# Fileset [s41467-025-63698-3.pdf](https://mdr.nims.go.jp/filesets/ef242d1b-524f-4ab5-89aa-e1940131a291/download) ## Creator Hung-Yu Yang, Joseph J. Cuozzo, Anand Johnson Bokka, Gang Qiu, Christopher Eckberg, Yanfeng Lyu, Shuyuan Huyan, Ching-Wu Chu, [Kenji Watanabe](https://orcid.org/0000-0003-3701-8119), [Takashi Taniguchi](https://orcid.org/0000-0002-1467-3105), Kang L. Wang ## Rights [Creative Commons BY Attribution 4.0 International](https://creativecommons.org/licenses/by/4.0/) ## Other metadata [Field-resilient supercurrent diode in a multiferroic Josephson junction](https://mdr.nims.go.jp/datasets/5de6c077-66f9-47c4-b1b2-98aaec3f7fcb) ## Fulltext Field-resilient supercurrent diode in a multiferroic Josephson junctionArticle https://doi.org/10.1038/s41467-025-63698-3Field-resilient supercurrent diode in amultiferroic Josephson junctionHung-Yu Yang 1 , Joseph J. Cuozzo2,3, Anand Johnson Bokka 1,4,Gang Qiu 1, Christopher Eckberg 1, Yanfeng Lyu5, Shuyuan Huyan 6,Ching-Wu Chu 6,7, Kenji Watanabe 8, Takashi Taniguchi 9 &Kang L. Wang 1The research on supercurrent diodes has surged rapidly due to their potentialapplications in electronic circuits at cryogenic temperatures. To unlock thisfunctionality, it is essential to find supercurrent diodes that can work con-sistently at zero magnetic field and under ubiquitous stray fields generated inelectronic circuits. However, a supercurrent diode with robust field toleranceis currently lacking. Here, we demonstrate a field-resilient supercurrent diodeby incorporating a 2D multiferroic material into a Josephson junction, andobserved a pronounced supercurrent diode effect at zeromagneticfield.Moreimportantly, the supercurrent rectification persists over a wide and bipolarmagnetic field range beyond industrial standards for field tolerance. By the-oretically modeling a multiferroic Josephson junction, we unveil that theinterplay between spin-orbit coupling and multiferroicity underlies the unu-sual field resilience of the observed diode effect. This work introduces multi-ferroic Josephson junctions as a new field-resilient superconducting device forcryogenic electronics.Semiconductor diodes are fundamental electronic components cru-cial for rectifying, regulating, and controlling the flow of electricalcurrent in electronic circuits and systems, playing a pivotal role in thefunctionality of a wide range of devices from power supplies to digitalelectronics1. Supercurrent diodes, which rectify the zero-resistancesupercurrent in superconductors, play key functions in digital elec-tronics at cryogenic temperatures. For example, in an electronic flip-flop memory, a binary bit can be represented by the current goingthrough one armor the other; this can be achieved similarly by placingsupercurrent diodes on each arm and controlling their rectificationdirections2.More importantly, for a cryogenicmemory application, thereadout can be done through the supercurrent diode effect (SDE) that,in principle, leads to low power consumption and an infinite on/offratio, thanks to the zero resistance in the superconducting state2–4.In the past few years, supercurrent diodes have been foundextensively in various systems under a magnetic field5–13 while only afew work at zero magnetic field. Among the zero-field supercurrentdiodes14–21, most of them require a magnetic field to polarize the fer-romagnetic component and initialize the diode; the ferromagnetismgrants the field-tunability to these diodes, while also makes themunable to work persistently over bipolar magnetic fields. For practicalapplications, ubiquitous stray fields in a common circuit environment(up to 10mT) can easily flip the supercurrent rectification directionandmake this type of diode unreliable22. Currently, a clear strategy forReceived: 18 November 2024Accepted: 26 August 2025Check for updates1Department of Electrical and Computer Engineering, University of California, Los Angeles, CA, USA. 2Materials Physics Department, Sandia NationalLaboratories, Livermore, CA, USA. 3Department of Physics, The University of Texas at El Paso, El Paso, TX, USA. 4Department of Materials Science andEngineering, University of California, Los Angeles, CA, USA. 5School of Science, Nanjing University of Posts and Telecommunications, Nanjing, China.6Department of Physics and Texas Center for Superconductivity, University of Houston, Houston, TX, USA. 7Lawrence Berkeley National Laboratory, Berkeley,CA, USA. 8Research Center for Electronic and Optical Materials, National Institute for Materials Science, Tsukuba, Japan. 9Research Center for MaterialsNanoarchitectonics, National Institute for Materials Science, Tsukuba, Japan. e-mail: hungyuyang@ucla.edu; wang@ee.ucla.eduNature Communications | (2025) 16:9287 11234567890():,;1234567890():,;http://orcid.org/0000-0002-4737-9826http://orcid.org/0000-0002-4737-9826http://orcid.org/0000-0002-4737-9826http://orcid.org/0000-0002-4737-9826http://orcid.org/0000-0002-4737-9826http://orcid.org/0009-0009-6487-8422http://orcid.org/0009-0009-6487-8422http://orcid.org/0009-0009-6487-8422http://orcid.org/0009-0009-6487-8422http://orcid.org/0009-0009-6487-8422http://orcid.org/0000-0003-2248-3253http://orcid.org/0000-0003-2248-3253http://orcid.org/0000-0003-2248-3253http://orcid.org/0000-0003-2248-3253http://orcid.org/0000-0003-2248-3253http://orcid.org/0000-0002-3564-8443http://orcid.org/0000-0002-3564-8443http://orcid.org/0000-0002-3564-8443http://orcid.org/0000-0002-3564-8443http://orcid.org/0000-0002-3564-8443http://orcid.org/0000-0003-0999-2440http://orcid.org/0000-0003-0999-2440http://orcid.org/0000-0003-0999-2440http://orcid.org/0000-0003-0999-2440http://orcid.org/0000-0003-0999-2440http://orcid.org/0000-0003-3955-7095http://orcid.org/0000-0003-3955-7095http://orcid.org/0000-0003-3955-7095http://orcid.org/0000-0003-3955-7095http://orcid.org/0000-0003-3955-7095http://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/0000-0002-9363-1279http://orcid.org/0000-0002-9363-1279http://orcid.org/0000-0002-9363-1279http://orcid.org/0000-0002-9363-1279http://orcid.org/0000-0002-9363-1279http://crossmark.crossref.org/dialog/?doi=10.1038/s41467-025-63698-3&domain=pdfhttp://crossmark.crossref.org/dialog/?doi=10.1038/s41467-025-63698-3&domain=pdfhttp://crossmark.crossref.org/dialog/?doi=10.1038/s41467-025-63698-3&domain=pdfhttp://crossmark.crossref.org/dialog/?doi=10.1038/s41467-025-63698-3&domain=pdfmailto:hungyuyang@ucla.edumailto:wang@ee.ucla.eduwww.nature.com/naturecommunicationsfield-resilient supercurrent diodes that canwork at zeromagnetic fieldand tolerate stray fields in electrical circuits remains lacking.The SDE is governed by the symmetry properties; the breaking ofinversion and time-reversal symmetries simultaneously is essential forSDE, regardless of the material platform23–25. For example, a 2Dsuperconductor with Rashba spin-orbit coupling (RSOC) breaking theinversion symmetry, and an applied in-plane transversemagnetic fieldbreaking time-reversal symmetry, exhibits SDE23. In this study, weemployed NiI2, a 2D multiferroic material, in a van der Waals (vdW)Josephson junction (JJ) to create a field-resilient supercurrent diode.The coexisting spiral magnetic order and ferroelectric order in NiI2naturally break both inversion and time-reversal symmetry(Fig. 1a)26–29, presumably satisfying symmetry requirements for SDE.Furthermore, the coupling between magnetic and electric ordersmakes a multiferroic more robust against the magnetic field (e.g.,coercivity enhancement)30,31, granting the field-resilience for SDE.Lastly, the strong magnetoelectric coupling in multiferroics enablescontrollable switching of magnetic order32–34 and potentially theswitching of SDE by electrical gates. Incorporating this non-volatilityand gate tunability into supercurrent diodes could open the door topractical cryogenic memory devices.ResultsZero-field SDE in a multiferroic vdW JJSince the multiferroic order in NiI2 persists down to the 2Dmonolayer(ML) limit35–37, we exfoliated a NiI2 flake of 4 MLs thick to facilitate theJosephson coupling while keeping the multiferroic order. It is then re-assembled with two NbSe2 flakes to make a NbSe2/NiI2/NbSe2 verticalvdW JJ (NiI2 JJ in short), thanks to the freedom to manipulate vdWmaterials with the 2D transfer assembly technique (Fig. 1b, see alsoMethods and Supplementary Fig. 1). Figure 1c shows a typical V − Icharacteristic of the NiI2 JJ. The quantities relevant to SDE are thecritical currents for opposite bias directions, Ic+ and Ic−, at which the JJtransitions from a superconducting state to a normal state. The criticalcurrent difference ΔIc ≡ Ic+ − ∣Ic−∣ =−118 μA and the diode rectificationefficiency η � Ic+�jIc�jIc+ + jIc�j � �8% were obtained. The difference in mag-nitude also allows us to define a diode working range (gray stripes inFig. 1c), within which the supercurrent only flows in one direction butnot the other (Fig. 1d). The consistent switchingwith repetitive currentbiasing cycles (see also Supplementary Fig. 2) shows the robustness ofthe SDE in the NiI2 JJ at zero field.To further confirm the zero-field SDE in the multiferroic NiI2 JJ, aNbSe2/few-layer graphene/NbSe2 vdW JJ (Gr JJ) was fabricated as areference device, and different tests were performed to confirm theobserved zero-field SDE is intrinsic (Fig. 1e). If the heating effect issignificant, the rectification efficiency should flip sign between thesetwomeasurements18. We found that the diode rectification efficiency ηof the Gr JJ stayed near zero and that of NiI2 JJ remained ~−8%, showingthe heating effect was insignificant in the SDE of both devices.Next, opposite in-plane fields (±H∥) were applied to train themagnet and devices, and then V − I characteristics were measured atzero field. Here, we utilized the following fact to simulate the effect ofstray fields:With a large positive (negative)magneticfield up to severaltesla being applied through themagnet of our measurement system, asmall negative (positive) remnant field on the order of ~1mT couldremain after the field is set to zero38. For a field-resilient supercurrentdiode, η must not flip its sign for opposite training fields to continuerectifying supercurrent in the same direction under stray fields. AsFig. 1 | 2D Multiferroic NiI2 and zero-field supercurrent diode effect in the NiI2van derWaals (vdW) Josephson junction (JJ). a Crystal structure andmultiferroicorder of NiI2, which consists of a spiral magnetic order (described by the wavevector q!28) and an in-plane ferroelectric order ( P!29). The yellow arrow on the Niatoms represents the spin direction, and the shaded area represents the spin spiralplane. b Device geometry of the NiI2 JJ with a 4 monolayer (ML) NiI2. c V − I char-acteristic of the NiI2 JJ. 0-p, p-0, 0-n, and n-0 refer to curves with current sweepingfrom 0 μA to + 1000 μA, + 1000μA to 0 μA, 0 μA to − 1000μA, and − 1000 μA to0 μA. The critical currents Ic+ (600μA) and Ic− (718 μA) are defined by the firstcritical jump in V in the 0-p and 0-n (switching) curves, respectively. The gray-shaded area denotes the diode working range defined by Ic+ and Ic−.d Demonstration of supercurrent rectification with Ibias = ± 650μA. e Comparisonof zero-field supercurrent diode rectification efficiency (η= Ic+ �jIc�jIc+ + jIc�j) between theNbSe2/few-layer graphene/NbSe2 JJ (Gr JJ) and the NiI2 JJ under different current-sweeping and field-training protocols. The magnetic field was set to oscillate tozero from 3 T before performing the 0p0n0 and 0n0p0 measurements. Themeasurements for 0p0n0 and 0n0p0 tests are repeated five times to acquire errorbars, which are smaller than themarker size for both cases. The 0p0n0 and 0n0p0refer to opposite current-sweeping protocols, where a positive bias current isapplied first in the 0p0n0 measurement and a negative bias current is applied firstin the 0n0p0measurement, respectively. The training fields ±H∥ = ± 1 T were usedfor both devices. The field training was performed at T = 10 K.Article https://doi.org/10.1038/s41467-025-63698-3Nature Communications | (2025) 16:9287 2www.nature.com/naturecommunicationsshown in Fig. 1e, the η of NiI2 JJ surprisingly remained negative ~ − 8%after both ±H∥ training, in strong contrast to the Gr JJ, where its ηflipped the signbetween the ±H∥ training. Aswill bediscussed inFig. 2,our Gr JJ exhibits a pronounced SDE with anti-symmetric field depen-dence, with η ~ ± 20% for H∥ ~ ± 1mT, respectively. The nonzero butopposite η values of the Gr JJ after ±H∥ training are thus false-positivezero-field SDE and are a result of remnant fields induced by the fieldtraining, in agreement with Fig. 2. The tests and comparison demon-strated in Fig. 1e show that the zero-field SDE in the multiferroic NiI2 JJis not only intrinsic but alsofield-resilient. In theNiI2 JJ, η also surpassesthe values reported among the systems that do not require a fieldinitialization for the zero-field SDE (ηmax � 3% in both Fe(Te,Se)/Fe(Te,Se) vdW JJ14 and NbSe2/Nb3Br8/NbSe2 vdW JJ18).Field resilience of the SDE in NiI2 JJTo demonstrate the robustness of zero-field SDE in the NiI2 JJ understray fields, we measured the field dependence of the SDE. The V − Icharacteristics of the NiI2 JJ were acquired with in-plane fields (H∥)ranging from + 24mT to 0mT (Fig. 2a, top panel), and 0mT to− 24mT (bottom panel), over which the multiferroic order persists(Supplementary Fig. 3). A consistent negative diode rectification effi-ciency was observed over H∥= ± 24 mT, with negative bias-inducedcritical transitions occurring beyond the gray stripe (Fig. 2a), definedas the range of critical transitions for positive bias. The unidirectionalsupercurrent rectification is directly linked to an unusual fielddependence of SDE, which has a minute antisymmetric componentand adominant symmetric component. Such afielddependencedefiesthe typical anti-symmetric field dependence of SDE, where an externalmagnetic field solely controls the time-reversal symmetry.5,6,10,21.The dominant symmetric in-plane field dependence is furthershown by extracting Ic+ and ∣Ic−∣ at each field (Fig. 2b, top panel) andcalculating their corresponding η (bottom panel). Again, the datapoints representative of ∣Ic−∣ are always above Ic+ betweenH∥= ± 24mT,showing a robust negative SDE regardless of reversing the magneticfield direction. The symmetry Ic+ (+H∥) = ∣Ic−∣ (−H∥) is expected forsupercurrent diodes supported by magnetochiral anisotropy, but ourNiI2 JJ shows a distinct field dependence owing to a differentmechanism responsible for non-reciprocity. Importantly, η consists ofa predominantly symmetric, dome-shaped field dependence. Such anunusual field dependencemakes it possible to draw the widest bipolardiode working range reported so far over ± 10mT (~ 8000 A/m, themaximumfield toleranceof industrialMRAMdevicesmanufacturedbyEverspin39),wherewe canuse the same amount of current biased in theopposite directions to rectify the supercurrent. Thus, a bipolar figureof merit can be defined as FR ≡ ΔIR(current rectificationrange) ×ΔHbpR(bipolar field rectification range), as the area of theyellow block shown in Fig. 2b. For our device, FR over ± 10mT is on theorder of 103mT ⋅ μA, which is two orders of magnitude larger than theexisting supercurrent diode where a bipolar diode working range maybe defined (the maximum of FR in NbSe2/Nb3Br8/NbSe2 JJ is about101mT ⋅ μA18).We highlight the unique field-resilient SDE in the NiI2 JJ by com-paring its field dependence to the Gr JJ (Fig. 2b, bottom panel). For theGr JJ, the SDE therein exhibits an anti-symmetric field dependence of ηwith multiple sign changes, corresponding to the lobes of the Fraun-hofer interference pattern (see Supplementary Fig. 4a). ThemaximaofIc for opposite current biases shift from zero to opposite fields due tothe self-field effect induced by the cross-junction geometry, whichfurther leads to an SDE40,41. We expect the field-anti-symmetric SDEwithout a bipolar working range to be typical of vdW JJ with a non-magnetic barrier and a cross-junction geometry. On the contrary, theinterference pattern of the NiI2 JJ was “truncated" for the positivecurrent bias, while preserved for the negative current bias (see Sup-plementary Fig. 4b). The pattern thus leads to a persistent negative η,with a dominant symmetric field dependence and awide bipolar diodeworking range establishing the field-resilient SDE in NiI2 JJ. The generalFig. 2 | In-plane field dependence of the supercurrent diode effect in the NiI2 JJ.a Top panel: V − I characteristic of the NiI2 JJ with 0 mT 0 breaking time-reversal symmetry (TRS), and the (q ⋅ k) term is associated with thespin-orbit coupling induced by the spin texture M(r). The spinpolarization of the exchange spin splitting term is determined by theform of M(r). Here we use an M(r) consistent with the spin texture inNiI235–37.Wediscretize theHamiltonian inEq. (1) andperformnumericalsimulations of a helimagnetic JJ shown in Fig. 4b. Using tight-bindingsimulations, we calculate theAndreev bound state spectrumof the JJ tofind its current-phase relationship (CPR). To model the NiI2 tunnelbarrier, we include a potential barrier hb =Ubarrier δ(x). Additionaldetails are described in the Methods section.In Fig. 4c, we present the CPR with and without RSOC for qoriented along x and y. Here we assume T =0 unless otherwise stated.The global extrema of the CPR correspond to Ic±. We see Ic+ = ∣Ic−∣whenαR =0. The absence of SDE when αR =0 is due to the exchange inter-action generating an effective Zeeman field anti-commuting with thespin-orbit interaction originating from the spiral spin texture (secondterm in Eq. (2)). Since the broken TRS and inversion symmetries cor-respond to terms in the Hamiltonian having orthogonal spin polar-ization, a non-reciprocal supercurrent cannot develop46. When αR> 0,this no longer holds, and an SDE develops with a maximum efficiencyof ~6%whenq∥y. Thus, the combinationof helimagnetismandRSOC inthe JJ is sufficient to result in a zero-fieldSDE.Wehave alsoperformedaphenomenological depairing momentum analysis that leads to asimilar conclusion (see Methods and Supplementary Fig. 10 fordetails).Next, we consider the effects of an external magnetic field anddiscuss how a symmetric-in-field SDE generally emerges in a helimag-netic JJ. To simulate the effects of a magnetic field, we consider anadditional term in Eq. (2): hZ = gμBðB � σÞ=ΔZ=2ðB̂ � σÞ, where B̂ is aunit vector parallel to B. When the helimagnet spin texture and RSOCcoexist in the JJ, η is an even function ofΔZ if hZ anti-commuteswith theterms in the Hamiltonian that are: (i) linear in k parallel to the currentdirection and (ii) proportional to Jexc. When hZ obeys both anti-commutation relations, the BdG spectral gap closes symmetricallywith ±ΔZ and η is a purely even function of hZ (see “Methods”). Indeed,as calculated in Fig. 4d, a Zeeman splitting along the current direction(B =Bx) leads to a symmetricmodulation of η inΔZ, i.e., a symmetric-in-field SDE, regardless of the orientation of q. For B = (0, By, Bz), η willgenerally have a mixed functional dependence on the applied field(Supplementary Fig. 7). However, we emphasize that the symmetricfield dependence is ubiquitous in helimagnetic JJs and is the key to thefield resilience in NiI2 JJ (see also Supplementary Fig. 10). This is instrong contrast to other sources of non-reciprocal switching currentsassociated with magnetochiral anisotropy (MCA)7,8,12, finite-momentum superconductivity23,25,47, Meissner currents10,24 or self-field effects41,43,48, which are predicted to result in antisymmetric fielddependence of η as we demonstrated in the Gr JJ reference device.The simulated temperature scaling of ΔIc at zero field for heli-magnetic JJs is presented in Fig. 4e; the simulations reveal a non-monotonic behavior regardless of the direction of q. We note that inour simulations we ignore thermal effects associated with domainrearrangement in NiI2 and other structural changes since we are con-cernedwith temperatureswell below theCurie temperatureofNiI2.Wealso note that the temperature scaleweuse in simulations correspondsto temperatures T≲ 1 K, which are below the experimental conditions.Due to computational limitations on simulating the actual device sizeand geometry, we analyze possible sources of non-monotonic tem-perature scaling in our minimal model and set aside a more detailedquantitative model for future study. The exchange interaction asso-ciatedwith the helimagnet pushes the JJ close to a0-π transition,wherea significant second harmonic contribution develops (orange bands inFig. 4f) due to Andreev bound state energy level crossings at zeroenergy49. Since these states lie near zero energy, their contribution tothe CPR is more quickly washed out at finite temperatures comparedto even lower energy states (blue bands in Fig. 4f), which favor a ϕ = 0ground state. The competition between the supercurrent carried bystates near zero energy and that by lower states leads to the non-monotonic scaling shown in Fig. 4e. Thus, a plausible explanation forthe non-monotonic temperature dependence of SDE observed in theArticle https://doi.org/10.1038/s41467-025-63698-3Nature Communications | (2025) 16:9287 4www.nature.com/naturecommunicationsFig. 3 | Non-monotonic temperature dependence of supercurrent diode effectin the NiI2 JJ. a V − I characteristic (switching curves) measured at different tem-peratures. b V − ∣I∣ characteristic recorded at T ≤ 5 K. The solid and dashed linesrepresent 0-p sweep and 0-n sweeps, respectively. The critical transitions arepointed out by short black line segments with varied widths. c Ic+ and ∣Ic−∣ as afunction of temperature. The inset zooms in on the data at T = 4K, where the signchange of η appears. The error bars correspond to the 2 μA spacing between thediscrete current values at which data were collected. d η normalized by the max-imum jηmaxj as a function of temperature for both NiI2 JJ at zero field and Gr JJ atnonzero field. ηmax is −10% and −20% for NiI2 and Gr JJ, respectively.Fig. 4 | Multiferroic JJ simulation. a Schematic of the cross junction device wherethe supercurrent density Js tends to residenear the surfaces of the superconductingelectrodes. b Schematic of the planar junction corresponding to the SC/heli-magnet/SC cross-sectionmarked by the red rectangle in panel (a). c The simulatedjunction CPR with (solid) and without (dashed) RSOC for q∥x and q∥y. Unlessotherwise stated, parameters used in simulations are: Δ =0.4t, μ = 1.57t,αR =0.004ta, Jexc =0.3t, Ubarrier = 4t, jqj=0:01 πa, Lx,s = 300a, Lx,n = 3a, Ly = 10a, andξexc = 5a, where t = ℏ22m*a2 and a is the tight-binding lattice constant. d Diode rectifi-cation efficiency η versus Zeeman splitting along x with RSOC for q∥x and q∥y.e Critical current difference ΔIc = Ic+ − ∣Ic−∣ versus temperature with RSOC. f Thesimulated Andreev bound state spectrum for q∥y and B =0.Article https://doi.org/10.1038/s41467-025-63698-3Nature Communications | (2025) 16:9287 5www.nature.com/naturecommunicationsexperiment is thermal fluctuations preferentially washing out super-current carried by Andreev bound states responsible for higher har-monics of the CPR because of exchange interactions in NiI2. It is notedthat the scaling behavior depends on the details of Andreev boundstates and may be modified as other parameters change (see Supple-mentary Fig. 8)50,51.Lastly, we discuss the effects of an electric polarization P in amultiferroic JJ from our simulations (see “Methods” and Supplemen-tary Fig. 9 for details). Between ±P∥y we see a change in the CPR,indicating that the SDE can be tuned by flipping P. The latter caseoccurs because flipping P simultaneously flips q along the currentdirection, whose effect on the SDE is also revealed in Fig. 4d. In addi-tion, it is noted that the ferroelectric order in NiI2 is closely linked tothe strong SOC of iodine atoms, which could enhance the SDEin multiferroic JJs. Our simulation suggests that tuning electricpolarization could uniquely manipulate and enhance SDE inmultiferroic JJs.Our work presents the first demonstration of a field-resilientsupercurrent diode meeting an industrial standard of field-tolerance(± 10mT) using a multiferroic NiI2 vdW JJ. The key observation lies inthe supercurrent diode that operates persistently not only at zerofield but also under bipolar magnetic fields, matching with industrialstandards for field tolerance. This invention overcomes the sig-nificant limitation in conventional supercurrent diodes, which aredriven by external magnetic fields and are susceptible to disruptionby stray fields. Our simulations qualitatively capture the mainobservations of zero-field SDE, field-resilient SDE, and non-monotonic temperature dependence of the SDE in NiI2 JJ. Our theo-retical modeling suggests that the combination of RSOC with heli-magnetism plays a key role in the SDE in NiI2 JJ, and these featuresmay prevail in helimagnetic JJs. We point out the possibility ofmanipulating and enhancing the SDE by electrical gating in multi-ferroic JJs, which is an exciting tuning knob to explore in the future.The discovery may lead to the technology development of multi-ferroic supercurrent diodes with high field tolerance and tunability,and can be combined with strategies for enhancing diode efficiencyto open up new possibilities for practical applications in cryogenicelectronic circuits.MethodsCrystal growthSingle crystals of NiI2 were grown by the chemical vapor transporttechnique. The starting materials were mixed in a stoichiometric ratio(Ni: I2 = 1: 1, 500mg in total) and sealed in 7-inch long silica tubes undervacuum. The tubes were placed in a single-zone tube furnace, with oneend at the center. The temperature of the furnace was set to 580 °C at3 °C/minute, dwelt for 60 h, and then set to room temperature at thesame rate. Black single crystals formed at the cold end of the tubes ashexagonal thinflakes.X-raydiffraction patterns (BrukerD8ECO)of thesingle crystals showed a clear (003) characteristic peak at 2θ = 13.42degrees, in agreement with the crystal structure reported in the Inor-ganic Crystal Structure Database (ICSD).High-quality NbSe2 single crystals were prepared using the iodinevapor transport method52. Stoichiometric amounts of Nb (99.9%; AlfaAesar) and Se (99.5%; Alfa Aesar) powders were sealed in an evacuatedquartz tube (1/2 inch diameter) with 2mg/cm3 of iodine as the trans-port agent, and introduced horizontally into a tube furnace. Thetemperaturewas slowly increased to 725 °C,maintained for 3 days, andfollowed by furnace cooling down to room temperature. The largeplatelet single crystal picked out from the resulting sample was sealedon one side in another quartz tube along with a newmixture of Nb, Se,and iodine on the other side and heated through the same procedure.Subsequently, large and high-quality NbSe2 single crystals wereobtained.Device fabricationThe bottom contact electrodes were fabricated on SiO2/Si sub-strates using photolithography and electron beam evaporation(Ti/Au, 10/40 nm). Thin flakes of h-BN, NbSe2, and NiI2 wereexfoliated onto SiO2/Si substrates using Scotch tape. To assemblethe NiI2 vdW JJ, a piece of h-BN was first picked by the dry transfertechnique14,53, using polypropylene carbonate (PPC) polymer spin-coated on polydimethylsiloxane (PDMS) as the stamp. Once theh-BN is picked up, other flakes of the JJ were picked up in thefollowing order: top NbSe2, NiI2, and then bottom NbSe2. Occa-sionally, the structure that the h-BN has picked up may bereleased on the next target flake and be heated to increase thecohesion between different layers to facilitate the pick-up pro-cess. After the entire stack of flakes was completed, the h-BN/NbSe2/NiI2/NbSe2 vdW JJ structure was released on the bottomcontacts and was ready for transport measurements withoutfurther fabrication. During the dry transfer process, the JJ areawas covered by h-BN the entire time to prevent contaminationdue to polymer residue. The graphite/NiI2/graphite tunnel junc-tion was fabricated in the same way. For the Gr JJ and NbSe2/NbSe2 devices, the bottom NbSe2 flakes were exfoliated ontoSiO2/Si substrates using Scotch tape. Other flakes were exfoliatedon PDMS and then transferred on top of the bottom NbSe2 flakeone by one. After the entire device stack was completed, it waspicked up using PPC and released on the bottom contacts. Thetransfer process was performed in an Ar-filled glove box with H2Oand O2 levels below 1 ppm using a home-built transfer stage. Thetwo-point contact resistance between different pins was below100 ohms.Transport measurementsResistance and V − I characteristics were measured in a physicalproperty measurement system (PPMS, Quantum Design Inc.). Thetemperature dependence of resistance was taken with the low-frequency lock-in technique (< 10Hz) with a 2 μA AC current excita-tion. For the V − I characteristics, DC voltages were measured by aKeithley 2182 nanovoltmeter and a DC current bias was applied by aKeithley 6221 current source. The critical current was extracted by firsttaking the derivative of V v.s. I data, and the current value correspondsto the first peak in dV/dI v.s. I was marked as the critical current. If thetransitions were sharp, a constant cutoff voltage may be applied toextract the critical currents. We found that the choice of extractionmethods does not lead to a significant difference in the interpretationof the data. The switching curves were employed to extract criticalcurrent, unless stated otherwise. Before zero-field measurements, themagnetic field was set to 1 T and then oscillated to zero above thetransition temperature of NbSe2 tominimize the effect of the remnantfield on the device behavior.Numerical simulationsWe simulate the current-phase relationship (CPR) of the multiferroic JJusing the following tight-binding Bogoliubov-de Gennes Hamiltonian:HðBdGÞ =Xrnψyrnð4+ q2=4Þt � μ+UdipðrnÞ+Ubarrierδxn , 0� �τz � σ0h iψrn+XrnψyrnΔðxÞZ ðrnÞ2τz � σx + JexcðrnÞτ0 � σy � ΔðrnÞτy � σy" #ψrn+X< rn , rm >δyn , ymψyrn�tτz � σ0 + iαRτ0 � σx + itqyhðrn, rmÞτ0 � σz� �ψrm+X< rn , rm >δxn , xmψyrn�tτz � σ0 � iαRτz � σy + itqxhðrn, rmÞτ0 � σz� �ψrm,ð3Þwhere ψrn= ðcrn", crn#, cyrn", cyrn#ÞT, and cyrn ,ρσ (crn , ρσ) is the creation(annihilation) operator for an electron at site rn with spin σ, and τi andσi are Pauli matrices. The JJ is defined by the regions − Lx,s− Lx,n/Article https://doi.org/10.1038/s41467-025-63698-3Nature Communications | (2025) 16:9287 6www.nature.com/naturecommunications2 ≤ x ≤ Lx,s + Lx,n/2 and − Ly/2 ≤ y ≤ Ly/2. Then we haveUdipðrÞ=κdipðP � rÞ, �Lx, n=2≤ x≤ Lx, n=20, otherwise�ΔðxÞZ ðrÞ= ΔðxÞZ , �Lx,n=2≤ x ≤ Lx,n=20, otherwise(JexcðrÞ=Jexc jxj≤ Lx,n=2 + ξexc0, otherwise�ΔðrÞ=Δeiϕ=2, x < � Lx,n=2Δe�iϕ=2, x > Lx,n=20, otherwise8><>:hðrn, rmÞ=1 jxnj, jxmj≤ Lx,n=2 + ξexc0, otherwise�,ð4Þwhere ξexc is the characteristic length scale of the exchange proximityeffect in the superconducting leads. To calculate the CPR, we diag-onalize the tight-binding Hamiltonian to solve for eigenvalues {ϵn(ϕ)}.At temperature T, the CPR for a short ballistic junction is ref. 54Isðϕ,TÞ= � 2eℏXntanhϵn2kBT� �dϵndϕ: ð5ÞIn our simulations, we take the superconducting gap to be constantand only consider kBT ≤0.05Δ, where the suppression of Δ accordingto BCS theory is negligible. Using a lattice constant of 10 nm and aneffective electron mass of 0.03 times the bare electron mass, thesuperconducting gap is estimated to be 5meV. This is certainly largerthan the gap inNbSe2, but it allows formore faster simulations withoutcompromising the qualitative accuracy of our results. None of ourconclusions about the zero field SDE, bipolar field resilience, or non-monotonic T dependence are changed by considering a smallersuperconducting gap in our simulations. Simulation results arepresented in Supplementary Figs. 7 and 8.Here, we discuss the effect of an electric polarization P in a mul-tiferroic JJ on its SDE. Numerically, we approximate the electricpolarization with an effective dipole approximation resulting in anelectric potential Udip = κdip(P ⋅ r), where κdip characterizes the perme-ability of the multiferroic layer. Owing to the perfect conductivity ofthe superconducting electrodes, we consider an electric polarizationconfined to the normal region of the JJ. Furthermore, we constrainP × q∥ + z as is required for spin-spiral multiferroic ordering. Supple-mentary Fig. 9a-c show the Andreev bound state spectra of the mul-tiferroic JJ with RSOC. Supplementary Fig. 9d shows the T =0 CPRwith∣P∣ > 0. At T =0 and for ±P∥x, we find that flipping the sign of P∥x doesnot affect the diode rectification efficiency or polarity. Here, theasymmetry introduced in the junction by P leads to an asymmetricnormal resistance, similar to typical ferroelectric diodes.55. On theother hand, for ±P∥y, flipping P results in a change in the CPR since qalong the current direction is simultaneously flipped. In general, thetunability of the CPRwith P depends on the details of the junction anda more systematic study is needed to determine how to optimize theelectric tunability of the CPR by manipulating P.Depairing momentum analysisWe can consider the heuristic argument given by Yuan and Fu23 toexplore the diode effect in the superconducting helimagnet as itrelates to finite Cooper pair momentum associated with a currentbias. Consider the effect of a depairing momentum ℓ on the energyspectrum of the superconducting helimagnet, where theHamiltonian in Eq. (2) is replaced byhBdGðk, lÞ=hðk + l=2Þ � μ ΔΔ μ� T�1hðk � l=2ÞT� �: ð6ÞHere we focus on ℓ = ℓxx. The key to the heuristic argument given byYuan and Fu for a Rahsba superconductor with an in-plane Zeemanfield is that an asymmetry in the closing of the spectral gap(manifestation of the diode effect) arises when the Zeeman field isperpendicular to ℓ (i.e., current direction). Mathematically, thiscondition is a consequence of the form of the spin-orbit coupling,e.g., for ℓ = ℓxx, the spin-orbit term and Zeeman terms in theHamiltonian are aligned � ‘x +ΔðyÞZ� �σy, effectively shifting thedepairing momentum, see Supplementary Fig. 10a, b. Hence, if thedepairing momentum term in the spin-orbit interaction is perpendi-cular to the Zeeman field, then there is no asymmetry in the closing ofthe spectral gap with ℓ. Given the general form of the spin-orbitinteraction and effective Zeeman splitting in a helimagnet in theabsence of an external magnetic field, we see that it is not possible toobserve an asymmetry in the closing of the spectral gap with ℓ. Thisimplies centrosymmetric superconducting helimagnets generally willnot show a diode effect associated with a depairing momentummechanism. Now, if we consider Rashba spin-orbit coupling (RSOC) asdiscussed in themain text, wefind that a non-reciprocal critical currentdevelops in our simulations. Incorporating RSOC into the helicalsuperconductivity analysis above, the SDE in the depairingmomentumemerges as an asymmetric suppression of the gap with the depairingmomentum, see Supplementary Fig. 10c–f.To picture the even-in-H SDE observed in the experiment, it’shelpful to consider how hZ affects the spectral gap of a super-conducting helimagnet with RSOC. Introducing a depairingmomentum into the BdG Hamiltonian will result in an indirect gapclosing in the dispersion, as discussed above. Phenomenologically,the indirect gap closing in superconductors with SDE will beasymmetric in the depairing momentum23. Now, the Zeeman effecttends to suppress the spectral gap of a superconductor with spin-singlet pairing due to a spin population imbalance. In our case, wefind SDE will be symmetric in ΔZ when hZ causes the spectral gap toclose directly, i.e., it does not contribute to an indirect spectral gapsuppression, favoring a finite depairing momentum. This is shownexplicitly in Supplementary Fig. 10g–j, where the effect of thedepairing momentum is symmetric in ΔðxÞZ whereas this ideal sym-metry is lifted with ΔðzÞZ .Data availabilityThe data that support the findings of this study are available within thearticle and its Supplementary Information files. All data generatedfrom this study are available from the corresponding authors uponrequest.Code availabilityThe codes that support the findings of this study are available from thecorresponding authors upon request.References1. Sze, S. M., Li, Y. & Ng, K. K. Physics of Semiconductor Devices (JohnWiley & Sons, Hoboken, 2021).2. Matisoo, J. The tunneling cryotron—a superconductive logic ele-ment based on electron tunneling. Proc. IEEE 55, 172–180 (1967).3. Buck, D. A. The Cryotron—a superconductive computer compo-nent. Proc. IRE 44, 482–493 (1956).4. Alam, S., Hossain, M. S., Srinivasa, S. R. & Aziz, A. Cryogenicmemory technologies. Nat. Electron. 6, 185–198 (2023).5. Ando, F. et al. 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Crystallogr.44,1272–1276 (2011).Article https://doi.org/10.1038/s41467-025-63698-3Nature Communications | (2025) 16:9287 8https://qdusa.com/siteDocs/appNotes/1070-207.pdfhttps://qdusa.com/siteDocs/appNotes/1070-207.pdfhttps://www.everspin.com/file/882/downloadhttps://www.everspin.com/file/882/downloadwww.nature.com/naturecommunicationsAcknowledgementsH.Y.Y. thanks Fazel Tafti at Boston College for generously providingaccess to his laboratory facilities for the growth of NiI2 single crystals.H.Y.Y. thanks Margarita Davydova, Adolfo O. Fumega, Yi Tseng, ConnorA. Occhialini, Jonathan Gaudet, and Ilya Sochnikov for the fruitful dis-cussions. J.J.C. thanks Enrico Rossi for helpful discussions and FrançoisLéonard for his critical reading of the manuscript. K.L.W. acknowledgesthe support of the U.S. Army Research Office MURI program underGrants No. W911NF-20- 2-0166 and No. W911NF-16-1-0472. J.J.C. is sup-ported by an LDRD. We acknowledge the use of the Nano and PicoCharacterization Lab in the California NanoSystems Institute at UCLA.Sandia National Laboratories is a multi-mission laboratory managed andoperated by National Technology & Engineering Solutions of Sandia,LLC (NTESS), a wholly owned subsidiary of Honeywell International Inc.,for the U.S. Department of Energy’s National Nuclear Security Adminis-tration (DOE/NNSA) under contract DE-NA0003525. This written work isauthoredby an employee ofNTESS. The employee, not NTESS, owns theright, title and interest in and to thewrittenwork and is responsible for itscontents. Any subjective views or opinions that might be expressed inthe written work do not necessarily represent the views of the U.S.Government. The publisher acknowledges that the U.S. Governmentretains a non-exclusive, paid-up, irrevocable, worldwide license topublish or reproduce the published form of this written work or allowothers to do so, for U.S. Government purposes. The DOE will providepublic access to results of federally sponsored research in accordancewith the DOE Public Access Plan. K.W. and T.T. acknowledge supportfrom the JSPS KAKENHI (Grant Numbers 21H05233 and 23H02052) andWorld Premier International Research Center Initiative (WPI), MEXT,Japan. Y.L. acknowledges the support from the National Natural ScienceFoundation of China (grant No. 12104238). We acknowledged the use ofthe software VESTA56 for drawing the atomic structure shown in Fig. 1.Author contributionsH.Y.Y. and K.L.W. conceived the project and designed the experiments.H.Y.Y. synthesized the NiI2 crystals. Y.L., S.H., and C.W.C. synthesized theNbSe2 crystals. T.T. and K.W. provided and characterized bulk h-BNcrystals. H.Y.Y. and C.E. performed atomic force microscopy measure-ments. G.Q. fabricated the bottom contact electrodes. H.Y.Y. fabricatedthe NiI2 JJ, NbSe2/NbSe2, and graphite/NiI2/graphite devices. A.J.B. andH.Y.Y. fabricated the Gr JJ device. H.Y.Y. performed the transport mea-surements. H.Y.Y. and J.J.C. analyzed the transport data. J.J.C. developedthe theoretical model and performed the numerical simulations. H.Y.Y.,J.J.C., and K.L.W. wrote the manuscript with inputs from all authors.Competing interestsThe authors declare no competing interests.Additional informationSupplementary information The online version containssupplementary material available athttps://doi.org/10.1038/s41467-025-63698-3.Correspondence and requests for materials should be addressed toHung-Yu Yang or Kang L. Wang.Peer review information Nature Communications thanks MuhammadNadeem, and the other anonymous reviewer(s) for their contribution tothe peer review of this work. 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To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/.© The Author(s) 2025Article https://doi.org/10.1038/s41467-025-63698-3Nature Communications | (2025) 16:9287 9https://doi.org/10.1038/s41467-025-63698-3http://www.nature.com/reprintshttp://creativecommons.org/licenses/by/4.0/http://creativecommons.org/licenses/by/4.0/www.nature.com/naturecommunications Field-resilient supercurrent diode in a multiferroic Josephson junction Results Zero-field SDE in a multiferroic vdW JJ Field resilience of the SDE in NiI2 JJ Non-monotonic temperature dependence of SDE Theoretical modeling Methods Crystal growth Device fabrication Transport measurements Numerical simulations Depairing momentum analysis Data availability Code availability References Acknowledgements Author contributions Competing interests Additional information