, we propose its applications as a synaptic device in hardware neural networks and study the linearity performance of the synaptic devices.We map these resistance states to the weights of a neural network architecture.The network based on these devices is trained and tested on the MNIST dataset using a supervised learning algorithm.The system shows the accuracy performance up to 90% which is comparable to the majority of the beyond CMOS synaptic devices.The discrete resistance states across the range of temperatures open a possible application of these devices in cryogenic electronics for quantum computers.

CoF eB
Hall Resistor Model

Results and discussion
The fabricated crossbar spintronic devices based on the magnetic heterostructure are shown in Fig. 1 Likewise, the switching field keeps on increasing from 21 mT to for lower temperatures and switching becomes more gradual with each resistance state separated by discrete steps.The discrete behavior and gradual switching are attributed to the fact that on lowering temperature the saturation magnetization and anisotropy start increasing.This increases the stary field effects and the domain wall pinning to the edges.The thermal effects are high which reduces the domain wall pinning effect at this temperature.We observe discrete resistance states as all magnetic layers switch simultaneously at a 40 mT magnetic field.As we lower the temperature the anisotropy and saturation magnetization increase which increases the switching field as well as the stary field effect on different layers.Moreover, the thermally activated depinning is lowered resulting in the emergence of more discrete states as shown in Fig. 2. For the temperature T = 120 K we obtained 11 discrete resistance states as shown in Fig. 2(b).The ON/OFF ratio or memory window obtained of the devices is around 66 which is quite better compared to other spintronic devices where ON/OFF is around 3. Fur-thermore, the achieved ON/OFF ratio provides a reliable synaptic application of the device.
In Fig. 2  and sharp increase of RXY with increasing RXX, which is expected.But the discrete jumps indicate the increasing stray field effects at lower temperatures on the different ferromagnetic layers.Thus, pinning/deppining is increasing with lowering temperatures.
We furthermore simulated similar and scaled crossbars in the micromagnetic software MuMax. 30,31The simulation parameters such as saturation magnetization and anisotropy were taken from the experimental results (VSM).The parameters and simulation details are given in the In simulations, we considered crossbar nanotrack width from 100 nm to 300 nm in intervals of 50nm.When perturbed by the external magnetic field ranging from (-5000 Oe to 5000 Oe) we observe discrete magnetization switching for all the nanotrack widths.
The discrete magnetization behavior is most dominant for the lowest width W = 100 nm.
For the nanotrack length L = 1 um, 5 stable discrete magnetization states were observed as shown in Fig. 3(a).As the width increases the magnetization discrete switching behavior starts fading.Although 4 discrete states are observed for W = 250 nm, the switching field gap between the states is reduced.In 250 nm the magnetization switching is gradual whereas in 100 nm nanotrack, the magnetization switches in sharp steps as shown in Fig. 3(a).
In corresponding magnetization textures obtained from the simulations, we observe switching from stipe domains to stable skyrmions as the field changes.Fig. 4 shows the magnetization profile of the single FM layer at the different switching points.At zero magnetic field the  stripe domains are pinned to the track edges, With the application of the external magnetic field in the Z-axis we observe the depinning and stabilization of the skyrmions taking place.
The numbers [(1) to ( 6)] show the discrete switching points as shown in Fig. 3 and 4. For cases (1), ( 2) and ( 3) we see normalized magnetization switching from 0 to 0.7 while from ( 4) to ( 6) the normalized magnetization reaches a value of 0.9.Corresponding to switching points (1), ( 2) and ( 3) we observe the depinning and conversion of stripe domains into the skyrmions.This accounts for the maximum change (about 77%) in the magnetization of the device.After switching point (3) the skyrmions are stable and the external field reduces the size of the skyrmions as seen in the corresponding texture in Fig. 4 [( 4), ( 5) and ( 6)] and in Fig. 5.This increases the magnetization more linearly and overall change is about 23%.The skyrmion radius calculated using nearest linear interpolation reduces gradually from R = 10.92 nm to R = 4.64 nm.
The magnetic field ranging from (-5000 Oe to 5000 Oe) is applied perpendicular to the de-

Multilayer Spintronic Synapse
We repeat the hysteresis simulation to check the feasibility of using these multilayer spintronic devices as the synapses.As shown in Fig. 7(a) the measurement was repeated three times for the different temperatures to check the repeatability of the discrete resistance be- Where ρ 0 is the ordinary Hall resistivity which has negligible contribution in the magnetic materials, and second is the anomalous Hall resistivity.The third term represents the topological Hall resistivity added by the skyrmions and can be considered to have a very small contribution.
The emergent magnetic field is given by 32 Leading to topological resistivity The other method of reading the device is by tunnel magnetoresistance TMR.Depending upon the magnetization profile the resistance of the MTJ is given by, 33 Where R AP /R P are the antiparallel/parallel resistances and m/ mP is the free layer/pinned layer normalized magnetization.In micromagnetic simulations the current pulses with amplitude J c = −5 × 10 11 Am −2 , pushes the domain wall in the +x direction whereas the DW motion direction is reversed for J c = +5 × 10 11 Am −2 .Depending upon the DW position the net magnetization of the device varies which leads to the variation in the resistance of the device.Depending upon the reading mechanism [AHE -Eqn.1] We compute the resistance by mapping magnetization to the measured resistance.We further consider the [TMR-Eqn.4] reading to compute the synapse conductance evolution.The magnetization potentiation/depression of the 15layer and 20-layer synaptic device, with current pulses is shown in Fig. 8(a-b).When the DW starts moving away from the left edge, at the beginning we observe fast magnetization evolution because DW is going away from the edge which results in reduced demagnetization energy density, thus increased DW velocity.As the DW reaches the center reaches a minimum and with more current pulses Demagnetization energy starts gradually increasing until we reverse the current, this results in a sudden drop in the demagnetization energy due formation of a full Bloch DW in the perpendicular direction as shown in Fig. 8(d-e).On the application of J c = −5 × 10 11 Am −2 the demagnetization energy is minimized by the twist in the perpendicular axis, we observe the bottom 10 layers to be stable whereas the top 10 layers form an incomplete Bloch DW.For J c = +5 × 10 11 Am −2 the DW gains full rotation, and more layers flip such that the first 6-7 bottom layers are stable and the remaining 13 layers form a full Bloch DW, as clearly depicted in the contour plot of the cross-section in  For the same writing current density, and time, the performance of a 20-layer device is better.Thus, demagnetization energy can be utilized for reducing the writing energy dissipation in these multilayer devices.As seen in Fig. 10(a) the conductance/resistance switches sharply at the beginning of the positive current due to reduced demagnetization energy density, followed by the gradual switching as DW approaches the edges.This leads to the increased non-linearity NL of the synapse.We compute the NL by using the following methodology, Where, G LTP is the synaptic conductance, G min is the minimum conductance and G max is the maximum conductance achieved by the device, α is the non-linearity fitting parameter, P M is the maximum pulse number, β is the function of G min , G max , α and P M .To improve the linearity of the device, we propose varying pulse schemes as shown in Fig. 10    Multilayer Spintronics Devices as Cryogenic Memory for Scalable Quantum Computing Although Quantum Computers (QC) have seen a huge leap in development recently, the realization of a scale and compact QC is still a Challenge.The typical QC system has three major sub-systems Quantum substrate (q-bits), the control processor and a memory block.
Normally the q-bits are placed at a few mT temperatures while the control processor is placed at room temperature (300K).The two blocks are connected by the long control cables which work fine for a few q-bit systems.But this system faces scaling issues as for an increased number of q-bits the control cables have to increase.To overcome this issue the best option that has been explored is to keep the control processor (superconducting) at 4K itself as shown in Fig. 13(a). 35This scheme further demands the cryogenic memory to reduce thermal leakage.The other option is to consider a hierarchical system as shown in Fig. 13(a), which shows cryogenic memories at different temperatures.Considering the discrete resistance states sown by the fabricated device We propose an interesting idea where the multilayer spintronic devices having discrete resistance states could be used as the cryogenic memory for scalable QC systems of the future.Interestingly, we have shown a multilayer spintronic device exhibiting 6 states at 2K, 11 states at 60K, 11 states at 120K and finally 2 states at 300K.So, at low temperatures, the fabricated device can be used to store multiple control bits on a single device which is highly desirable considering the cooling system requirements needed for these memories.Moreover, the same device as memory across the ladder should reduce the issues of integration.We can anticipate a future hybrid computing system that involves a QC, cryogenic neuromorphic systems based on these memories and a CMOS system.
were defined using photolithography and lifted off by immersion in acetone with ultrasonic processing for 5 mins.

Characterization and Imaging
The magnetic characterization of the samples for thickness optimization was done using normal vibration sample magnetometry (VSM) at room temperature.After VSM we performed the imaging of the samples with multi-domain magnetic characteristics using magnetic force microscopy (MFM) based-Dimension Icon SPM.For probing we used CoIr coated MFM tip provided by Bruker Inc.The Hall measurements were done using a standard Hall measurement system Quantum Design PPMS capable of applying dc magnetic fields.We measured the crossbar devices at temperatures ranging from (2K to 300K) and at different magnetic fields depending upon the temperature.Lastly, a signal generator was used to supply voltage pulses through the MTJ, and an oscilloscope was used to measure the output voltage response of the devices.

Micromagnetics
Magnetic skyrmions are described using their topological or skyrmion number Q, calculated as follows 36 The spins projected on the XY-plane and normalized magnetization vector m can be determined by the radial function θ, vorticity Q v and helicity Q h : The vorticity number is related to the skyrmion number as follows: r→∞ cos(θ(r)) − cos(θ(0)) (10)   Micromagnetic simulations were performed using MuMax having the Landau-Lipschitz-Gilbert (LLG) equation as the basic magnetization dynamics computing unit.The LLG equation describes the magnetization evolution as follows: where m is the normalized magnetization vector, γ is the gyromagnetic ratio, α is the Gilbert damping coefficient, and is the effective MF around which the magnetization process occurs.The total magnetic energy of the free layer includes exchange, Zeeman, uniaxial anisotropy, demagnetization, and DMI energies.
where A is the exchange stiffness, µ 0 is the permeability, K u is the anisotropy energy density, H d is the demagnetization field, and H ext is the external field; moreover, the DMI energy density is then computed as follows: The spin-orbit torque is then added in the form of modified STT in MuMax.where θ SH is the spin Hall coefficient of the material, j is the current density, and d is the free layer thickness.The resistance of the proposed skyrmion MTJ synapse is then computed using the compact model presented in the main discussion Eqn.4. We then consider the magnetization profile of the free layer and feed it to our model, which computes the resistance of the MTJ device as follows: Table .1
Fig. 1(b).The magnetization of the magnetic layers is changed by the external magnetic ranging from (-650 mT to 650 mT).Fig. 3(b) shows the MFM image of the device showing the unperturbed multi-domain magnetic texture with stripe domains.Since the width of the Hall bar is 2 um and based on the thin film magnetic stack, we expect stabilization of the Néel-type domain wall having a width around 20 nm as revealed by micromagnetic simulations [Fig.6].The Hall measurements are performed using the standard lock-in technique.As shown in Fig.2(a) we observe discrete anomalous Hall resistance.For samples at room temperature, the magnetic anisotropy and saturation magnetization are small thus all magnetic layers switch at lower fields.At 300K the magnetization switches at 21 mT for the positive magnetic fields and 19 mT for the negative magnetic field.

Figure 3 .
Figure 3. (a) Discrete magnetization switching of the crossbar of different widths.(b) MFM imaging shows DW -pinning to edges.

Figure 4 .
Figure 4. Repeatability of the discrete magnetization behavior with the application of 1 ns magnetic field pulses.

Figure 5 .
Figure 5. Magnetization texture through the hysteresis loop shows switching occurring via stripe domain conversion into skyrmions.
vice.In the positive field regime, the Néel skyrmions with polarity +1 are stabilized from the stripe domain phase.While reducing the field from high to low, skyrmioniums are stabilized in the Hall bar which stabilizes into skyrmion polarity −1 as we increase the field in the -z-direction.Depending upon the direction of the magnetic field the skyrmions change the polarity from +1 to −1 and vice-versa (see SV1 and Fig.4 and 5).The experimental MFM images of the fabricated device and the micromagnetic MFM of the scaled device are shown in Fig.3(b) (bottom).In both cases, we observe clear skyrmion/domains pinning to the edges of the device.

Figure 8 .
Figure 8.(a) Normalized magnetization evolution and associated demagnetization energy: explaining the behavior of DW motion.(b) SOT controlled DW-Synapse: Magnetization profile (potentiation/depression) in 15-layer and 20-Layer device.(micromagnetic).(c) DW shape during negative and positive current explaining the sudden drop in demagnetization energy on reversal of current.(d-e) (f) Current controlled synapse (measured).

Figure 9 .
Figure 9. Contour depiction of the magnetization vector within the magnified cross-sectional region of (a) 10 layers (b) 20 layers.

Fig. 9 .
Fig. 9. Thus, resulting in reduced Demag energy, hence increased DW velocity.Furthermore, for the 20-layer device, we observe fast switching which indicates increased DW velocity, in comparison to the 15-layer device [see Fig. 8(b)].This phenomenon is explained by the inset Fig. 8(b), interestingly, we observe the lowering of the demagnetization energy with the increasing number of FM layers.due to the increased number of layers, the spins vertically rotate almost by π thus, forming the Bloch domain wall which reduces the demagnetization energy.Compared to the case of 15 layers the rotation is by about π 2 resulting in higher demagnetization energy.Fig. 8(c) shows the measured current-controlled device operation, here we applied the 200 us voltage pulses with amplitude 5V and time period 500 us across the length of the device.The signal generated across the transverse arm is collected by the oscilloscope.We observe potentiation of the transverse voltage which we attribute to the

2 (
schemes indicates that the proposed devices can learn and recognize the MNIST dataset with up to 90% accuracy.Which is very well in range for acceptable recognition performance benchmarked for other memristors and ideal software-based 3-layer FCNN.The system level read energy and write energy is 1.47 × 10 −4 J and 4.8 × 10 −3 J.The read latency and write latency are 1.98 × 10 −2 s and 2.38 × 10 −1 s.These results provide a clear benchmark for the realization of hardware neural accelerators based on the DW-MTJ devices.

Figure 11 .
Figure 11.Illustration of the 3-Layer FCNN architecture for MNIST data recognition.Recognition accuracy increases throughout 125 epoch training for different write pulse schemes and the ideal case.

Figure 12 .
Figure 12.The recognition accuracy is above 89% for all cases.
a J = ℏ 2M S eµ 0 θ SH j d and p = sign (θ SH ) j × n (b)we show the obtained resistance states at different temperatures, at 300K only