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Hiroto Masuda, Yuta Yamane, Takaaki Dohi, Takumi Yamazaki, Rajkumar Modak, [Ken-ichi Uchida](https://orcid.org/0000-0001-7680-3051), Jun'ichi Ieda, Mathias Kläui, Koki Takanashi, [Takeshi Seki](https://orcid.org/0000-0003-3195-7051)

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[Efficient Manipulation of Magnetic Domain Wall by Dual Spin‐Orbit Torque in Synthetic Antiferromagnets](https://mdr.nims.go.jp/datasets/c0071104-d162-4c26-9d0e-c3796786ca38)

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Efficient Manipulation of Magnetic Domain Wall by Dual Spin‐Orbit Torque in Synthetic AntiferromagnetsRESEARCH ARTICLEwww.advancedscience.comEfficient Manipulation of Magnetic Domain Wall by DualSpin-Orbit Torque in Synthetic AntiferromagnetsHiroto Masuda, Yuta Yamane, Takaaki Dohi, Takumi Yamazaki, Rajkumar Modak,Ken-ichi Uchida, Jun’ichi Ieda, Mathias Kläui, Koki Takanashi, and Takeshi Seki*Current-induced domain-wall motion (CIDWM) in a synthetic antiferromagnetis a key phenomenon for developing potential high-density-packed magneticdomain-wall memory with fast operation. Here, CIDWM is reported in theantiferromagnetically-coupled two Co layers through the Ir interlayersandwiched by the two Pt layers: Pt/Co/Ir/Co/Pt. The top and bottom Ptlayers play a role for generating the spin current coming from the spin Halleffect, which gives rise to the dual spin-orbit torque (SOT) acting on theperpendicular magnetizations of the Co layers. Although a simple argumentwould predict that SOTs from top and bottom Pt layers cancel each other out,the dual SOT nucleates a reversed magnetic domain and drives the CIDWMeffectively at current density of the order of 1011 A m−2. This study alsoexamines the effect of antisymmetric interlayer exchange coupling (AIEC) onCIDWM. A positive correlation between the magnitude of AIEC and thedomain wall velocity is found, whereas the current density required fornucleating the reversed domain shows a negative correlation with themagnitude of AIEC. These facts suggest that the existence of AIEC improvesthe performance of CIDWM. The present results provide a new avenue todesign SOT domain wall devices based on a synthetic antiferromagnet.H. Masuda, T. Yamazaki, K. Takanashi, T. SekiInstitute for Materials ResearchTohoku UniversitySendai 980-8577, JapanE-mail: takeshi.seki@tohoku.ac.jpY. YamaneFrontier Research Institute for Interdisciplinary SciencesTohokuUniversitySendai 980-8578, JapanY. Yamane, T.DohiResearch Institute of Electrical CommunicationTohokuUniversitySendai 980-8577, JapanThe ORCID identification number(s) for the author(s) of this articlecan be found under https://doi.org/10.1002/advs.202514598© 2025 The Author(s). Advanced Science published by Wiley-VCHGmbH. This is an open access article under the terms of the CreativeCommons Attribution License, which permits use, distribution andreproduction in any medium, provided the original work is properly cited.DOI: 10.1002/advs.2025145981. IntroductionArtificial magnetic systems with an an-tiferromagnetic alignment of the layers,which exploit the interlayer exchange cou-pling (IEC) in magnetic multilayers, are atreasure trove of functionalities for spin-tronics applications.[1–4] The ferromagneticand nonmagnetic layers in a nanoscaleheterostructure can each play a differentrole, making the total system highly func-tional. For example, two ferromagnetic lay-ers such as Co separated by a nonmagneticlayer such as Cu, Ru, or Ir exhibit an an-tiferromagnetic alignment due to a long-range IEC, and the magnitude of IEC, i.e.,the strength of the antiferromagnetic cou-pling, can be tuned by varying the layerthicknesses.[5–7] Such a controllability of an-tiferromagnetic properties is a feature thatis not found in bulk antiferromagnets. Arecent research trend in spintronics, aim-ing to utilize the characteristics of anti-ferromagnetic materials such as the lowT. Dohi, M. KläuiInstitut für PhysikJohannes Gutenberg-Universität MainzStaudingerweg 7, 55128 Mainz, GermanyR. Modak, K.-ichi UchidaResearch Center for Magnetic and Spintronic MaterialsNational Institute for Materials ScienceTsukuba 305-0047, JapanR. Modak, K.-ichi UchidaDepartment of Advanced Materials Science, Graduate School of FrontierSciencesThe University of TokyoKashiwa 277-8561, JapanJ. Ieda, K. TakanashiAdvanced Science Research CenterJapan Atomic Energy AgencyTokai 319-1195, JapanT. SekiCenter for Science and Innovation in SpintronicsTohoku UniversitySendai 980-8577, JapanT. SekiInternational Center for Synchrotron Radiation Innovation SmartTohoku UniversitySendai 980-8577, JapanAdv. Sci. 2025, 12, e14598 e14598 (1 of 9) © 2025 The Author(s). Advanced Science published by Wiley-VCH GmbHhttp://www.advancedscience.commailto:takeshi.seki@tohoku.ac.jphttps://doi.org/10.1002/advs.202514598http://creativecommons.org/licenses/by/4.0/http://creativecommons.org/licenses/by/4.0/http://crossmark.crossref.org/dialog/?doi=10.1002%2Fadvs.202514598&domain=pdf&date_stamp=2025-10-17www.advancedsciencenews.com www.advancedscience.commagnetic susceptibility, lack of the magnetic stray field, andhigh antiferromagnetic resonance frequencies, is called antifer-romagnetic spintronics.[8] The antiferromagnetic structures arti-ficially formed in magnetic multilayers are a suitable platformfor systematic study of the antiferromagnetic spintronics thanksto the controllability of their antiferromagnetic properties asmentioned above. Also, perpendicular magnetic anisotropy canbe induced at the interfaces in a multilayer, which realizes aperpendicularly-magnetized synthetic antiferromagnet. In addi-tion, the broken inversion symmetry at the interfaces gives rise tothe interfacial Dzyaloshinskii-Moriya interaction, leading to for-mation of topological magnetic structures such as a skyrmion.[9]Particularly, the antiferromagnetic skyrmion observed in an IECmultilayer [10–13] is of interest due to the drastically changed spindynamics resulting from the antiferromagnetic coupling of thelayers. The synthetic antiferromagnets are also useful for de-veloping high-performance spintronic devices,[14–17] particularlybased on domain walls (DWs). A previous study demonstrateda fast current-induced domain-wall motion (CIDWM) in a syn-thetic antiferromagnet Pt/(Co/Ni)/Ru/(Co/Ni).[17] They exploitedthe exchange coupling torque as well as the spin orbit torque(SOT) induced by the spin Hall effect (SHE) in Pt.[18]Our previous study [19] realized a current-induced magnetiza-tion switching in Pt/Co/Ir/Co/Pt multilayers. The two Co lay-ers were perpendicularly magnetized and either antiferromag-netically or ferromagnetically coupled through the Ir interlayer,depending on the Ir layer thickness. The dual SOT originatingfrom the top and bottom Pt layers acts on the magnetizations inthe two Co layers. Through magnetic domain observation of theSOT switching, we found that the antiferromagnetic alignmentis favorable for stable and efficient SOT-switching operations.Apart from the SOT-related phenomena, an antisymmetricIEC (AIEC) between the two ferromagnetic layers was observedin Pt/Co/Ir/Co/Pt with wedge-shaped layers.[20] The AIEC isinduced due to the broken inversion symmetry along the in-plane direction, which was first theoretically predicted,[21] thenexperimentally observed.[22,23] After the early work confirmingthe existence of AIEC,[22–24] the following studies revealed thecharacteristics of AIEC,[20,25–35] e.g., the relation between IECand AIEC.[20,25,26] The conventional, symmetric IEC energy is ex-pressed as JAF(mA ·mB), where JAF denotes the antiferromagneticcoupling strength andmA andmB are the unit vectors represent-ing the magnetizations in the two ferromagnetic layers, A and B.On the other hand, the AIEC energy is expressed asDAIEC · (mA ×mB), where DAIEC is the AIEC vector determined by system sym-metry. With the film normal direction along the z direction andthe inversion symmetry breaking along the y direction, DAIEC ap-pears along the x direction. TheAIEC prefers a noncolinear align-ment of mA and mB, leading to chiral magnetic configurationsthat can be exploited to realize artificial 3D topological magneticstructures.[36] Microscopic mechanisms of AIEC and its applica-tions to the spintronic devices are therefore attracting consider-able attention. Several experimental studies demonstrated thatthe AIEC allows the field-free SOT switching thanks to the in-plane effective field originating from the AIEC field.[28–31] How-ever, there is no experimental elucidation how the AIEC field af-fects the CIDWM. Also, the behavior of DW under the dual SOTapplication is not a trivial issue because a simple picture of dualSOT gives the cancellation between the SOTs from top and bot-tom spin Hall layers. Considering the complex layer stacking in-corporated into the current spintronics devices, the understand-ing of themechanism and process of the SOTs coming frommul-tiple layers is remarkably important from the viewpoint of notonly an academic interest but also an efficient device operation.This paper presents a combined experimental and theoreticalstudy on CIDWM in a perpendicularly-magnetized synthetic an-tiferromagnet Pt/Co/Ir/Co/Pt with AIEC. We find that the dualSOT can effectively drive DWM in the presence of in-plane field,despite the opposite polarization of the spin current injected fromthe top and bottom Pt layers. We find that the AIEC can reducethe current density required for DW nucleation and increase theDW velocity. The experimental observations are consistent withour numerical simulation. The present results provide a new di-rection to design DW devices using a synthetic antiferromagnet.2. Experimental ResultsThe following layer stackings were deposited on thermally oxi-dized Si substrates using a magnetron sputtering at room tem-perature: Si-O Subs.//Ta (2)/Pt (3)/Co (0.65 or tCo)/Ir (1.3)/Co(0.9)/Pt (3)/Ta (1) (thickness in nanometer). Figure 1a illustratesthe central layer stacking together with the magnetization con-figuration of two Co layers. The 1.3 nm-thick Ir layer leads to theantiferromagnetic IEC, and the 1.3 nm thickness is the secondpeak position of oscillatory behavior of IEC strength as a functionof the Ir interlayer thickness.[19] Thanks to the interfaces with thePt layers, the top and bottom Co layers are perpendicularly mag-netized. In order to intentionally break the in-plane spatial inver-sion, the bottom Co layers were designed to have a wedge shape(Figure 1b). In our previous study,[20] the wedged Co layer was ef-fective to induce the AIEC. As discussed later, although there areseveral sources for the AIEC except the wedge shape, implyingthat the AIEC field is determined bymultiple contributions as wereported in another paper,[35] we consider that the wedge shapebecomes one of major sources breaking the in-plane spatial in-version. For the Co-wedged samples, tCo denotes the thickness ofwedged bottom Co layer, and the ranges of tCo were set to be 0.6≤tCo ≤ 1.1 nm, 0.4≤ tCo ≤ 1.4 nm, and 0.3≤ tCo ≤ 1.8 nm,which cor-respond to the thickness gradient ∇tCo of 0.6 × 10−7, 1.1 × 10−7,and 1.7 × 10−7, respectively. For the thin film without the wedgedlayer, the Co layer thickness was fixed at 0.65 nm, which is callednon-wedged sample in this study. It is noted that out-of-plane di-rection is the easymagnetization direction for all tCo in this study,which was confirmed by measuring the polar magneto-opticalKerr effect loops (Figure S1, Supporting Information).In order to observe magnetic domain structures and character-ize their domain wall motion, magneto-optical Kerr effect imag-ing was employed in this study. As depicted in Figure 1c, the ob-served domain image mainly reflects net magnetization, whichis the same direction as the top Co magnetization because thetop Co layer is thicker than the bottom Co layer. The possiblemagnetic structures in the domain wall, that is, Néel-type andBloch-type domain walls are also illustrated in Figure 1d. Sincethe dual-SOT acts on the magnetic moments of Co layers un-der the electric current application, the effective magnetic fieldof damping-like (DL) SOTHDL-SOT is also depicted in Figure 1e.The thin films were patterned into aHall-bar-shape (Figure 2a)with a 5 μm width-channel. The direction of wedge shape in theAdv. Sci. 2025, 12, e14598 e14598 (2 of 9) © 2025 The Author(s). Advanced Science published by Wiley-VCH GmbH 21983844, 2025, 48, Downloaded from https://advanced.onlinelibrary.wiley.com/doi/10.1002/advs.202514598, Wiley Online Library on [29/12/2025]. See the Terms and Conditions (https://onlinelibrary.wiley.com/terms-and-conditions) on Wiley Online Library for rules of use; OA articles are governed by the applicable Creative Commons Licensehttp://www.advancedsciencenews.comhttp://www.advancedscience.comwww.advancedsciencenews.com www.advancedscience.comFigure 1. Schematic illustration of stacking structures together with the magnetization configuration of two Co layers for a) non-wedged sample and b)wedged sample. c) Expected magneto-optical Kerr image for a sample with tail-to-tail (light gray) and head-to-head (dark gray) magnetic domains, wherethe tail-to-tail domain possesses an upward net magnetization while the head-to-head domain possesses a downward net magnetization. d) Illustrationof magnetic structures inside Néel-type and Bloch-type domain walls. e) Effective field of damping-like (DL) spin-orbit torque (SOT) HDL-SOT acting onthe top and bottom Co magnetic moments.Figure 2. Characterization of symmetric interlayer exchange coupling (IEC) and antisymmetric IEC (AIEC). a) Schematic illustration of a Hall-bar devicewith the coordinate, where the in-plane field angle of Hip is defined as the angle ϕAS from the x-axis. b) Transverse resistance Rxy as a function ofperpendicular magnetic fieldHz for the device of the non-wedged sample. c) Rxy curves for the device with ∇tCo = 1.1 × 10−7, where 𝜇0Hip = 50 mT wasapplied at ϕAS = 120° (red curve) and 300° (black curve). d) ϕAS dependence of the unidirectional shift in switching field ΔHsw for the device with ∇tCo= 1.1 × 10−7 at 𝜇0Hip = 50 mT. The red and blue circles denote ΔHsw obtained from Hsw in the positive and negative field regions, respectively. Thesolid curves are the fitting results with cosine function. e) 𝜇0ΔHsw,max and f) ϕAS as a function of ∇tCo, where the red and blue marks denote the resultsobtained fromHsw in the positive and negative field regions, respectively. 𝜇0ΔHsw,max and ϕAS are the fitting parameters of 𝜇0ΔHsw = 𝜇0ΔHsw,max cos(ϕ– ϕAS), which was used in d).Adv. Sci. 2025, 12, e14598 e14598 (3 of 9) © 2025 The Author(s). Advanced Science published by Wiley-VCH GmbH 21983844, 2025, 48, Downloaded from https://advanced.onlinelibrary.wiley.com/doi/10.1002/advs.202514598, Wiley Online Library on [29/12/2025]. See the Terms and Conditions (https://onlinelibrary.wiley.com/terms-and-conditions) on Wiley Online Library for rules of use; OA articles are governed by the applicable Creative Commons Licensehttp://www.advancedsciencenews.comhttp://www.advancedscience.comwww.advancedsciencenews.com www.advancedscience.comFigure 3. a) Experimental setup for the current-induced domain wall motion (CIDWM) observation using the magneto-optical Kerr microscope. b)Magneto-optical Kerr images of CIDWM for the non-wedged device at 𝜇0Hx = 50 mT. Top (bottom) panel shows the contrast change after applying jc= 2.7 × 1011 A m−2 with a pulse width of 500 ns in the +x (−x) direction. c) Velocity of DWM vdw as a function of in-plane magnetic field Hx for thenon-wedged device under the application of jc = 2.7 × 1011 A m−2. Red (blue) circles represent the data obtained for the device with the initial state ofhead-to-head (tail-to-tail) configuration. d) vdw as a function of jc for the non-wedged device and the devices with ∇tCo = 0.6 × 10−7, 1.1 × 10−7, and 1.7× 10−7, in which 𝜇0Hx = 50 mT was applied.bottom Co layer is along to the x-axis of cartesian coordinates asshown in Figure 1b. Figure 2b displays the transverse resistanceRxy as a function of perpendicular magnetic field Hz for the de-vice of the non-wedged sample, whereRxymainly comes from theanomalous Hall effect proportional to the perpendicular compo-nent of net magnetization of two Co layers. The two Co magneti-zations are antiferromagnetically aligned at lowHz, and those aresaturated ferromagnetically as Hz is increased to 200 mT. Simi-lar to the non-wedged sample, all the samples exhibit the two Comagnetizations coupled antiferromagnetically each other due tothe symmetric IEC.In order to evaluate the magnitude of AIEC, the Rxy–Hz curveswere measured with the additional in-plane magnetic field Hip.The in-plane field angle of Hip is defined as the angle ϕAS fromthe x-axis (see Figure 2a). Figure 2c shows the Rxy–Hz curves forthe device with ∇tCo = 1.1 × 10−7, where 𝜇0Hip = 50 mT wasapplied at ϕAS = 120° (red curve) and 300° (black curve). In thepresence of AIEC, the application of Hip leads to the asymmetryin the up-to-down (UD) and down-to-up (DU) switching fieldsfor the net magnetization due to the preferred magnetic chiral-ity dictated by the AIEC. As a result, the unidirectional shift ofRxy – Hz curve appears by applying Hip. The magnitude of uni-directional shift, related to the AIEC, is represented by ΔHsw,which is obtained from the difference in the switching fieldsHswwith Hip at ϕAS and ϕAS+ 𝜋. The value of ΔHsw is an indicatorof the magnitude of AIEC. Figure 2d plots the ϕAS dependenceof 𝜇0ΔHsw for the device with ∇tCo = 1.1 × 10−7 at 𝜇0Hip = 50mT. The experimental data are fitted by 𝜇0ΔHsw = 𝜇0ΔHsw,maxcos(ϕAS – ϕAS). 𝜇0ΔHsw,max represents the magnitude of AIEC,and ϕAS is the direction of AIEC, which corresponds to the in-plane direction orthogonal to DAIEC. 𝜇0 is the permeability ofthe vacuum. Figure 2e,f summarize 𝜇0ΔHsw,max and ϕAS, respec-tively, as a function of∇tCo.Here,∇tCo = 0means the non-wedgedsample. Originally we anticipated that the increase of ∇tCo sim-ply increases themagnitude of AIEC (ΔHsw,max) and the directionAIEC (ϕAS) is aligned along the wedge direction. As can be seen,however, the device with ∇tCo = 1.1 × 10−7 exhibits the largestΔHsw,max among the present devices. Even the non-wedged sam-ple shows non-negligible ΔHsw,max. In addition, the ϕAS deviatesfrom the expectation, that is, the x-axis (ϕAS = 0° or 180°). Thesefacts suggest that apart from the wedge shape in the bottomCo layer there exist other sources providing the AIEC, e.g., thethickness inhomogeneity and/or the growth-induced magneticanisotropy. Those other contributions were suggested also in pre-Adv. Sci. 2025, 12, e14598 e14598 (4 of 9) © 2025 The Author(s). Advanced Science published by Wiley-VCH GmbH 21983844, 2025, 48, Downloaded from https://advanced.onlinelibrary.wiley.com/doi/10.1002/advs.202514598, Wiley Online Library on [29/12/2025]. See the Terms and Conditions (https://onlinelibrary.wiley.com/terms-and-conditions) on Wiley Online Library for rules of use; OA articles are governed by the applicable Creative Commons Licensehttp://www.advancedsciencenews.comhttp://www.advancedscience.comwww.advancedsciencenews.com www.advancedscience.comvious studies.[19,23,35] Thus, the direction and magnitude of AIECcannot precisely be controlled by changing the thickness gradientin this study. Nevertheless, by introducing the wedge-shaped Colayers with different thickness gradients, a series of samples ex-hibiting different AIEC fields allow us to examine the influenceof AIEC on the CIDWM.Figure 3a is the setup for the CIDWM observation using themagneto-optical Kerr microscope. The representative results aregiven in Figure 3b, which were observed for the non-wedged de-vice. One sees that there are two gray contrasts: dark gray andlight gray. The dark gray and light gray regions correspond tothe magnetic domains with the head-to-head and tail-to-tail con-figurations, respectively, of magnetic moments between the topand bottom Co layers as depicted in Figure 1c. For the presentCIDWM experiment, the reversed magnetic domain was nucle-ated at a certain position in the wire when the current pulse witha certain current density jc was applied. Although this reverseddomain nucleation procedure is not a precisely-controlled man-ner, we could successfully nucleate the reversed domain in al-most the middle of wire. The domain nucleation was attributableto the switching due to the dual SOT. The positions of DWsare denoted by the white arrows. The top (bottom) panel showsthe contrast change after the application of jc = 2.7 × 1011 Am−2 and with a pulse width of 500 ns in the +x (−x) direc-tion, where 𝜇0Hx = 50 mT was applied. The DW moves alongthe electric current direction (opposite to the direction of elec-tron flow) with increasing the number of current pulse applica-tion. This tendency can be explained with the scenario of DWMinduced by SOT.[37–39] The spin Hall effect in the Pt and/or Irlayer generates the spin current interacting with the Co magne-tizations. According to the SOT switching experiment reportedpreviously,[19] the major source of SOT is the spin Hall effectin the Pt layers while the spin Hall effect in the Ir interlayer isnot significant. Thus, the SOT coming from the top and bot-tom Pt layers act on the top and bottom Co magnetizationsindividually.The velocity of DWM vdw is evaluated from the distance of DWmovement and the duration of current pulse. Figure 3c plots vdwas a function ofHx for the non-wedged device under the applica-tion of jc = 2.7 × 1011 A m−2. The red (blue) circles representthe data obtained for the device with the initial state of head-to-head (tail-to-tail) configuration. Considering the experimentalsituation depicted in Figure 1, the tail-to-tail region having theupward net magnetization (↑) is created in the head-to-head re-gion having the downward net magnetization (↓) and the regionwith ↑ is expanded by the CIDWM. Thus, the experiment startingfrom the head-to-head configuration corresponds to the CIDWMfor the up-down (↑↓) DW while the tail-to-tail initial configura-tion leads to the down-up (↓↑) DW. Both cases exhibit the linearchanges in vdw against Hx, but show the opposite signs in theslopes. As can be seen, vdw is almost equal to zero at 𝜇0Hx = 0mT.These experimental facts indicate that in line with previous find-ings the contribution of spin transfer torque within the Co layersis negligible while the SOT is the dominant source of CIDWM.The detailed discussion will be given later. Figure 3d summarizesvdw as a function of jc for the non-wedged device and the deviceswith ∇tCo = 0.6 × 10−7, 1.1 × 10−7, and 1.7 × 10−7, in which 𝜇0Hx= 50 mT was applied. After the nucleation of reversed domainat a certain jc, which is defined as the nucleation current den-Figure 4. Effect of AIEC on nucleation current density jnucl and vdw for theCIDWM. a) jnucl obtained at𝜇0Hx = 50mT as a function ofΔHsw,max. b) vdwas a function of ΔHsw,max, where vdw was evaluated under the applicationof jc = 2.3 × 1011 A m−2 and 𝜇0Hx = 50 mT.sity jnucl, vdw nonlinearly increases with increasing jc for all thedevices.To discuss the effect of AIEC on the CIDWM, we plots the jnuclobtained at 𝜇0Hx = 50 mT as a function of ΔHsw,max in Figure 4a.One can see that there is a negative correlation between jnucl andΔHsw,max. Namely, the AIEC field promotes the nucleation ofreversed domain under the dual SOT application. On the otherhand, vdw clearly increases with ΔHsw,max as shown in Figure 4b,where vdw was evaluated under the application of jc = 2.7 × 1011 Am−2 and 𝜇0Hx = 50 mT. At this condition, the fastest vdw was ob-tained to be 31 m s−1 for the device with ∇tCo = 1.1 × 10−7, whichis one order of magnitude larger than the vdw for the non-wedgeddevice. The positive correlation between vdw and ΔHsw,max meansthat the AIEC field plays a role for the efficient CIDWM. Accord-ing to the previous works,[27,35] the oblique sputter-depositionor the selection of nonmagnetic interlayer with large spin-orbitcoupling can enhance the magnitude of AIEC, leading to thefurther improvement of CIDWM efficiency. One may be won-dering how the degree of compensation between top and bottomCo magnetizations affects vdw. A previous work reported that theclosely compensated state leads to the fast vdw.[17] Although thewedged bottom Co layers give a spatial change in the degree ofcompensation, we do not observe any relation between vdw and∇tCo in the present system. In addition, one may think why evenAdv. Sci. 2025, 12, e14598 e14598 (5 of 9) © 2025 The Author(s). Advanced Science published by Wiley-VCH GmbH 21983844, 2025, 48, Downloaded from https://advanced.onlinelibrary.wiley.com/doi/10.1002/advs.202514598, Wiley Online Library on [29/12/2025]. See the Terms and Conditions (https://onlinelibrary.wiley.com/terms-and-conditions) on Wiley Online Library for rules of use; OA articles are governed by the applicable Creative Commons Licensehttp://www.advancedsciencenews.comhttp://www.advancedscience.comwww.advancedsciencenews.com www.advancedscience.comthe y-directional AIEC field positively affects DW velocity. Weconsider that the present case is still far from the ideal CIDWMshowing the linear correlation between vdw and jc. Rather thenucleation energy and the pinning potential for DW determinethe process for CIDWM, which may be affected by the AIECfield. This is a possible explanation for the fact that the AIECfield positively affects DW velocity regardless of ϕAS.3. Theoretical Calculation and DiscussionIn order to understand the CIDWM by dual SOT, we carryout micromagnetic simulations in a synthetic antiferromagneticnanowire with a custom-developed code. Here, we focus to elu-cidate the following two points: i) How the dual SOT can drivethe DWM despite that a simple argument predicts that the spininjections from the top and bottom Pt layers with the oppositespin polarizations lead to a net zero effect on the magnetizationdynamics. ii) How the AIEC affects the CIDWM.We model our synthetic antiferromagnet by the following sur-face magnetic energy density (U),U = JAFmA ⋅mB + DAIEC ⋅(mA ×mB)+ A∑i=x,y,z[tA(𝜕imA)2+ tB(𝜕imB)2] − K[tA(mA,z)2 + tB(mB,z)2]−𝜇0MsH ⋅(tAmA + tBmB)(1)where A is the exchange stiffness, K is the perpendicular mag-netic anisotropy constant,Ms is the saturation magnetization,His the externalmagnetic field, and tA(B) is the thickness of the layerA (B). The dynamics ofmμ (μ =A, B) are described by the coupledLandau-Lifshitz-Gilbert (LLG) equations𝜕m𝜇𝜕t= −𝛾m𝜇 ×H𝜇 + 𝛼m𝜇 ×𝜕m𝜇𝜕t− 𝛾m𝜇 ×(m𝜇 ×HSOT𝜇)(2)where 𝛾 is the gyromagnetic ratio and 𝛼 is the damping con-stant. The effective magnetic fields Hμ are defined by H𝜇 = −(𝜇0Mst𝜇)−1(𝛿U/𝛿m𝜇). The last term in Equation (2) describes thedual SOT, which is characterized by the effective fieldsHSOT𝜇= ±ℏ𝜃SH2e𝜇0Mst𝜇jcy (3)with the upper (lower) sign corresponding to μ = A (B) and 𝜃SHthe effective spin Hall angle.Under the surface energy density with H = 0, the system canaccommodate a stable DW in equilibrium.[40] We prepare a BlochDW as the initial state, i.e., the magnetizations rotate in the yzplane in the DW region, and then examine the dynamics of theDW in the presence of current and magnetic field. We choose aBloch DW since both the dual SOT andHx act to stabilize a Blochstructure: The dual SOT with Equation (2) simply tries to alignmA and mB along + y and − y, respectively, while a Bloch struc-ture can also reduce the Zeeman energy by allowing for the mag-netizations to slightly cant toward the x direction. We assume|DAIEC| to be sufficiently small that the influence of the AIEC onthe DW structure can be ignored. The parameter set used is:Ms= 1.1 × 106 A m−1, 𝛼 = 0.06, JAF = 0.5 × 10−3 J m−2, A = 1 ×10−11 J m−1, K = 2 × 105 J m−3, tA = 0.9 nm, and tB = 0.65 nm.The values ofMs, K and JAF are taken from experimental data onour Co/Ir/Co system, [19] 𝛼 from reported values for similar sys-tems, [41] and A from a typical value for ferromagnets.[42] We in-troduce the in-plane angle 𝜃D(= ϕAS − 𝜋/2 ) of the AIEC as DAIEC= |DAIEC| (cos 𝜃D, sin 𝜃D, 0).Figure 5a plots the calculated vdw as a function ofHx under theapplication of jc = 2.7 × 1011 A m−2, where the magenta (cyan)symbols correspond to the results for the up-down (down-up)DW. Here, the AIEC is set to |DAIEC| = 0.007JAF and 𝜃D = 45°.The calculation reproduces quantitatively well the major exper-imental features observed in Figure 3c: the linear dependenceof vdw on Hx, the sign reversal of vdw between the up-down anddown-up DW configurations, and no efficient CIDWM withoutHx.Figure 5b shows the jc dependence of the calculated vdw withseveral different |DAIEC|, where 𝜃D = 45° and 𝜇0Hx = 50 mT. vdwexhibits linear dependence on jc, and shifts vertically as |DAIEC|varies. The nonzero vdw at jc = 0 is due to the combined effect ofthe AIEC andHx,[40] as discussed inmore detail below. The resultin Figure 5b confirms that the dual SOT ismainly responsible forthe observed DWM. The calculated CIDWM shows zero thresh-old current density, in contrast to the experiment (Figure 3d). Thethreshold in jc for CIDWMmay be attributed to the potential bar-rier for nucleating the reversed domains as well as pinning po-tentials due to impurities, which are not taken into account in thepresented calculation.Displayed in Figure 5c is the 𝜃D dependence of vdw, with jc= 2.7 × 1011 Am−2 and 𝜇0Hx = 50 mT. As elaborated on shortly,this 𝜃D dependence originates from the fact that only the y com-ponent ofDAIEC gives a major contribution to vdw. Figure 5d plotsthe experimentally-observed vdw as a function of 𝜃D. It is difficultto make a direct and systematic comparison between the exper-iment and calculation for technical reasons. The number of ex-perimental data points is limited, because only a small numberof devices with the desired tCo can be obtained from the wedgedsamples. In addition, precise control of the direction and magni-tude of the AIEC field remains difficult in experiments. Despitethese limitations, however, our results clearly demonstrate thatthe DW velocity can be tuned by engineering the AIEC. A moredirect comparison between the experimental and numerical re-sults is given in Figure S2 (Supporting Information).Here, we consider the physical mechanism underlying theDWM driven by the dual SOT. For the sake of simplicity, we as-sume the antiferromagnetic limit where tA = tB and JAF is by farthe most dominant energy scale in U. Starting from the coupledLLG equations (2), we rewrite them in terms of the Néel vectorn = mA−mB2and the canting moment m = mA+mB2, where |m| ≪ 1because of the strong antiferromagnetic exchange coupling. Fol-lowing the procedure given in [40] but now with the dual SOTincluded, it can be shown that m is expressed as a function of n:In a static state,m = 1HIECn ×(−n ×H +HAIEC + ΔHSOT)(4)where Δ HSOT = HSOTA −HSOTB , and HIEC and HAIEC are the ef-fective fields associated with the IEC and AIEC, respectively. TheAdv. Sci. 2025, 12, e14598 e14598 (6 of 9) © 2025 The Author(s). Advanced Science published by Wiley-VCH GmbH 21983844, 2025, 48, Downloaded from https://advanced.onlinelibrary.wiley.com/doi/10.1002/advs.202514598, Wiley Online Library on [29/12/2025]. See the Terms and Conditions (https://onlinelibrary.wiley.com/terms-and-conditions) on Wiley Online Library for rules of use; OA articles are governed by the applicable Creative Commons Licensehttp://www.advancedsciencenews.comhttp://www.advancedscience.comwww.advancedsciencenews.com www.advancedscience.comFigure 5. a) Calculated vdw as a function ofHx under the application of jc = 2.7 × 1011 A m−2. The magenta (cyan) marks represent the calculated valuesfor the up-down DW (down-up DW). b) Calculated vdw as a function of jc with changing DAIEC, where 𝜇0Hx was set to be 50 mT. c) Calculated vdw as afunction of the in-plane angle of DAIEC, 𝜃D under the application of jc = 2.7 × 1011 A m−2, and 𝜇0Hx = 50 mT. d) Experimental vdw as a function of 𝜃Dunder the application of jc = 2.3 × 1011 A m−2 and 𝜇0Hx = 50 mT.first term in Equation (4) simply represents the field-inducedcanting moment. Interestingly, as indicated by the second andthird terms, the AIEC and the dual SOT play the equivalent rolewhen it comes to their contribution to m. As n ≈ ±z in each do-main, the y component of HAIEC + ΔHSOT develops the x com-ponent ofm in the domains, which directly couples toHx via theZeeman interaction. The DW structure formed by m followingthat of n is therefore driven into motion by Hx, accompanied bythe entire DWM. The part due toΔHSOT is the CIDWMdue to thedual SOT, amechanismwhich has never been discussed.We notethat, while the part due toHAIEC has been long known in the con-text of bulk antiferromagnets,[40] where HAIEC originates ratherfrom the crystalline symmetry, it has never been demonstratedfor a DW in a synthetic thin film system. If |DAIEC| becomes suf-ficiently large, the AIEC could affect vdw via stabilizing a partic-ular DW configuration (Néel, Bloch or intermediate) dependingon 𝜃D. While there are possible directions for further theoreticalanalysis, these are beyond the scope of the current work and haveto be reserved for another study.4. ConclusionThe roles of dual SOT and the AIEC for the CIDWM were ex-perimentally and theoretically studied for the perpendicularly-magnetized synthetic antiferromagnets using a Pt/Co/Ir/Co/Ptmultilayer. The electric current application nucleates a reversedmagnetic domain and shows the displacement of the domainwallexisting between the head-to-head and tail-to-tail domains. Fromthe electric current direction for CIDWM and magnetic field de-pendence of vdw, we can conclude that the dual SOT plays themajor role for CIDWM. The AIEC field contributed to the reduc-tion of the current density required for nucleating the revised do-main and leads to an increase in vdw. These facts suggest thatthe existence of AIEC leads to the improvement of performanceof CIDWM in these specially designed devices. To understandour results, we developed an appropriate theoretical model forCIDWM by dual SOT with AIEC. Our results provide a new av-enue to design highly efficient SOT domain-wall devices basedon a synthetic antiferromagnet.5. Experimental SectionThin Film Preparation and Device Fabrication: The multilayer stacksof Ta (2)/Pt (3)/Co (0.65 or tCo)/Ir (1.3)/Co (0.9)/Pt (3)/Ta (1) (thicknessin nanometer) were deposited on a Si-O substrate using dc magnetronsputtering at room temperature with an Ar pressure of 0.4 Pa. Beforedeposition, the chamber was evacuated to a base pressure below 6.0× 10−6 Pa. The area of deposited films was 9 × 9 mm2, and tCo wasAdv. Sci. 2025, 12, e14598 e14598 (7 of 9) © 2025 The Author(s). Advanced Science published by Wiley-VCH GmbH 21983844, 2025, 48, Downloaded from https://advanced.onlinelibrary.wiley.com/doi/10.1002/advs.202514598, Wiley Online Library on [29/12/2025]. See the Terms and Conditions (https://onlinelibrary.wiley.com/terms-and-conditions) on Wiley Online Library for rules of use; OA articles are governed by the applicable Creative Commons Licensehttp://www.advancedsciencenews.comhttp://www.advancedscience.comwww.advancedsciencenews.com www.advancedscience.comcontinuously varied in the length of 9 mm using a linear moving shutter.The thin films were patterned into a Hall-bar-shape using electronbeam lithography and Ar-ion milling. The channel width was 5 μm. Theelectrical contact pads of Cr (20 nm)/Au (200 nm) were fabricated usingphotolithography and ion-beam sputtering.Transport Property Measurement: The transverse resistance Rxy wasdetected by applying an ac charge current of 20 μA with a frequency of9997 Hz using a lock-in amplifier SR830. Rxy as a function of out-of-planemagnetic field Hz was measured with and without the additional in-planemagnetic field Hip at room temperature.Magneto-Optical Kerr Effect Imaging: The domain wall motion was vi-sualized using a commercial Evicomagnetics GmbHKerrmicroscopy withan in-plane magnetic field coil. A pulse-shaped charge current with a pulsewidth of 500 ns was applied in a device using a function generator Agilent33250A. The amplifier with a gain of 40 dB was connected between a func-tion generator and a device. The pulse-shaped signal was detected usingan oscilloscope Tektronix OPO7354. The external magnetic fields in therange of from 30 to 100 mT were applied during the experiments.Supporting InformationSupporting Information is available from the Wiley Online Library or fromthe author.AcknowledgementsThe authors thank T. Sasaki for her help to do the film deposition by ionbeam sputtering, and S. Mitani for his help for polar magneto-opticalKerr effect measurement. The device fabrication was partly carried outat the Cooperative Research and Development Center for Advanced Ma-terials, IMR, Tohoku University. This work was supported by JSPS KAK-ENHI Grant-in-Aid for Scientific Research (A) (JP23H00232, JP24H00409),MEXT Initiative to Establish Next-generation Novel Integrated CircuitsCenters (X-NICS) Grant Number JPJ011438, and ERATO “Magnetic Ther-mal Management Materials” (No. JPMJER2201) from Japan Science andTechnology Agency (JST). The group in Mainz acknowledges funding bythe Deutsche Forschungsgemeinschaft (DFG, German Research Foun-dation) – TRR 173/3 – 268565370 Spin+X (Projects B02, B13, and A01)and the European Union through the Horizon 2020 and Horizon Eu-rope projects under Grant Agreement No. 101070290 (NIMFEIA) and EICPathfinder OPEN grant 101129641 (OBELIX) and the European ResearchCouncil through the Synergy Grant No. 856538 (3D MAGiC as well as theDAAD through a PPP collaborative grant between Mainz and Tohoku.Conflict of InterestThe authors declare no conflict of interest.Data Availability StatementThe data that support the findings of this study are available from the cor-responding author upon reasonable request.Keywordsantisymmetric interlayer exchange coupling, magnetic domain wall mo-tion, spin orbit torque, synthetic antiferromagnetReceived: July 31, 2025Revised: September 11, 2025Published online: October 17, 2025[1] P. Grünberg, R. Schreiber, Y. Pang, M. B. Brodsky, H. Sowers, Phys.Rev. 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Edwards, A. Umerski, Phys. Rev. B 2014, 90,014420.[42] Y. Yamane, J. Ieda, S. Maekawa, Appl. Phys. Lett. 2012, 100,162401.Adv. Sci. 2025, 12, e14598 e14598 (9 of 9) © 2025 The Author(s). Advanced Science published by Wiley-VCH GmbH 21983844, 2025, 48, Downloaded from https://advanced.onlinelibrary.wiley.com/doi/10.1002/advs.202514598, Wiley Online Library on [29/12/2025]. See the Terms and Conditions (https://onlinelibrary.wiley.com/terms-and-conditions) on Wiley Online Library for rules of use; OA articles are governed by the applicable Creative Commons Licensehttp://www.advancedsciencenews.comhttp://www.advancedscience.com Efficient Manipulation of Magnetic Domain Wall by Dual Spin-Orbit Torque in Synthetic Antiferromagnets 1. Introduction 2. Experimental Results 3. Theoretical Calculation and Discussion 4. Conclusion 5. Experimental Section Supporting Information Acknowledgements Conflict of Interest Data Availability Statement Keywords