A Spin‐Orbit Torque Switch at Ferromagnet/Antiferromagnet Interface Toward Stochastic or Memristive Applications via Tailoring Antiferromagnetic Ordering

Antiferromagnet (AFM) has currently participated in the spin‐orbit torque (SOT) technology due to its great potential to be applied to the field‐free SOT switching and to promote the thermal stability of MRAM. However, the effect of varying AFM ordering on the SOT switching and the associated properties is still not comprehensively understood. This work reports how an AFM ordering modifies the strength of Dzyaloshinskii–Moriya‐interaction (DMI) in a heavy metal (Pt)/FM (Co)/AFM (IrMn) trilayer and its effects on SOT switching. Increasing the AFM ordering reflects the enhanced exchange bias through increasing IrMn thickness appears to significantly reduce the DMI strength of the trilayer. Controlling the IrMn thickness appears to serve as a unique switch to activate memristivity/stochasticity in the devices via tailoring AFM ordering on exchange bias: The strong AFM ordering via increasing IrMn thickness enables to increase the stability of multi‐levels for SOT switching, which promotes the memristivity for neuromorphic application. On the contrary, the weak AFM ordering via reducing IrMn thickness will lead to significant stochasticity for the physically unclonable functionality. This work demonstrates an intrinsic tuning over the AFM ordering will serve as a switch to turn the SOT device into a stochastic/memristive cell to bridge probabilistic and neuromorphic computing.


Introduction
The heavy metal/ferromagnet (FM) bilayer is a building block for the spinorbit torque (SOT)-type magnetoresistive random access memory (MRAM), which has been regarded as a solution to address the issue of reliability of the spin-transfer torque MRAM caused by the same read/write architecture. [1]With the charge current flowing through the heavy metal, an SOT can be generated at the heavy metal/FM interface and leads to the magnetization switching upon the mirror symmetry of FM is broken by using a structural [2,3] or magnetic approach. [1,4][7] It has been found the strong DMI in the heavy metal/FM bilayer would result in the Néel type chiral domain wall once the reversed domain is formed at the first stage of applying SOT. [7,8]An external field collinear to the applied current is to break the chiral symmetry in the Néel wall so the asymmetric domain wall velocity can be driven with SOT, and the external field often increases with increasing the DMI strength to make the net SOT switching accomplished. [9,10]herefore, control over the DMI via interfacial engineering in the heavy metal/FM bilayer soon becomes an important issue, which significantly influences the properties of SOT switching and the related applications.
Among several approaches to control the DMI strength, the mainstream is to explore how to vary the heavy metals and modify the heterointerface to tailor DMI in the SOT devices.On the other hand, an emergent field of using an antiferromagnet (AFM) for field-free SOT switching has been demonstrated together with a memristivity. [11,12]A fundamental issue in the AFM-based SOT device appeared in this research area: How does the presence of AFM influence the DMI of the adjacent FM layer in the magnetic heterostructure?In most cases, the AFM adjacent to FM would lead to an exchange bias (H ex ) at the AFM/FM interface, which also modifies the exchange interaction within the FM layer through the interfacial exchange coupling.This issue has been proposed but so far has not been comprehensively understood. [13,14]his study attempts to uncover the effects of an AFM ordering on the DMI strength and the associated SOT switching properties in a heavy metal (Pt)/FM (Co)/AFM (IrMn) trilayer.16] This study shows the DMI strength reduces as increasing the AFM ordering of IrMn, which can be characterized by using the field-assisted SOT switching and the loop-shift method. [3,9]The inverse correlation between DMI and H ex in the trilayer suggests that AFM ordering should play a role in mediating the exchange coupling within the Co layer through the H ex indirectly.As a result, the established AFM ordering significantly reduces DMI strength, leading to the reduction of the external field required for a complete SOT switching.Furthermore, the enhanced AFM ordering promoted reversible SOT switching with an ideal memristivity for neuromorphic computation. [17]n the counterpart, the reduced AFM ordering in the sample would induce stochasticity into the trilayer, which would benefit the physically unclonable functionality (PUF). [18]Consequently, tuning over the AFM ordering through the AFM thickness would serve as a switch to turn the SOT device into a stochas-tic/memristive cell to bridge probabilistic and neuromorphic computing. [17]

Results and Discussion
Figure 1a shows the stack structure of the Pt/Co/IrMn trilayer, in which the thickness of IrMn ranging from 0 to 10 nm is a variable in this study.In the trilayer, Pt at the bottom is to generate a spin current to switch the perpendicular magnetization of Co on top via the spin Hall effect. [19,20]IrMn with various thicknesses is employed to study the effects of AFM ordering on the DMI strength through monitoring the evolution of H ex .Figure 1b shows the optical microscope image of the Hall-cross device, which allows the direct current (DC) and pulse current applied along the xdirection and the anomalous Hall effect measurement along the y-direction.Figure 1c presents the hysteresis loops with the thickness dependency of IrMn, in which the H ex increases monotonically with increasing the thickness of IrMn until 8 nm (IrMn (8 nm)).On the contrary, coercivity (H c ) appears to increase when IrMn is thinner than 4 nm but subsequently drops to ≈500 Oe when IrMn is thicker than 8 nm.This H ex (H c ) evolution versus IrMn thickness plotted in Figure 1d is similar to the results of Pt/Co/IrMn-related literature, [14,15] suggesting the AFM ordering of IrMn should be fully established while IrMn is thicker than 8 nm.Further increasing IrMn thickness would not influence the H ex significantly because the bulk order might have a limited effect on the interface.Besides, the anisotropy field (H k ) appears to After the characterization of the magnetic properties of the devices, the focus was turned to characterize the properties of SOT switching.Figure 2a,b exhibits the H x -dependent SOT switching curves for IrMn (2 nm) and IrMn (8 nm) device, respectively.Figure 2a shows the switchable portion of IrMn (2 nm) appears to reduce at H x ≈ 400 Oe.The switchable component taken with H x = 200 Oe drops to 50% relative to the one taken with H x = 1000 Oe, which is highlighted by the shadow region in Figure 2a.On the contrary, in Figure 2b, the switchable portion of IrMn (8 nm) appears to be sustainable even with the H x smaller than 250 Oe. Figure 2c demonstrates the H x -dependent SOT switching ratio for various IrMn thicknesses.With increasing IrMn thickness, the required H x for complete SOT switching is reduced, as shown in Figure 2c.Based on the previous studies, the variations of H x required for a complete switching may be associated with the issue of the symmetry breaking on the chiral Néel domain wall (Figure S1, Supporting Information), which may reveal the changes in the DMI strength of the trilayer upon varying IrMn's thickness.It seems that the threshold H x for a complete SOT switching can be used as an indicator of the DMI strength.To further confirm this concept, we carried out a loop-shift method to quantitatively obtain the DMI effective field (H DMI ). [3,9]igure 3a demonstrates the R xy -H z curves of IrMn (2 nm) taken with ± 10 mA under an H x = 1200 Oe.The shifted R AHE -H z curves suggest an effective field along the perpendicular direction is induced accompanied with the current applied, thus leading to a current-induced bias field on the R xy -H z curve.Figure 3b shows the plots of shifted field versus various current amplitudes, featuring an ideal linear correlation.This result perfectly supports the SOT-induced effective field along the ± z direction, therefore, the magnetization will be switched once the current reaches the threshold to make a single stable magnetization state on the R xy -H z curve. [9,10]Notably, the slope in Figure 3b also reflects the SOT efficiency (ΔH/I write ) under a given H x .Figure 3c plots the SOT efficiency as a function of H x and the saturated efficiency can be observed above a threshold H x , which is defined as the H DMI obtained by the loop-shift method. [9,10]Above H DMI , the applied H x would completely break the chiral symmetry of the Néel wall, and thus the complete SOT switching occurs (please see Figure S1, Supporting Information, for details).Figure 3d summarizes the thickness dependency of IrMn on the H DMI taken by using a loopshift method (blue dots) and the required H x for complete SOT switching (pink dots).The trend of the two results shows good consistency although the values are slightly scattered, which suggests the required H x for complete SOT switching may provide a qualitative evaluation of the DMI strength among systems.Both trends coincide with the evolution of H ex (purple dots).As mentioned in Figure 1c, the AFM ordering starts to be robust upon the thickness at ≈6-8 nm, and herein the H ex gets saturated and the H DMI becomes unchanged above IrMn of 8 nm.This observation strongly suggests that AFM ordering indeed influences the DMI strength in the trilayer device, which can be qualitatively and quantitatively approached by using the H x -dependent SOT switching and loop-shift method, respectively.Notably, the H DMI of the Pt/Co bilayer (IrMn-free sample) was ≈2700 Oe (Figure S2, Supporting Information), which was at a comparable level with the H DMI of the IrMn (2 nm) sample.The result suggests incorporating IrMn onto the Pt/Co bilayer may give rise to a limited effect on modifying the DMI of Co, further supporting the significant effect arising from the AFM ordering.
In addition to the evolution of the DMI strength upon modifying the AFM ordering in the IrMn layer, we notice the SOT switching properties also change significantly.Electrically, both IrMn (2 nm) and IrMn (8 nm) devices demonstrate multi-levels as demonstrated in Figure S3 (Supporting Information) as other associated literature, [5,11,12,[21][22][23] but the details appear to be considerably different between the two devices.Enhancing the AFM ordering was observed not only to reduce the H DMI but also to stabilize the reversal stability during the SOT switching.H x = 500 Oe for IrMn (8 nm) and IrMn (2 nm), respectively.This characterization was performed beginning with a negative initialization pulse to set magnetization upward (reset) and then randomly gave a positive current pulse to drive the SOT switching downward (set).The pulse sequences are shown on the top panel of Figure 4a,b, and bottom panels show their corresponding R xy as the magnetization state of IrMn (8 nm) and IrMn (2 nm), respectively.As a result, IrMn (8 nm) demonstrates welldefined multi-levels on the repeating read/write characterization, in which the intermediate R xy state appears to be precisely determined by the specific pulse amplitude.Because the reading currents to get the R xy were all applied with a 1 ms delay after the writing pulse, the obtained R xy should suggest the remarkable memristivity of IrMn (8 nm).On the counterpart, IrMn (2 nm)  exhibits significant variations on the intermediate R xy state after giving a specific current pulse, especially at the pulse (≈30 mA) with ≈50% switching probability.This stochasticity reflected by the R xy variation may be attributed to the drifting effect on the domain wall propagation during SOT switching or even the effect of random domain nucleation. [22,24]Namely, stochasticity occurs once the magnetic film lacks the preferred nucleation sites and pinning sites for domain wall propagation. [5,11,23]On the contrary, IrMn (8 nm) ideally demonstrates very stabilized intermediate states during the read/write characterization, leading to remarkable memristivity, [21,23] which has not been carefully studied in the previous literature.We ascribe this issue to the wide distribution of the anisotropy strength in the AFM layer as observed in the system of PtMn/Pt, [25,26] Mn 2 Au, [27] and Pt/NiO, [28] featuring a gradual AFM domain reversal.Therefore, the memristivity of IrMn (8 nm) may arise from the varied anisotropy strength of exchange-coupled Co/IrMn domains at the interface, giving rise to the preferred nucleation sites for the reversed domains and the pinning sites for domain wall propagation because some local Co/IrMn domains are robust but some local Co/IrMn domains are weak.(Figure S4, Supporting Information).
In order to micromagnetically understand the origin of stochasticity and memristivity, Figure 5a-f exhibits several images taken by magneto-optical Kerr effect microscope for the intermediate states of the IrMn (2 nm) and IrMn (8 nm) after giving an identical reset/set current pulse for the SOT switching in each device, respectively.For IrMn (2 nm), the domain configura-tion at the intermediate state appears to be varied time-by-time as highlighted by the rectangles of the yellow dash, which may confirm the former statement on the lack of preferable nucleation and pinning site for SOT switching.This leads to the stochasticity of the device once the domain configuration at the intermediate state cannot be precisely controlled.It should be noted that the AHE signal is electrically sensitive to the domain configuration at the vicinity of the intersection of the Hall bar. [29,30]ny significant changes in the domain structure in the vicinity of the Hall cross would give rise to the variation in the AHE output as observed on the IrMn (2 nm) device (Figure S5, Supporting Information), serving as the origin of the stochasticity.On the counterpart, the IrMn (8 nm) shows a quite reproducible domain configuration upon performing the random read/write characterization.It may suggest the distribution of the local Co/IrMn coupling strength would give rise to the preferred nucleation sites followed by propagation.Note that, the reversed domain did not appear to be at the edge of the device for both IrMn (2 nm) and IrMn (8 nm), therefore, we can reasonably exclude the possible Oersted field-driven reversal in the device. [5,31]Based on these results, increasing the AFM ordering was found to reduce the DMI strength, accompanied with the reduction of the H x , and to stabilize the intermediate states during the SOT switching.Therefore, the device with strong AFM ordering (IrMn (8 nm)) may serve as an ideal candidate for the neuromorphic computing technology, based on the remarkable memoristivity. [11,12]However, the lack of AFM ordering (IrMn (2 nm)) would give rise to no preferable nucleation site and the propagation pinning site in the Co layer, thus the stochasticity was observed.Interestingly, we found this stochasticity can be applied to generate a digitbased random number, as demonstrated in our prototype test in Figure 6.
Figure 6a shows the stochasticity of the IrMn (2 nm) device based on the R xy variation on the repeating write/read characterization taken by reset (−35 mA)/set (30 mA) pulse current cycle for 82 times.Because the SOT switching to the intermediate state with ≈50% switching probability shows the largest variation, this stochasticity on the AHE output can be applied to a digit-based physically unclonable functionality.Herein, we intentionally set a judge line (blue dash) at the center of the variation (≈0.023Ω), so it can help assign the binary signal to 1 (black) or 0 (white) once the AHE output is above or below, respectively.Figure 6b shows the results of the random number sequences obtained at three different segments in Figure 6a, highlighted by purple, blue, and green.After randomly picking up the three different segments of the random number sequence, two significant characteristics should be noticed: 1) the random number output shows no bias (50% for "1" and 50% for "0") and 2) there is no specific pattern on the output sequence.Both signatures suggest an ideal randomness of the IrMn (2 nm) device, which may have the potential to be applied to PUF for addressing privacy issues.The AFM ordering may serve as a critical switch to turn the AFM/FM bilayer to be either a memristive cell or a stochastic cell to functionally fit two opposite facets of SOT applications. [17]o far, this study has shown the opposite development between the AFM ordering and the DMI strength, leading to the transition of the associated SOT switching properties in the Pt/Co/IrMn trilayer device.][36] However, the enhanced AFM ordering on the presence of H ex would boost the uni-directional anisotropy of FM.It would significantly suppress the spin canting so the DMI would be reduced after this magnetic competition.This result has not been comprehensively studied in the previous literature [13,14] and the FM/AFM exchange may play a role in modifying the DMI strength in the FM layer.

Conclusion
This study reports the effect of AFM ordering on the development of DMI strength in a Pt/Co/IrMn trilayer SOT device and the resulting effect on the SOT switching properties.The increased AFM ordering via increasing IrMn thickness will be reflected on the increased H ex , which appears to be well established upon IrMn reaching 8 nm.The threshold H x to achieve a complete SOT switching serves as an indication of the DMI strength, reducing with increasing the AFM ordering of IrMn.This opposite evolution between AFM ordering and H DMI has been also quantitatively examined by using the well-established loop-shift method and the results were consistent with those obtained by using H x -dependent SOT switching.This tuning on DMI can serve as a switch to tailor the stability of the intermediate state during SOT switching, in which the low DMI with high AFM ordering (IrMn (8 nm)) would lead to memristivity to be applied to neuromorphic computing and the strong DMI with low AFM ordering (IrMn (2 nm)) would lead to stochasticity to be applied to the PUF-related applications.

Experimental Section
Device Fabrication: Film stack Si/SiO 2 /Ta2/Pt5/Co1/IrMn(t)/Ti3 was deposited using a magnetron sputtering technique in a chamber with a basal pressure of 4 × 10 −8 torr, where the number after each layer stands for the thickness in nanometer.t, ranging from 0 to 10 nm, stands for the thickness of IrMn and is the only variable in this study.During the film deposition, a magnetic field of 300 Oe was applied normally to the substrate to facilitate a single H ex on hysteresis loop and the substrate was spinning to ensure the deposition uniformity.The magnetism of the as-deposited films was characterized utilizing a vibrating sample magnetometer (VSM) at 300 K. Subsequently, the films were patterned into a Hall bar device with 10 μm in width and 40 μm in length.A Ta(10)/Pt(100) electrode was deposited using the lift-off technique for the following transport measurements.
Measurement: AHE measurement was performed by applying a direct current (DC) of 1 mA along the longitudinal channel of the device under a perpendicular magnetic field (H z ) and simultaneously collecting the voltage along the transverse channel of the device.SOT switching was performed using a pulse current (I Write ) with various amplitudes and with a H x collinear to the current channel of the device.After a SOT pulse current of 0.3 ms duration, a 1 mA DC was applied to obtain the AHE signal (R xy ) for tracking the magnetization state.Loop-shift method was performed by measuring the AHE curves with various DCs and a given H x .The SOT efficiency defined by the linear correlation between shifted H z and DC amplitude was plotted as a function of the H x applied during the loop-shift measurement.H DMI was acquired from the critical H x to yield a saturated SOT efficiency.Repeating write/read characterization was performed beginning with a reset-pulse current to initialize the magnetization state upward and then applying a set-pulse current to trigger the magnetization switching.After each set/reset-pulse current, a 1 mA DC current was applied to collect the AHE signal to confirm the changes in the magnetization state.This set/reset operation was repeated five times and turned to the next group of cycles with increased set-pulse current until it reached the complete switching downward.

Figure 1 .
Figure 1.Magnetic characterizations on Pt/Co/IrMn trilayer with IrMn-thickness-dependence. a) Stacking and magnetic structure of Pt/Co/IrMn trilayer and the experimental geometry of spin-orbit torque switching.b) Optical microscopic image of the Pt/Co/IrMn trilayer device patterned into a Hall bar geometry with 40 μm in length and 10 μm in width.c) Hysteresis loops of Pt/Co/IrMn trilayer with IrMn-thickness-dependence. d) Plot of H c (black), H ex (red), and H k (blue) for Pt/Co/IrMn with varying IrMn thickness.Their corresponding axes are arrowed.

Figure 2 .
Figure 2. H x -dependent SOT switching to approach the effect of AFM order on H DMI strength.a) H x -dependent SOT switching for IrMn (2 nm) device.The shadow region in (a) highlights the incomplete SOT switching curves taken under an H x ≤ 400 Oe.b) H x -dependent SOT switching for IrMn (8 nm) device.Except for the critical current, all the curves in (b) are without distinguishable difference.c) Plots of H x -dependence on the switching ratio for IrMn (2 nm), IrMn (4 nm), IrMn (6 nm), and IrMn (8 nm) from top to bottom panel.The H x threshold , required for the full switching, decreases with increasing IrMn thickness, where the switching ratio is defined in terms of the change of R xy taken under a given H x related to the change of R xy taken at H x = 1000 Oe.The reduced H x threshold can be regarded as an indirect indication of the reduced H DMI strength in each system.
Figure 4a,b demonstrates a repeating read/write characterization with a

Figure 3 .
Figure 3. Loop-shift method to obtain H DMI of Pt/Co/IrMn trilayer device.a) Representative AHE loop-shift measurement for IrMn (2 nm) taken by using a DC current of ± 10 mA.b) Plots of shifted H z as a function of current applied for AHE as shown in (a).c) Plots of SOT efficiency versus H x , which is defined by the slope in (b).The H DMI is defined by the H x value to yield a saturated SOT efficiency as indicated by the blue dash.d) Plots of H DMI , H ex , and H x to yield a complete SOT switching as a function of IrMn thickness.Note: H ex herein is presented in an absolute value to avoid potential confusion because the increased H ex is with a negative sign in this study.

Figure 4 .
Figure 4. Repeating write/read characterization for (a) IrMn (8 nm) and (b) IrMn (2 nm) device.Set/reset pulse sequence to treat devices (upper panel) and the resulting R xy taken with a H x = 500 Oe (bottom panel).Each R xy state was taken with a 1 ms delay after the writing pulse.A remarkable memristivity is demonstrated in the IrMn (8 nm) sample but a considerable stochasticity at the intermediate states is revealed in the IrMn (2 nm) sample.

Figure 5 .
Figure 5. Magnetic morphology is characterized by using a magneto-optical Kerr microscope.a-c) Domain images of IrMn (2 nm) device taken after giving an identical reset (−35 mA)/set (28 mA) pulse cycle.The differences among (a)-(c) are highlighted by the rectangles of the yellow dash for a better comparison.d-f) Domain images of IrMn (8 nm) device taken after giving an identical reset (−48 mA)/set (37 mA) pulse cycle.

Figure 6 .
Figure 6.A prototype demonstration of a random number generator based on the stochasticity of IrMn (2 nm).a) Stochasticity measurement of IrMn (2 nm) 82 times based on the repeating write/read characterization in Figure 4(a).The reset and set pulse current are −35 and 30 mA, respectively.A judge line was set at the center of variation (≈0.023Ω) for assigning 1 (black) and 0 (white) once the AHE output was obtained.b) Results of the random number sequences obtained at three different segments in (a), highlighted by purple, blue, and green.No significant bias or specific pattern in the random number sequences was observed.