Multi-level anomalous Hall resistance in a single Hall cross for the applications of neuromorphic device

We demonstrate the process of obtaining memristive multi-states Hall resistance (RH) change in a single Hall cross (SHC) structure. Otherwise, the working mechanism successfully mimics the behavior of biological neural systems. The motion of domain wall (DW) in the SHC was used to control the ascend (or descend) of the RH amplitude. The primary synaptic functions such as long-term potentiation (LTP), long-term depression (LTD), and spike-time-dependent plasticity (STDP) could then be emulated by regulating RH. Applied programmable magnetic field pulses are in varying conditions such as intensity and duration to adjust RH. These results show that analog readings of DW movement can be closely resembled with the change of synaptic weight and have great potentials for bioinspired neuromorphic computing.

decrease its membrane potential. The synaptic weight between the neurons is then directly related to the membrane potential as well as the time interval between the signal that neuron receives and the signal that the neuron transmits 29,30 . This time-dependency of the synaptic weight is also known as spike-timing-dependent plasticity (STDP) 31,32 . Shown in the top part (blue shaded region) of Fig. 1(b) is the synapse connection strength (w ij ) as a function of time. The pre, post1, and post2, correspond to the input signal of the neuron, and the two possible cases of output signals that the neuron exerts relative to the input signal. As can be inferred from the illustration, we can see that the synaptic strength will be decreased when the neuron exerts the output signal (post1) before the input signal (pre); on the other hand, the synaptic strength will be increased when the input signal (pre) comes before the output signal (post2). The decrease of the synaptic strength is appropriately termed as long-term depression (LTD), while the increase of the synaptic strength over a considerable amount of time is termed as long-term potentiation (LTP) 33,34 .
The bottom part (red shaded region) of Fig. 1(b) shows how the synaptic weight is represented as the Hall resistance (R H ) reading in the SHC device. In particular, we show that the input and output signals are now represented by the external magnetic field pulses to z direction (H z ); LTD now occurs due to the application of the negative H z , while LTP is excited through the application of positive H z . The time interval of the pre and post signals (Δt), which determines the extend of LTD and LTP in biological neuro system, is now represented by the duration and strength of the field pulses, with shorter Δt corresponding to stronger or longer field pulse. Figure 1(c) shows the Kerr microscopy image of the SHC device. The layer structure of the SHC is Ta(4 nm)/ Pt(3 nm)/[Co(0.6 nm)/Pt(6 nm)] n=4 with a capping layer of [Co(0.6 nm)/Pt (2 nm)] with two electrodes. Afterwards, the SHC was patterned to a wire width of 10 μm by the conventional photo-lithography process. Cr (5)/Au (100) electrode was patterned at a size of 50 μm 2 for the electrical measurement. Two large triangular pads are also connected with two electrodes electrically. The DW was initially nucleated as a bubble-like domain at the triangular top pad. The bubble-like domains were then expanded by applying field pulses along the perpendicular direction of the sample plane which resulted in the DW being pushed into the SHC. Therefore, the top pad acts as the pre-neuron, where the information-carrying DW is nucleated. Inset shows the enlarged image of the SHC where a DW from the pre-neuron (top pad) travelled across the microwire and settled in the vicinity of the SHC. The dark area corresponds to the part where the magnetization of the microwire pointed along the +z direction (up domain). Afterwards, the DW motion in the Hall cross is detected by observing the change in the Hall resistance (ΔR H ) and Kerr microscopy simultaneously. The more specific DW configuration can be investigated using the AHE method, which is simpler method in the fabrication process and allow direct measurement of the magnetization. As the DW moves forward within the SHC structure, multi-level resistances were observed at the SHC depends on the DW position or area of up domain. The relation between the multi-level R H of the SHC and the DW position were then confirmed using the Kerr images [35][36][37] . Furthermore, the stimulus can be replaced by spin transfer torque and/or spin orbit torque, and the reading with TMR is also possible for the real devices improving cyclability, CMOS compatibility, and large ON/OFF ratio 38 .
For demonstration of memristive behavior of the SHC device, we show that the Hall resistance of the SHC, R H , changes according to the applied field history. The measured R H values are normalized into the range [−1, 1] as shown in Fig. 2(a,b). The DW position was also observed by Kerr microscopy, simultaneously. Oe~−210 Oe, respectively. By subjecting the SHC to three different field sweep history, we observe three different Hall resistance cycles which is the characteristic of memristor. It must be mentioned that the observed memristive behavior in this SHC device is different from our previous work 39 , where we reported the memristive behaviors in multiple Hall crosses.

Ltp and LtD based on the DW motion in the SHc.
To demonstrate the synaptic capabilities of the device, first we show that the SHC is able to mimic the LTP and LTD behaviors. The analogue responses of R H due to the DW motion in the SHC are shown in Fig. 3(a,c) in accordance with Kerr images shown in Fig. 3(b,d), respectively. Several levels of the R H were obtained in the SHC during the DW propagation which emulates the LTP/ LTD of biological synaptic weights. The gradual increment/decrement of the R H were obtained by the propagation of two different types of DWs; the increase in R H is attributed to the movement of UD-DW, while the decrease in R H is attributed to the movement of DU-DW, as shown in Fig. 3(c,d), respectively. To create the UD-DW/DU-DW, the structure was first saturated by H z , which is greater than the coercivity (~320 Oe). Then, followed by an opposite field of ±H z to nucleate and expand the Up/Down domains in the nucleation pad. We applied positive/negative pulses to position Up/Down domain at the entrance of the SHC. The successive field pulses with an intensity smaller than previous are applied to expand the Up/Down domains in the SHC, as shown in Fig. 3(b-i,d-i). Afterwards, the DWs are propagated along the SHC and the microwire via the application of driving field pulse at +231.8 Oe/−188.7 Oe with a duration time of 0.8 s/0.6 s. As can be seen from Fig. 3(b-ii,iii), the gradual expansion of the Up domain (dark) corresponds to the gradual increase in the normalized R H value www.nature.com/scientificreports www.nature.com/scientificreports/ from −1 to +1. On the other hand, the gradual expansion of the Down domain (bright), as shown in Fig. 3(d-ii,iii) corresponds to the gradual decrease of the normalized R H value from +1 to −1. After the application of 9 driving field pulses, the DWs left the SHC and no further change in the R H was observed, as shown in Fig. 3 paring duration dependence of StDp. In addition to the multi-level feature of our device, we also show that the change in the potentiation and depression of the ΔR H can be controlled using the amplitude and the duration of the field pulses. Figure 4(a-e) shows that by adjusting the amplitude and the duration time of the driving pulses, the change in the increment of R H , i.e. ΔR H can be observed. Therefore, we investigate the distribution of ΔR H during R H change by applying identical field pulses in a train form (See the Supplementary Materials for additional details). For instance, in the UD-DW case, we applied pulse train with different amplitude and duration time as shown in Fig. 4(b-e). The result shows that ΔR H increases gradually within ~10 levels with symmetrical ΔR H as identical pulses are applied with amplitude +231 Oe and duration of 0.4 s in Fig. 4(b). When the amplitude of the pulses was increased to +237 Oe and the duration was increased to 0.5 s, an asymmetrical ΔR H was observed as a function of the pulse sequence Fig. 4(d,e). Thus, the tendency of ΔR H is classified into the two categories as shown in the Fig. 4(a-ii); 1) symmetrical case, which was obtained using low field amplitude and short pulse duration time; 2) asymmetrical case, which was obtained using high field and longer pulse duration time. In the symmetrical case, the gradual change in ΔR H can be attributed to the more uniform DW propagation in the SHC. This also enables the relatively larger number of R H states (~13 states) to be implemented at the SHC. The fitting result in Fig. 4(a-ii) indicates that the DW motion is reliable and uniform with the maximum peak height ΔR H of 0.12 Ω, and 0.17 Ω while FWHM was 5.20, and 3.70 as shown in Fig. 4(a-i) red, blue curves.
On the other hand, the erratic change in ΔR H in the asymmetrical case can be attributed to the disproportionate expansion of the DW within the SHC, Kerr image shows that the UD-DW is pinned and depinned from top-left and right edge corners in succession during the propagation process. In the initial steps (pulse 1-4), the ΔR H was relatively small (<0.075), since the UD-DW is pinned to the two top corners of the SHC. The maximum value of ΔR H is realized when the UD-DW is depinned from the top two corners and the up domain rapidly expands within the SHC (pulse 5-9). Afterward, the ΔR H decreases sharply again, when the UD-DW is pinned by the bottom-right corner of the SHC (pulse 10-12). Asymmetrical forms with the ΔR H changes are observed with the maximum peak height at ΔR H 0.28 Ω and 0.27 Ω while the FWHM were 2.30 and 2.34 in Fig. 4(a-ii) yellow, green curves. The green line peaks have been observed through the depinning of UD-DW by top corner of the SHC when the 5 th field pulse is applied to the sample. The yellow peak could be obtained by the 7 th of pulse number. In the case of green, UD-DW moves along the wire faster, because the green line has the longer duration time than the yellow one.
StDp learning rule of the SHc. As mentioned in the beginning, aside from the capabilities perform LTP and LTD, the SHC device is also capable to show the STDP capabilities which is one of the crucial aspects of a synaptic device. In the device, the pulse timing dependency is inversely represented by the pulse duration. For instance, in a standard biological synapse, shorter pulse interval between the pre-and post-synaptic spikes typically results in larger change in the synaptic weight; this feature is realized in the SHC device by applying pulses with stronger intensity or longer duration time. Figure 5(a) shows the relation between the average of the change in the Hall resistance (ΔR H ) as a function of τ d . The average value is used here as in each case of τ d , the SHC undergoes various multi-state reading of R H . In the case of potentiation, a maximum ΔR H of 0.13 Ω was obtained when τ d was set to 0.9 s. Similarly, for the case of depression, we obtained a maximum change of −0.11 Ω at τ d = 0.9 s. In the nonlinear curve fitting, each ΔR H slope is fitted to the exponential term Δ = τ R Ae www.nature.com/scientificreports www.nature.com/scientificreports/ are 0.75 s and −0.67 s for potentiation and depression, respectively. The emulation of biological synapse function such as STDP would then be possible by combining a circuit which transforms spike timing information into field pulse duration information with the SHC device. The details of ΔR H as a function of both pulse sequence and τ d are shown in Fig. 5(b). As discussed previously, larger change in ΔR H can be seen with larger τ d for both potentiation and depression cases. By utilizing this information, we can then continuously perform the potentiation and depression to change the synaptic weight of the SHC device, as shown in top image of Fig. 5(c) as an example. The bottom image of Fig. 5(c) shows the corresponding field sequence, the applied field intensity was +228 Oe and −217 Oe, with the duration of each pulse fixed at 0.5 s. Here, the fixed pulse duration corresponds to a fixed time interval in STDP. www.nature.com/scientificreports www.nature.com/scientificreports/ The dependence of the multi-state Hall resistance of the SHC with respect to the various pulse duration time τ d is shown in Fig. 6. As discussed before, longer τ d corresponds to shorter time interval in the STDP scheme. Here, both Fig. 6(a,b) show that the positive and negative pulses trains with various τ d can be used to adjust the potentiation and depression in the output signal. Alternating positive and negative pulses trains were employed to create five sharp and narrow R H spikes with different peak values in Fig. 6 (a,b). The different values of R H from the device depending on the applied pulse condition represent the capabilities of SHC to mimic the variable neural weight change in various spike timing different state.
conclusion Contribution of this work may be summarized as follows. We have shown the formation of multi-state R H obtained via the implementation of identical and non-identical field pulse with varying strength, polarity, and duration of pulses. It is worth noting that the input stimulus (pulses) amplitude and duration are below ~few hundred Oersted and milliseconds. Furthermore, the stimulus can be replaced by spin transfer torque and/or spin orbit torque, and the reading with TMR (tunneling magneto-resistance) is also possible for the real devices 40,41 . From device perspective, the use of DW and analogue R H with modulated ΔR H is potentially useful for cognitive and parallel computing in an artificial neuromorphic device. Overall, our device is simple, intuitive, and optimizable. We note that this work served to demonstrate the proof of concept experiments to realize such DW synapses for future ultralow-power intelligent neuromorphic system. Future work might be an implementation of on-chip cross-array, which would complete the building blocks towards integrated and biologically-inspired DW based neuromorphic device which is capable of adaptive STDP learning rule. In such device, the input to the postsynaptic neuron is determined by the multiplication of the output voltage of the presynaptic neuron and the synaptic weights in a crossbar array architecture. It has been shown that such architecture minimizes the power consumption for reading/writing and offers high connectivity and storage density that is comparable to previous CMOS-only hardware 42 . As for the concern regarding the value of the Hall resistance of our SHC device, the value is indeed much smaller compared to other technique such as the TMR reading of MTJ 43 , one possibility to circumvent this issue is by pairing the SHC device with a transistor, in similar spirit to how the signal is enhanced in a p-bit design 44 .

Methods
film and patterned structure. The magnetic film of the SHC was deposited on the Si/SiO 2 substrate using dc magnetron sputtering. The magnetic layers are comprised of Ta(4 nm)/Pt(3 nm)/[Co(0.6 nm)/Pt(6 nm)] n=4 with a capping layer of [Co(0.6 nm)/Pt (2 nm)]. In this structure, Ta layer acts as a buffer layer for the adhesion of the heavy metal to the Si/SiO 2 substrate [45][46][47] . One of the advantages of our film structure (n ≥ 3) is that DWs can be easily nucleated and driven at low field range ~ 150-300 Oe due to structure defects, interface corners, and so on.