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Pingfan Gu, Cong Wang, Dan Su, Zehao Dong, Qiuyuan Wang, Zheng Han, [Kenji Watanabe](https://orcid.org/0000-0003-3701-8119), [Takashi Taniguchi](https://orcid.org/0000-0002-1467-3105), Wei Ji, Young Sun, Yu Ye

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[Multi-state data storage in a two-dimensional stripy antiferromagnet implemented by magnetoelectric effect](https://mdr.nims.go.jp/datasets/dc4bcda0-9478-4433-a299-3ec4ba5fa6b3)

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Multi-state data storage in a two-dimensional stripy antiferromagnet implemented by magnetoelectric effectArticle https://doi.org/10.1038/s41467-023-39004-4Multi-statedata storage in a two-dimensionalstripy antiferromagnet implemented bymagnetoelectric effectPingfan Gu1,2, Cong Wang 3,4, Dan Su5, Zehao Dong1, Qiuyuan Wang1,Zheng Han6,7,8, Kenji Watanabe 9, Takashi Taniguchi 10, Wei Ji 3,4 ,Young Sun11 & Yu Ye 1,2,8,12A promising approach to the next generation of low-power, functional, andenergy-efficient electronics relies on novel materials with coupled magneticand electric degrees of freedom. In particular, stripy antiferromagnets oftenexhibit broken crystal and magnetic symmetries, which may bring about themagnetoelectric (ME) effect and enable the manipulation of intriguing prop-erties and functionalities by electrical means. The demand for expanding theboundaries of data storage and processing technologies has led to thedevelopment of spintronics toward two-dimensional (2D) platforms. Thisworkreports the ME effect in the 2D stripy antiferromagnetic insulator CrOCl downto a single layer. By measuring the tunneling resistance of CrOCl on theparameter space of temperature, magnetic field, and applied voltage, weverified the ME coupling down to the 2D limit and probed its mechanism.Utilizing themulti-stable states andMEcoupling atmagnetic phase transitions,we realize multi-state data storage in the tunneling devices. Our work not onlyadvances the fundamental understanding of spin-charge coupling, but alsodemonstrates the great potential of 2D antiferromagnetic materials to deliverdevices and circuits beyond the traditional binary operations.The field of spintronics concerns the processing of digital information,where an external stimulus, preferably an electrical stimulus, is appliedto control the spin order in a magnetic system that acts as a “0" or “1"digital bit. As a more common magnetic ground state than ferro-magnetism, antiferromagnetism has received increasing attention inrecent years due to its promising prospect for spintronic devices, suchas their robustness against external perturbations, no stray fields, andultrafast dynamics1. More intriguingly, antiferromagnets often man-ifest complicated spin configurations and phase transitions, openingup the possibility to implement new data storage logic superior toconventional binary algorithms. However, the negligible net magneti-zation also makes it difficult to read out or electrically manipulate theantiferromagnetic order, which is desired for information technology.As a result, formidable efforts have been devoted to switchingReceived: 27 January 2023Accepted: 25 May 2023Check for updates1State Key Laboratory for Mesoscopic Physics and Frontiers Science Center for Nano-optoelectronics, School of Physics, Peking University, Beijing, China.2Collaborative Innovation Center of QuantumMatter, Beijing, China. 3Beijing Key Laboratory of Optoelectronic Functional Materials andMicro-Nano Devices,Department of Physics, Renmin University of China, Beijing, China. 4Key Laboratory of Quantum State Construction andManipulation (Ministry of Education),Renmin University of China, Beijing, China. 5Beijing National Laboratory for Condensed Matter Physics, Institute of Physics, Beijing, China. 6State KeyLaboratory of Quantum Optics and Quantum Optics Devices, Institute of Optoelectronics, Taiyuan, China. 7Collaborative Innovation Center of ExtremeOptics, Shanxi University, Taiyuan, China. 8Liaoning Academy of Materials, Shenyang, China. 9Research Center for Functional Materials, National Institute forMaterials Science, Tsukuba, Japan. 10International Center for Materials Nanoarchitectonics, National Institute for Materials Science, Tsukuba, Japan. 11Centerof Quantum Materials and Devices, and Department of Applied Physics, Chongqing University, Chongqing, China. 12Yangtze Delta Institute of Optoelec-tronics, Peking University, Nantong, China. e-mail: wji@ruc.edu.cn; youngsun@cqu.edu.cn; ye_yu@pku.edu.cnNature Communications |         (2023) 14:3221 11234567890():,;1234567890():,;http://orcid.org/0000-0002-5297-9586http://orcid.org/0000-0002-5297-9586http://orcid.org/0000-0002-5297-9586http://orcid.org/0000-0002-5297-9586http://orcid.org/0000-0002-5297-9586http://orcid.org/0000-0003-3701-8119http://orcid.org/0000-0003-3701-8119http://orcid.org/0000-0003-3701-8119http://orcid.org/0000-0003-3701-8119http://orcid.org/0000-0003-3701-8119http://orcid.org/0000-0002-1467-3105http://orcid.org/0000-0002-1467-3105http://orcid.org/0000-0002-1467-3105http://orcid.org/0000-0002-1467-3105http://orcid.org/0000-0002-1467-3105http://orcid.org/0000-0001-5249-6624http://orcid.org/0000-0001-5249-6624http://orcid.org/0000-0001-5249-6624http://orcid.org/0000-0001-5249-6624http://orcid.org/0000-0001-5249-6624http://orcid.org/0000-0001-6046-063Xhttp://orcid.org/0000-0001-6046-063Xhttp://orcid.org/0000-0001-6046-063Xhttp://orcid.org/0000-0001-6046-063Xhttp://orcid.org/0000-0001-6046-063Xhttp://crossmark.crossref.org/dialog/?doi=10.1038/s41467-023-39004-4&domain=pdfhttp://crossmark.crossref.org/dialog/?doi=10.1038/s41467-023-39004-4&domain=pdfhttp://crossmark.crossref.org/dialog/?doi=10.1038/s41467-023-39004-4&domain=pdfhttp://crossmark.crossref.org/dialog/?doi=10.1038/s41467-023-39004-4&domain=pdfmailto:wji@ruc.edu.cnmailto:youngsun@cqu.edu.cnmailto:ye_yu@pku.edu.cnantiferromagnets through spin torques from exchange bias2, spin-orbit torque3 and spin-galvanic effect4, etc.Apart from the above-mentioned “external" approaches, the“internal" approach to antiferromagnetic spintronics rests uponmaterials with coupled degrees of freedom5–7 such as magneticmoment, electric polarization and strain, which are often referred to asthe magnetoelastic or magnetoelectric materials8. However, as thetransitionmetald electrons are supposed to repel the tendency for off-center ferroelectric distortion9, the coexistence of magnetic momentand electric polarization is hard to achieve. The coupled energy terms,as well as the electric polarization, require materials with low crystaland magnetic symmetry. Improper magnetic ferroelectrics10,11 wherethe ferroelectricity originated from spin-order-driven inversion sym-metry breaking are considered to be an ideal platform to realize themutual clamping of the order parameters of ferroelectricity andantiferromagnetism12–14. Based on the spin frustration and spin-orbitcoupling theories, three spin-structure-induced electric polarizationmechanisms have been established, namely the exchange strictionmodel15, the inverse Dzyaloshinskii-Moriya interactionmodel16 and thep-d hybridization model17.To further explore ME-based fundamental physics and developpractical applications for information devices, it is inevitable toextend the research to the two-dimensional (2D) limit18–23. Recently,multiferroicity resulting from inverse Dzyaloshinskii-Moriyainteraction24,25 and p-d hybridization26 have been evidenced in vander Waals materials. Nevertheless, the direct coupling betweenmagnetic moment and electric polarization in the 2D limit has notbeen reported. The air-stable van der Waals insulator CrOCl, with astripy antiferromagnetic ground state and thus both broken rota-tional symmetry and translation symmetry perpendicular to thestripes27, appears to be a potential candidate to exhibit the intrinsic2D ME effect. The magnetic phase transitions and magnetoelasticcoupling effect of CrOCl have been verified in the 2D limit27,28previously. In addition, exotic quantum Hall effects29 and insulatorphases30 were observed in the graphene/CrOCl heterostructures,implying rich physics in this fascinating material.In this work, we report the intrinsic ME effect in CrOCl down tothe 2D limit by tunneling transport measurement. The I − V curve ofthe CrOCl tunneling device exhibits obvious hysteresis below theNéel temperature, signaling an electric phase transition accom-panying the magnetic phase transition. The metastable states aresupposed to result from the antiferroelectric dipoles in the low-temperature phase, which was evidenced by first-principles calcu-lations and dielectric measurements. We also realize direct manip-ulation of resistance states through electric and magnetic fieldsweeps, demonstrating a data storage device with continuouslyadjustable outputs. The metastable states in the first-order phasetransition resulting from theME coupling break through the barriersof write-in and read-out information in antiferromagnets and hope-fully can open an effective route for multi-state memories with highstorage density, nonvolatility, low energy consumption, and smallmemory cell.Results and discussionTo understand the intrinsic ME effect, we start with the energy cou-pling terms for the ground state of CrOCl. As reported by severalneutron scattering results31–33 and confirmed by DFT calculations27,34,CrOCl transforms into the↑↑↓↓ stripy AFMground state at ~ 14 K. Themagnetic frustration drives the crystal from the orthorhombic spacegroup Pmmn (Fig. 1a) to the monoclinic space group P21/m(Fig. 1b)32,33,35. Despite the monoclinic distortion, the space inversionoperation P preserves in the ↑↑↓↓ ground state due to the specialzigzagatom-chain structure ofCrOCl. The twosublayers of a single vander Waals layer are spatially inverse to each other, thus preventingspontaneous electric polarization from appearing. However, based onthe symmetryoperations of stripy antiferromagnets, we canobtain theCr O Clbadxyzc10 20 304567893.063.073.083.09-0.3-0.2-0.10.00.00.20.40.6M (mμ B/Cr3+)T (K)εrΔε r/εr(0T) (%) M (μB /Cr 3+)μ0H (T)0 2 4 6α = 90° α = 90.07°1 Å 0.01 e·ÅFig. 1 | Magnetic and dielectric properties of bulk CrOCl. a Crystal structure ofCrOCl above the Néel temperature with the Pmmn space group in a unit cell.b Crystal structure of CrOCl below the Néel temperature with the P21/m spacegroup in a unit cell. The structural parameter α that defines the crystal symmetry islabeled in the unit cell. The vectors on each atom represent the atomicdisplacements (magnified 100 times), while the dashed boxes and open arrowsrepresent the calculated antiferroelectric polarizations of different Cl-Cr-O chains.cTemperaturedependenceof relative permittivity εr andmagneticmomentof bulkCrOCl crystal. d Δεr/εr(0 T) versus out-of-plane magnetic field and the corre-sponding M −H curve at 2 K.Article https://doi.org/10.1038/s41467-023-39004-4Nature Communications |         (2023) 14:3221 2free energy in the wave form36,37:F =12ra∣Ak∣2 +12rs∣Sq∣2+ λ1 ðSq � SqÞA*k + c:c:h i+ 2λ2∣Sq∣2∣Ak∣2ð1Þwhere Sq is the amplitude of spin density modulation with the wavevector of q and Ak is the corresponding lattice modulation with thewave vector of k. ra, rs, λ1 and λ2 are constant parameters of thematerial. Minimizing the free energy, we obtain the lattice modulationin a collinear spin configuration:Ak =λ1raSq � Sq + c:c: ð2ÞThe lattice modulation, consequently, can only be present withk = ± 2q. In other words, a long-range magnetic wave order with aperiod of 4b (b is the lattice constant along the crystalb-axis) induces astrain wave with half of its period, 2b. The displacements of the atomsin CrOCl have been verified and resolved by neutron scattering32,33 andX-ray diffraction experiments35. Our density functional theory (DFT)calculations also confirm the displacements of atoms in the ↑↑↓↓ground state with a period of 2b, (Fig. 1b), showing similar displace-ment directions and magnitudes as the neutron scatteringexperiments33. Based on the above phenomena, we can regard the↑↑↓↓ stripy AFM phase as an “antiferroelectric" order consisting ofthe electric dipoles of the distorted Cl-Cr-O chains away from theinversion center (dashedboxes in Fig. 1b). Therefore, ordered effectivedipoles are formed as indicated by the open arrows in Fig. 1b, while theelectric dipole of each atom is provided in Supplementary InformationFig. S1. Both the contributions of ions and electrons to polarization aretaken into account by the Born effective charge method (seeMethods).To further investigate the two-fold distorted order and the MEeffect, we conducted dielectric and pyroelectric measurements inCrOCl crystals. The pyroelectric current exhibits a small but obser-vable peak at the Néel temperature, which can be attributed to theantiferroelectric domains locally breaking the inversion symmetry (seedetailed discussions in Supplementary Information Fig. S2 and S3).Correspondingly, the relative permittivity εr of CrOCl shows a sharpincrease of ~ 0.01 at ~ 14 K (the εr − T curve in Fig. 1c) with decreasingtemperature. It should be noted that the layer thickness experiences asudden expansion at the Néel temperature32, which tends to result in adecrease in the measured capacitance, as C = εrε0Sd (see Methods). As aresult, the increase in εr can only be attributed to the appearance ofadditional tunable dipoles. Most importantly, both the pyroelectricpeaks and the change of εr completely accord with the Néel tem-perature where the net moment drops (the M − T curve in Fig. 1c),evidencing that the structural phase transition is a product of MEcoupling. In other words, the symmetry-allowed ME coupling termguarantees that there is a corresponding relationship between themagnetic order and the electric order, so when the magnetic orderexperiences phase transitions, the electric order transforms corre-spondingly. This is thebasic concept of theMEeffect inCrOCl, which isalso manifested in the phase transitions under the magneticfield (Fig. 1d).According to the previous report27, CrOCl transforms into thecollinear ↑↑↑↓↓ phase under an external out-of-plane field of ~4.5 T (the M −H curve in Fig. 1d). Our calculations show that inthe ↑↑↑↓↓ phase, the crystal relaxes to an orthorhombic struc-ture (see Supplementary Information Table S1), in which theatomic displacements and the electric dipoles show a period of5b. Under an external electric field of 0.07 V/Å (close to theexperimental values of the tunneling measurements below), the↑↑↓↓ phase produces a net polarization of 116.50 μC/m2, which iseight times larger than that of the ↑↑↑↓↓ phase (14.42 μC/m2).Correspondingly, the measured εr undergoes a decrease upon themagnetic phase transition to the ↑↑↑↓↓ phase (Fig. 1d), so wecan simply estimate the additional polarization from the dielec-tric measurement, ΔP = Δεr · ε0E ≈ 61.98 µC/m2, very close to thepolarization difference between the ↑↑↓↓ and ↑↑↑↓↓ phasesof ~ 102.11 µC/m2 under the same electric field. This suggests thatin the ↑↑↓↓ structurally distorted phase, there is anothermechanism that produces the additional electric polarizationunder an external field, possibly the canting of the antiferro-electric dipoles. On the contrary, the ↑↑↑↓↓ phase is ratherstructurally stable and the electric dipoles can hardly be adjustedby the external field.Now that we have demonstrated the existence of spin-inducedadditional electric polarization in bulk CrOCl, from a macroscopicperspective, we would expect the interactions between the electricand magnetic degrees of freedom and consequently the manipulationof the spin order by the electric field, or vice versa. To achieve a largeelectric field in ultra-compact nanodevices, we fabricated verticaltunneling devices based on single- to few-layer CrOCl flakes (Fig. 2a).Cross-structured few-layer graphite stripes are used to contact theCrOCl tunneling layer, and the whole device is encapsulated by hex-agonal boron nitride (h-BN). The electric field in CrOCl can reach ~ 0.1V/Å, where the spin-induced electric dipoles are expected to bepolarized and have a substantial impact on the tunneling current.We first demonstrate the influence of the additional electricpolarization in CrOCl flakes through the hysteresis of the I−V curves.Here we show the tunneling current of a CrOCl device with a thicknessof ~9.1 nm (approximately 12 layers), labelled as device 1. As shown inFig. 2b, the tunneling currents in the sweep-up and the sweep-downprocesses deviate significantly from each other under the sameapplied voltage at a temperature of 2 K, manifesting as an obviousclockwisehysteresis. In sharp contrast, the I−V curve at 20K (above theNéel temperature) shows no sign of hysteresis. The electric hysteresiscan be further viewed in the 2D map of temperature and bias voltage(Fig. 2c), where the current polarization ρ is defined asρ = (Rup −Rdown)/(Rup + Rdown). Clearly, ρ exhibits non-zero valuesbelow ~ 12 K, in perfect accordance with the Néel temperature of theexfoliated CrOCl27. The clockwise hysteresis results in a negative ρunder positive bias and a positive ρ under negative bias. The absolutevalue of ρ decreases with increasing temperature and eventuallybecomes zero at the Néel temperature (Fig. 2c, d), implying the dis-appearance of the additional polarization as the antiferromagneticorder collapses. From the R − T curves of different sweeping processesat 5 V (Fig. 2e), it can be seen that in the sweep-up process, the resis-tance drops significantly (entering a lower resistance state) below theNéel temperature, while in the sweep-down process, the resistanceincreases (entering a higher resistance state). The above phenomenaindicate that the direction of the additional polarization, in otherwords, the configuration of the dipole order, dominates in the changeof the measured tunneling resistance upon the magnetic phase tran-sition. The resistance at − 5 V exhibits almost antisymmetric behavior,as shown in Supplementary Information Fig. S4.Asmentioned earlier, in the absenceof adjustable electric dipoles,the ↑↑↑↓↓ phase under an external magnetic field is rather structu-rally stable. The resistances under different electrical sweeping pro-cesses converge at the transition field (Fig. 2f) and show completelydifferent magnetoresistance behaviors at the ↑↑↓↓ phase (see detailsin Supplementary Information Fig. S5 and S6), which implies the dis-appearance of the I −V hysteresis in the↑↑↑↓↓ phase and is in perfectagreement with our theory. The hysteresis of the I − V curve in the↑↑↓↓ state can be observed in all CrOCl devices of varying thicknesses(Supplementary Information Fig. S7) down to monolayer. Suspendingthe sweeping process at a specific voltage, the resistance value relaxesArticle https://doi.org/10.1038/s41467-023-39004-4Nature Communications |         (2023) 14:3221 3slowly with a time constant of several hours (see SupplementaryInformation Fig. S12),which is highly reproducible as shown in a single-layer CrOCl device (device 2 in Fig. 2g).We note that in tunneling devices, extrinsic factors such as elec-tromigration, oxygen vacancy redistribution, or charge trappings mayalso result in such hysteresis behaviors38. However, the fact that thehysteresis accompanies the magnetic transitions distinguishes it as anintrinsic characteristic of CrOCl. In addition to Fig. 2, wepresent the 2Dmap of ρ over the entire voltage range (Supplementary InformationFig. S8 and S9), the hysteresis behavior in different devices (Supple-mentary Information Fig. S7) and in different temperature-sweepingprocesses (Supplementary Information Fig. S10) to exclude the pos-sible extrinsic origins. Consequently, the additional polarization, orthe tilting of electric dipoles is supposed to be the most plausiblephysical mechanism to explain the I −V hysteresis. Holding the sim-plest idea that the external field induces an additional polarizationfrom the antiferroelectric order and thus modifies the tunneling bar-rier, we employed a tunneling model to explain the hysteresis beha-viors of the I − V curve (see calculation details in SupplementaryInformation Fig. S13). The graphite stripes we used as contact elec-trodes are not perfectlymetallic, so the surface charges induced by thenet polarization are not completely screened by the graphite stripesand the depolarization electric field is therefore not zero39,40. Based onthe material parameters, we modeled the redistributed energy profileand simulated the I − V curve of the CrOCl tunneling device. Thesimulated current polarization ρ is ~ 1%, perfectly reproducing ourexperimental results, so we may obtain a thorough understanding ofthe hysteresis and relaxation behaviors in CrOCl tunneling devices(Supplementary Information Fig. S11-13). The ramping electric fieldacts as an electric excitation to tilt the electric dipoles, resulting in ahigher tunneling current, while the interactions between spin andcharge tend to relax the system to the antiferroelectric ground statewith a lower current. In addition to the I −V hysteresis, the structuralmodulation of the ↑↑↓↓ phase under the electric field also leads todifferent magnetoresistance behavior with varying bias voltage, asshown in Supplementary Information Fig. S14 and S15.Switching the tunneling resistance between different metastablestates resulting from ME coupling by sweeping the electric field pro-vides us with design principles for magnetoelectronic devices. Wehave demonstrated that the magnetic transitions in CrOCl underexternal fields are first-order transitions with large hysteresis loops27.Therefore,wecan expect that the electricfield canadjust the tunnelingresistance to any meta-stable states inside the magnetic hysteresisloop by tilting the electric dipoles. From the I −B curve of tunnelingdevice 3 ( ~ 11.3 nm) at 5.5 V (Fig. 3a), the hysteresis closes at Bs=5.63 T,where CrOCl is believed to transform to the ↑↑↑↓↓ state. Subtractingthe current of the B-up curve from that of the B-down curve, we obtainthe maximum hysteresis occurs at B0=3.33 T (Fig. 3a). In other words,the spin configuration of CrOCl at 3.33 T is close to the ↑↑↓↓ AFMground state (low current) in the B-up cycle, but remains in the↑↑↑↓↓state (high current) in the B-down cycle. The maximum value of δI is~ 2 nA, 10% of the tunneling current. Similar to the operation in Fig. 2,we apply electric excitations by sweeping the bias voltage up and backto 5.5 V. After the electric excitation, the tunneling current changes to4.00510ρ (%)-5-10T (K)5 10 15 20 25 304.55.05.56.0-4.0-4.5-5.0-5.5-6.0V (V)T (K)5 10 15 20 25 3010152025 2 K20 KV (V)4.8 4.9 5.0 5.1 5.2I (nA)320330340350360R (MΩ)Vup = 5.0 VVdown = 5.0 VTNTmag222224226228230-15-10-5051015R (kΩ)Time (h)0 1 2 3 4 5 6 7V (V)a cbdegfρ (%)-6-4-202465.2 V5.0 V4.8 V-4.8 V-5.0 V-5.2 VVItGraphiteGraphiteh-BNh-BN280300320340R (MΩ)Vup = -5.0 VVdown = -5.0 Vμ0H (T)0 2 4 6TNFig. 2 | I −V hysteresis of CrOCl tunneling devices. a Illustration of the tunnelingdevice. b I −V curves of device 1 at 20 K (above the Néel temperature) and 2 K(below the Néel temperature). c 2D map of current polarization ρ as a function oftemperature and bias voltage. The green dashed line marks the Néel temperatureof the exfoliatedCrOCl.d ρ versus temperature at different voltages extracted fromb. e Resistance versus temperature of the CrOCl tunneling device at 5 V in differentsweeping processes. f Tunneling resistance versus out-of-plane magnetic field at−5 V in different sweeping processes. gReproduciblemanipulation of the resistancestates at−0.8 V by alternately changing the sweeping direction. Data in a–f wereobtained in device 1 ( ~ 9.1 nm CrOCl), while gwas obtained in device 2 (monolayerCrOCl) in parallel with a 10MΩ protection resistor.Article https://doi.org/10.1038/s41467-023-39004-4Nature Communications |         (2023) 14:3221 4an intermediate state following a slight relaxation and stabilizes at thestate for several hourswithout any sign of change. The current value ofthe intermediate state is determined by the electric excitation, speci-fically, by the sweeping rate and the peakvoltage. By applyingdifferentelectric excitations by design, we can switch the tunneling current toan arbitrary value between the highest (↑↑↑↓↓) and lowest (↑↑↓↓)current values, as demonstrated in Fig. 3b.It is worth noting that the relaxation process of the intermediatein Fig. 3b is much less than that at 0 T (Fig. 2g and SupplementaryInformation Fig. S12). This is because the external magnetic field hasovercome the energy barrier of the magnetic ground state and bringsthe spin configuration of CrOCl into a series of metastable states. As aresult, no longer will the ME coupling energy relaxes the crystal to theantiferroelectric ground state. Inotherwords, both themagneticorderand the electric order are amongst a series ofmetastable states and thesystem has entered neutral equilibrium, where the resistance state canbe manipulated both by the electric field and the magnetic field. Thenoise fluctuation of each state is less than 0.02 nA, whichmeans that asingle tunneling junction can store at least a decimal number if thedifferencebetween distinguishable adjacent states is set to be an order192021220.00.51.01.52.0μ0H (T)0 2 4 6 8I (nA)I (nA)δI (nA)3.33 T19.419.820.020.621.021.4I (nA)0 0.85 1.01 1.13 20.30.50.74.670.2a bc d5.63 T19.520.020.521.021.5Time (h)0 2 4 6 8 10 125.56.06.57.07.5V (V)Time (h)0 5 10 15 20 2519.520.020.521.021.5I (nA)μ 0H (T)3.54.04.55.0V (V)5.56.57.5efδ(μ 0H) (T)δV (V)20.021.022.08.0 T4.03 T3.73 T3.63 T3.53 T3.4μ0H (T)3.6 3.8 4.0 4.2 4.4I (nA)19.520.521.5Fig. 3 |Operationprinciples ofmulti-statedata storage. a I − B curve of theCrOCltunneling device at 2 K. The pink curve shows the differential currentδI = I(B)∣up− I(B)∣down. The critical field where δI reaches a maximum (at B0) and thehysteresis closes (at Bs) are annotated by black arrows. b Tunneling current overtime after several electric sweeps. The dashed lines represent the current values at3.33 T in Bdown and Bup sweeping cycles extracted from a. c I − B curves with dif-ferent magnetic sweep ranges. d 2D map of the tunneling current after designedelectric andmagnetic sweeps. e, f Tunneling current e after alternating electric andmagnetic sweeps. The corresponding magnetic and electric fields versus time areplotted in f. Data were obtained in device 3 ( ~ 11.3 nm CrOCl).Article https://doi.org/10.1038/s41467-023-39004-4Nature Communications |         (2023) 14:3221 5of magnitude larger than the noise fluctuation. After sweeping themagnetic field across Bs and back to B0, the junction can be reset to the↑↑↑↓↓ high current state, which means the erasing of the storedinformation.Likewise, to expand the capabilities of the device, the magneticfield can serve as another degree of freedom to tune the tunnelingresistance. Sweeping themagnetic field to a value below Bs and back toB0 also adjusts the tunneling current to an intermediate state, as shownin Fig. 3c. Accordingly, we can adjust the tunneling current to differentvalues with varying magnetic excitations, and set the current back tothe ↑↑↓↓ low current state with a large electric excitation as well.Repeating the previous electric sweeps following different magneticsweeps, we obtain a new set of current values. In this way, we con-structed a 5 × 5 2D list of different resistance states by electric andmagnetic excitations (Fig. 3d). The opposite dependence of the cur-rent on electric and magnetic excitations strongly evidences the MEcoupling in this system, as in the classical electrodynamics picture, themagnetic field flips the electron spins and the electricfield reverses theelectric dipoles. Following the counterclockwise hysteresis nature offirst-order transitions, the intermediate state should bemorepolarizedalong the control parameter than the initial state. At B = 3.33 T, themagnetic moment of the ↑↑↑↓↓ phase is definitely larger than that of↑↑↓↓phase, while the electric polarization is larger in the↑↑↓↓phaseat V = 5.5 V due to the fact that the additional polarization disappear inthe ↑↑↑↓↓ phase. As a result, sweeping the magnetic field can driveCrOCl from the ↑↑↓↓ state into the intermediate states, and symme-trically, sweeping the electric field can drive CrOCl from the ↑↑↑↓↓state into the intermediate states.We finally verified the repeatability of device operation as shownin Fig. 3e, f. The device is first set to the ↑↑↓↓ AFM ground state( ~ 19.4 nA) by a sufficiently large electric sweep of δV = 2 V, and thenreset to the↑↑↑↓↓ state ( ~ 21.4 nA) by themagnetic sweepofδB = 1.67T. The writing and erasing operations were repeated seven times, andthe high and low resistance states showed perfect stability. Further-more, it is worth mentioning that similar multi-state data storageoperation principles are also applicable at zero-field and to single-layerCrOCl devices (see Supplementary Information Fig. S16-18 and fol-lowing discussions). Due to the fact that the single-layer CrOCl sharesthe same magnetic and electric order as the multi-layer CrOCl (Sup-plementary Information Fig. S16), the ME coupling can also persistdown to the monolayer. The resistance of the single-layer tunnelingdevice can be set to two values by applying magnetic and electricsweeps, as shown in Supplementary Information Fig. S17. The onlydistinction in single-layer is that there are fewer metastable states sothe adjustable resistance range is lower, probably due to the thinnertunneling barrier and the absence of the interlayer dipole interactions.We should emphasize that, although the picture of tilting anti-ferroelectric dipoles under an electric field seems to be the most rea-sonable explanation for themulti-level resistanceandMEcoupling, it isso far a theoretical hypothesis and needs further direct experimentalevidence. Similar multi-level states as CrOCl have been reported inseveral other systems utilizing different mechanisms, such as themetal-insulator transition in VO241–43, ferroelectric switching inBaTiO344,45, and molecule trapping in WSe246. Although the operationof CrOCl tunneling devices is similar to that of VO2 and BaTiO3, theunderlying mechanisms are substantially different. Only one controlparameter, the electric field, can manipulate the one-dimensionalphase transitions in the previously reported materials. In contrast, theME effect in CrOCl enables themanipulation of tunneling resistance intwo degrees of freedom, the electric field and magnetic field, as illu-strated in Fig. 3d. We can write in the information either by electricexcitations or magnetic excitations and erase the information byanother. As a result, themulti-level resistancemanipulation in CrOCl isnot a simple extension of the new-typememristor, but a breakthroughin the fundamental concept of spintronics. It is also attractive toconsider the prospects of CrOCl compared to the conventional spin-tronic devices. CrOCl is air-stable and can be easily exfoliated into a 2Dform, providing much convenience for device fabrication. The intra-layer antiferromagnetic order of CrOCl prohibits stray fields, whichmeans that the area of the tunneling junction can be as small as pos-sible. As the operating current is ~ 101 nA, the writing current density inour reporteddevice is ~ 100 A/cm2. Thedevice is constructed entirely ofvan der Waals materials, so the device thickness can be controlled atthe atomic scale. Taken together, the CrOCl tunneling device cancontain ultra-high information density with ultra-low energy con-sumption utilizing the continuously adjustable outputs, and showsgreater potential in future data-storage applications compared topreviously reported materials.In summary, we have demonstrated the ME effect in the 2D stripyantiferromagnet CrOCl. By means of dielectric measurements, tun-neling measurements, and first-principles calculations, we verified theadditional contribution of electric polarization below the Néel tem-perature, which is possibly induced by the adjustable antiferroelectricdipoles. The ME coupling term gives rise to successive metastablestates that are rather stable and hardly degenerate over time, so thetunneling resistance of CrOCl can be set to arbitrary values via electricand magnetic excitations. The multi-state data storage realized inCrOCl may serve as a new paradigm with the potential to impactinformation technology, such as analog data storage and computationin an array of tunneling devices, stepping beyond Von Neumannarchitecture and enabling neuromorphic computing with low powerconsumption. Furthermore, the ME coupling in CrOCl may give rise tomore unexplored fantastic properties, highlighting the characteristicsof 2D antiferromagnetic materials and their promising potential infundamental research and spintronic applications.MethodsCrystal synthesis and characterizationsThemixture of powdered CrCl3 and Cr2O3 with a molar ratio of 1:1 anda total mass of 1.5 g was sealed in an evacuated quartz ampule. Theampule was then placed in a two-zone furnace where the source andsink temperatures for growth were set to 940 °C and 800 °C, respec-tively, and kept for two weeks. Subsequently, the furnace was slowlycooled to room temperature, and high-quality CrOCl crystals wereobtained. Magnetization measurements were performed by standardmodules of a Quantum Design PPMS.Dielectric and pyroelectric measurementsBoth pyroelectric measurements and dielectric measurements wereperformed on a TeslatronPT System, Oxford Instruments. Silver epoxywas painted on opposite sides of the sample as electrodes. For pyro-electricmeasurements, an electrometer (Keithley 6517B) was used as aDC voltage source and ammeter. When the temperature was stabilizedat 60K, an external electricfieldwas applied to the sample. The samplewas then cooled from 60 K to 2 K under different electric fields. Afterthe temperature was stabilized at 2 K, the electric field was removedand the temperature was increased to 60 K at a rate of 5 K/min. Duringthe heating process, the change of pyroelectric current with tem-perature was collected. The polarization can be obtained by integrat-ing the pyroelectric current with time. Dielectric measurements weremadeusing a capacitive bridgemeter (AH2700A). From2K to 50K, thechange in relative permittivity with temperature was measured byheating at the rate of 2 K/min. Magneto-dielectric effect at 2 K wasmeasured at a magnetic field sweep rate of 15 Oe/s from 0 to 8 T. Alltest frequencies are 20 kHz.Device fabricationFew-layer graphite, h-BN (10–30nm), and CrOCl flakes were obtainedby the scotch tape exfoliation method under ambient conditions.The heterostructures were then assembled with a conventionalArticle https://doi.org/10.1038/s41467-023-39004-4Nature Communications |         (2023) 14:3221 6pick-up-and-stack technique based on polypropylene carbonate(PPC)/polydimethylsiloxane(PDMS) polymer stacks placed on glass slides.Once encapsulated, the devices were annealed in a high vacuumwith amixed gas flow of H2 and Ar to remove residual PPC. Metal contact ofCr/Au (5/25 nm) electrodes were then defined using electron-beamlithography, reactive ion etching (in plasma of the CHF3/O2 mixture),electron beam evaporation, and lift-off processes.Electrical transport measurementsTransportmeasurementswereperformed in aHeliox3He insert systemequipped with a 14 T superconducting magnet. The lowest tempera-ture of the system is 1.6 K. To measure the I −V characteristics of thetunnel barrier and the magnetoresistance, a Keithley 2636B sourcemeter was used to apply a bias voltage and a standard two-probemodule was used tomeasure the tunneling current. To obtain intrinsicsignals and at the same timeexclude the possibility of the Joule heatingeffect, the tunneling current is limited to ~ 50 nA, so the total power ina junction of ~ 1 µm2 is merely ~ 0.3 µW.DFT calculationsOur DFT calculations were performed using the generalized gradientapproximation for the exchange-correlation potential, the projectoraugmented wave method47, and a plane-wave basis set implemented inthe Vienna ab-initio simulation package (VASP)48. Dispersion correctionwas made at the van der Waals density functional (vdW-DF) level49, withthe optB86b functional for the exchange potential50, and which wasproved to be accurate in describing the structural properties of layeredmaterials51 andwas adopted for structure related calculations. The shapeand volume of each supercell and all atomic positions were fully relaxeduntil the residual force per atom was less than 1 × 10−3 eVÅ−1 in our cal-culations. In VASP calculations, the kinetic energy cut-off for the plane-wave basis set was set to be 700eV for geometric and electronic struc-ture calculations. A k-mesh of 10 × 14 × 4was adopted to sample the firstBrillouin zone of the conventional unit cell of CrOCl bulk. The U and Jvalues of the on-site Coulomb interaction of the Cr d orbitals are 3.0 eVand 1.0 eV, respectively, as revealed by a linear response method52 andcomparison with the experimental results27. These values are compar-able to those adopted inmodeling CrSCl53 and CrI354. The Born effectivecharges were calculated using density functional perturbation theory55.The dipole moment of each atom is calculated by Pi =Z*i � μi, where Pi isthe dipole moment of the ion i in one unit cell, Ζi is the Born effectivecharge tensors and μi is the atomic displacement56. For calculations ofsingle-layer CrOCl, a sufficiently large vacuum layer over 20Å along theout-of-plane direction was adopted to eliminate the interaction amongmonolayer. The out-of-plane electric polarization of single-layer CrOClunder the external electric field is well defined in terms of the classicalmodel due to the presence of a vacuum layer, which is calculated byintegrating electron density times z-coordinate over the supercell.Data availabilityThe source data generated in this study have been deposited in theZenodo database under the accession code https://doi.org/10.5281/zenodo.7890630. Source data are provided with this paper.References1. Jungwirth, T., Marti, X., Wadley, P. & Wunderlich, J. Anti-ferromagnetic spintronics. Nat. Nanotechnol. 11, 231–241 (2016).2. Fukami, S., Zhang, C., DuttaGupta, S., Kurenkov, A. & Ohno, H.Magnetization switching by spin–orbit torque in anantiferromagnet–ferromagnet bilayer system. Nat. Mater. 15,535–541 (2016).3. Tsai, H. et al. Electrical manipulation of a topological anti-ferromagnetic state. Nature 580, 608–613 (2020).4. Wadley, P. et al. Electrical switching of an antiferromagnet. Science351, 587–590 (2016).5. Matsukura, F., Tokura, Y. & Ohno, H. Control of magnetism byelectric fields. Nat. Nanotechnol. 10, 209–220 (2015).6. Eerenstein, W., Mathur, N. & Scott, J. F. Multiferroic and magneto-electric materials. Nature 442, 759–765 (2006).7. Spaldin, N. A. & Ramesh, R. Advances in magnetoelectric multi-ferroics. Nat. Mater. 18, 203–212 (2019).8. Yang, J.-C., He, Q., Yu, P. & Chu, Y.-H. BiFeO3 thin films: a play-ground for exploring electric-field control of multifunctionalities.Annu. Rev. Mater. Res. 45, 249–275 (2015).9. Hill, N. A. Why are there so few magnetic ferroelectrics? J. Phys.Chem. B 104, 6694–6709 (2000).10. Cheong, S.-W. & Mostovoy, M. Multiferroics: a magnetic twist forferroelectricity. Nat. Mater. 6, 13–20 (2007).11. Tokura, Y., Seki, S. & Nagaosa, N. Multiferroics of spin origin. Rep.Prog. Phys. 77, 076501 (2014).12. Fiebig,M., Lottermoser, T., Fröhlich, D.,Goltsev, A. V. &Pisarev, R. V.Observation of coupled magnetic and electric domains. Nature419, 818–820 (2002).13. Lottermoser, T. et al. Magnetic phase control by an electric field.Nature 430, 541–544 (2004).14. Lorenz, B., Litvinchuk, A. P., Gospodinov, M. M. & Chu, C. Field-induced reentrant novel phase and a ferroelectric-magnetic ordercoupling in HoMnO3. Phys. Rev. Lett. 92, 087204 (2004).15. Sergienko, I. A., Şen, C. & Dagotto, E. Ferroelectricity in the mag-netic E-phase of orthorhombic perovskites. Phys. Rev. Lett. 97,227204 (2006).16. Katsura, H., Nagaosa, N. & Balatsky, A. V. Spin current and mag-netoelectric effect in noncollinear magnets. Phys. Rev. Lett. 95,057205 (2005).17. Jia, C., Onoda, S., Nagaosa, N. & Han, J. H. Bond electronic polar-ization induced by spin. Phys. Rev. B 74, 224444 (2006).18. Lin, X., Yang, W., Wang, K. L. & Zhao, W. Two-dimensional spin-tronics for low-power electronics. Nat. Electron. 2, 274–283 (2019).19. Sierra, J. F., Fabian, J., Kawakami, R. K., Roche, S. & Valenzuela, S. O.Van der Waals heterostructures for spintronics and opto-spintronics. Nat. Nanotechnol. 16, 856–868 (2021).20. Huang, B. et al. Electrical control of 2D magnetism in bilayer CrI3.Nat. Nanotechnol. 13, 544–548 (2018).21. Jiang, S., Shan, J. & Mak, K. F. Electric-field switching of two-dimensional vanderWaalsmagnets.Nat.Mater. 17, 406–410 (2018).22. Sharpe, A. L. et al. Emergent ferromagnetism near three-quartersfilling in twisted bilayer graphene. Science 365, 605–608 (2019).23. He, W.-Y., Goldhaber-Gordon, D. & Law, K. T. Giant orbital magne-toelectric effect and current-induced magnetization switching intwisted bilayer graphene. Nat. Commun. 11, 1–8 (2020).24. Ju, H. et al. Possible persistence of multiferroic order down tobilayer limit of van der Waals material NiI2. Nano Lett. 21,5126–5132 (2021).25. Song, Q. et al. Evidence for a single-layer van der Waals multi-ferroic. Nature 602, 601–605 (2022).26. Park, C. B. et al. Observation of spin-induced ferroelectricity in alayered van der Waals Antiferromagnet CuCrP2S6. Adv. Electron.Mater. 8, 2101072 (2022).27. Gu, P. et al. Magnetic phase transitions and magnetoelastic cou-pling in a two-dimensional stripy antiferromagnet. Nano Lett. 22,1233–1241 (2022).28. Zhang, M. et al. Spin-Lattice coupled metamagnetism in frustratedvan der Waals magnet CrOCl. Small 2300964 (2023).29. Wang, Y. et al. Quantum hall phase in graphene engineered byinterfacial charge coupling.Nat. Nanotechnol. 17, 1272–1279 (2022).30. Yang, K. et al. Unconventional correlated insulator in crocl-interfaced bernal bilayer graphene. Nat. Commun. 14, 2136 (2023).31. Noerlund Christensen, A., Johansson, T. & Quézel, S. Preparationand magnetic properties of CrOCl. Chem. Informationsdienst 6,1171–1174 (1975).Article https://doi.org/10.1038/s41467-023-39004-4Nature Communications |         (2023) 14:3221 7https://doi.org/10.5281/zenodo.7890630https://doi.org/10.5281/zenodo.789063032. Reuvekamp, P. G. Investigation into the magnetic and the structuralproperties of two low-dimensional antiferromagnets TiPO4 andCrOCl. Ph.D. thesis, University of Stuttgart (2014).33. Zhang, J. Temperature dependent magnetic order in FeOCl typecompounds. Ph.D. thesis, University of Bayreuth (2014).34. Jang, S. W. et al. Hund’s physics and the magnetic ground state ofCrOX (X= Cl,Br). Phys. Rev. Mater. 5, 034409 (2021).35. Angelkort, J., Wölfel, A., Schönleber, A., van Smaalen, S. & Kremer,R. K. Observation of strongmagnetoelastic coupling in a first-orderphase transition of CrOCl. Phys. Rev. B 80, 144416 (2009).36. Balatsky, A., Basov,D. &Zhu, J.-X. Inductionof chargedensitywavesby spin density waves in iron-based superconductors. Phys. Rev. B82, 144522 (2010).37. Zachar, O., Kivelson, S. & Emery, V. Landau theory of stripe phasesin cuprates and nickelates. Phys. Rev. B 57, 1422 (1998).38. Kaushik, N. et al. Reversible hysteresis inversion in MoS2 field effecttransistors. npj 2D Mater. Appl. 1, 1–9 (2017).39. Tsymbal, E. Y. & Kohlstedt, H. Tunneling across a ferroelectric.Science 313, 181–183 (2006).40. Zhuravlev, M. Y., Sabirianov, R. F., Jaswal, S. & Tsymbal, E. Y. Giantelectroresistance in ferroelectric tunnel junctions. Phys. Rev. Lett.94, 246802 (2005).41. Gao, X., Rosário, C. M. & Hilgenkamp, H. Multi-level operation inVO2-based resistive switching devices. AIP Adv. 12, 015218 (2022).42. Driscoll, T., Kim, H.-T., Chae, B.-G., Di Ventra, M. & Basov, D. Phase-transition driven memristive system. Appl. Phys. Lett. 95,043503 (2009).43. Rana, A., Li, C., Koster, G. & Hilgenkamp, H. Resistive switchingstudies in VO2 thin films. Sci. Rep. 10, 1–6 (2020).44. Chanthbouala, A. et al. A ferroelectric memristor. Nat. Mater. 11,860–864 (2012).45. Huang, W. et al. A high-speed and low-power multistate memorybased on multiferroic tunnel junctions. Adv. Electron. Mater. 4,1700560 (2018).46. Shen, H. et al. Multistate memory enabled by interface engineeringbased on multilayer tungsten diselenide. ACS Appl. Mater. Inter-faces 12, 58428–58434 (2020).47. Kresse, G. & Joubert, D. From ultrasoft pseudopotentials to theprojector augmented-wave method. Phys. Rev. B 59, 1758 (1999).48. Kresse, G. & Furthmüller, J. Efficiency of ab-initio total energy cal-culations for metals and semiconductors using a plane-wave basisset. Comput. Mater. Sci. 6, 15–50 (1996).49. Dion,M., Rydberg, H., Schröder, E., Langreth, D. C. & Lundqvist, B. I.Van derWaals density functional for general geometries. Phys. Rev.Lett. 92, 246401 (2004).50. Klimeš, J., Bowler, D. R. & Michaelides, A. Van der Waals densityfunctionals applied to solids. Phys. Rev. B 83, 195131 (2011).51. Qiao, J. et al. Few-layer tellurium: one-dimensional-like layeredelementary semiconductor with striking physical properties. Sci.Bull. 63, 159–168 (2018).52. Cococcioni, M. & De Gironcoli, S. Linear response approach to thecalculation of the effective interaction parameters in the LDA+Umethod. Phys. Rev. B 71, 035105 (2005).53. Wang, C. et al. A family of high-temperature ferromagnetic mono-layers with locked spin-dichroism-mobility anisotropy: MnNX andCrCX (X= Cl, Br, I; C= S, Se, Te). Sci. Bull. 64, 293–300 (2019).54. Jiang, P. et al. Stacking tunable interlayermagnetism in bilayer CrI3.Phys. Rev. B 99, 144401 (2019).55. Baroni, S., De Gironcoli, S., Dal Corso, A. & Giannozzi, P. Phononsand related crystal properties from density-functional perturbationtheory. Rev. Mod. Phys. 73, 515 (2001).56. Resta, R., Posternak,M.&Baldereschi, A. Towardsaquantum theoryof polarization in ferroelectrics: The case of KNbO3. Phys. Rev. Lett.70, 1010 (1993).AcknowledgementsThis work was supported by the National Key R&D Program of China(Grants Nos. 2022YFA1203904, 2022YFA1203902, 2021YFA1400300 and2018YFA0306900), theNationalNaturalScienceFoundationofChina (No.12250007), and Beijing Natural Science Foundation (Grant No. JQ21018).Y.S. acknowledges support from the National Natural Science Foundationof China (Grant No. 51725104). W.J. acknowledges support from StrategicPriority Research Programof theChineseAcademyof Sciences (Grant No.XDB30000000), and the National Natural Science Foundation of China(Grants No. 11974422 and No. 12104504). C.W. was supported by theChina Postdoctoral Science Foundation (2021M693479). Calculationswere performed at the Physics Lab of High-Performance Computing ofRenmin University of China, Shanghai Supercomputer Center. T.T.acknowledges support fromthe JSPSKAKENHI (GrantNos. 19H05790and20H00354) and A3 Foresight by JSPS.Author contributionsY.Y. and P.G. conceived the project. P.G. synthesized the CrOCl crystalsand fabricated the devices. P.G. conducted the transportmeasurementswith the help of Z.D., Q.W., and Z.H. C.W. conducted the DFT calcula-tions under the supervision of W.J. D.S. conducted the dielectric andpyroelectric measurement under the supervision of Y.S. K.W. and T.T.grew the h-BN bulk crystals. P.G. and Y.Y. drafted the manuscript. Allauthors discussed the results and contributed to the manuscript.Competing interestsAll authors declare the following competing interests: Chinese patent(no. 202210324321.1) for using CrOCl to implement multi-state datastorage in tunneling devices, which is now under consideration.Additional informationSupplementary information The online version containssupplementary material available athttps://doi.org/10.1038/s41467-023-39004-4.Correspondence and requests for materials should be addressed toWei Ji, Young Sun or Yu Ye.Peer review information Nature Communications thanks Su-Yang Xuand the other, anonymous, reviewer(s) for their contribution to the peerreview of this work. 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