Giant unusual anisotropic magnetoresistance enabled by hole-electron resonance in van der Waals heterostructures

Domain: physics
Published: 2026-01-16
Editorial outcome: major_revision

Abstract
The hole-electron resonance in two-dimensional WTe2 dynamically screens the built-in electric field, disrupting the scattering equilibrium constraints of conventional electron transport. Here, we propose utilizing the hole-electron resonance to achieve Coulomb force-unconstrained spin angular momentum transfer across the WTe2/Fe3GaTe2 interface, offering a novel platform for exploring unconventional spin transport phenomena. A clear signature of this mechanism is the observation of an unusual anisotropic magnetoresistance of 289%, which far exceeds conventional spin Hall magnetoresistance and cannot be explained by standard spin absorption or scattering models. Its angular profile deviates from the simple cosine-squared form but realigns after accounting for magnetization and field orientation, reflecting the interplay between hole-electron resonance and magnetization dynamics. Furthermore, chiral transverse transport with distinct symmetry transitions emerges within the hole-active temperature regime, originating from interfacial symmetry breaking and the inhomogeneous spin-orbital coupling. These findings highlight the essential roles of both electrons and holes in spin transport.

Introduction
Spintransportphenomena,suchasspinpumping1,2,spininjection3–6,spinHalleffect7–11, and spin-orbit torque12–16, constitute the fundamentalbasisforspintronicsresearchandapplications.Whilecurrentstudiesintheseareaspredominantlyfocusonelectroncarriers,therole of hole-electron interactions has received comparatively less attentiondespiteitsfundamentalimportance.

Recent advancements in two-dimensional (2D) van der Waals (vdW) materials have provided rich opportunities for exploring transportphenomena.Inparticular,2DWTe2hasemergedasaprototypical system for realizing hole-electron resonance17, whereboth electron and hole bands coexistat the Fermi level, as illustrated in Fig.1a,b.Undertheinfluenceofamagneticfieldorspin-orbitcoupling (SOC),electronandholedisplacementseffectivelyneutralizethetotal charge, suppressing the formation of an internal electric field, as depictedinFig.1c.Thischargecompensationmechanism,combined with enhanced carrier scattering, leads to a remarkably large and unsaturated magnetoresistance (MR)17–22. This phenomenon was experimentally observed17 and confirmed to arise from the nearly perfect hole-electron compensation in WTe2. Subsequent studies haveextensivelyexploredtheelectricaltransportpropertiesofWTe2, including its band structure characteristics19, anisotropic MR20,23,24, planarHalleffect25,26,andnonlinearHalleffects27–29.Importantly,while thesephenomenaproducelargeMR,theyarelargelyindependentof magnetic moments, limiting their direct applicability in spintronic devices.

Incorporating a hole-electron resonance system into a heterojunctionwithaferromagnetic(FM)materialintroducescarrieraccumulation and interfacial scattering, fundamentally altering spin transportdynamics.Inthiscontext,chargecompensationsuppresses the internal electric field, facilitating Coulomb force-unconstrained spin angular momentum transfer at the interface, as illustrated in Fig.1c.WTe2/FMinterfacethusservesasanidealplatformtoexplore theseunconventional spin transport processes. In magnetic heterostructures, interfacial effects such as spin absorption/reflection and interfacialelectricfieldsgiverisetomagnetoresistancephenomena. These include spin Hall magnetoresistance (SMR)30–32 and unusual anisotropic magnetoresistance (UAMR). The concept of UAMR is defined by the interfacial interactions. In WTe2-based magnetic heterostructures withinthehole-electronresonanceregime,theinterplaybetweenhole-electron resonance and interfacial magnetization can further modulatethemagnetoresistance,offeringastrategytoharnessthelarge MRofWTe2fornon-volatilespintronicapplications.

Here,weinvestigatehowhole-electronresonanceinteractswith the FM interface in anall-vdW WTe2/Fe3GaTe2 heterostructure. Our findingsdemonstratealargeUAMRintheplaneperpendiculartothe chargecurrent,whichdirectlycorrelateswithboththtemagnetization and hole-electron resonance. Furthermore, within the temperature regime dominated by hole-electron resonance, a chiral transverse transportresponseisobserved.Theseresultshighlightthecrucialrole ofbothelectronandhole carriersingoverningspin transport,providingvaluableinsightsforthedesignofspintronicmemorydevices basedonhole-electronresonancematerials.

Results
Hole-electronresonanceandUAMR
ThevdWheterostructureWTe2/Fe3GaTe2ispreparedviamechanical exfoliation.Fe3GaTe2isa2DvdWFMmaterialwithabulkCurietemperatureof~350K37–39(seeSupplementaryInformationS1).According to atomic force microscopy (AFM), the thicknesses of WTe2 and Fe3GaTe2 are determined to be 9nm and 26nm, respectively (see Supplementary Information S2). The schematic of the electrical transportmeasurementsisshowninFig.2a.ADCcurrentof10μAis appliedalongthea-axisofWTe2,correspondingtoacurrentdensityof ~2.38×103A/cm2,whereJouleheatingeffectsarenegligible40(Fig.S3). A9Tmagneticfieldisthenrotatedintheyz-plane(H⊥I)tominimize H–Iangleeffectsandhighlightmagnetization-inducedcontributions. To better analyze the sources of the magnetoresistances, we also fabricatedWTe2devicesandFe3GaTe2devicesforcomparisonwiththe WTe2/Fe3GaTe2heterostructure.Detailsofthesamplestructuresare listedintheSupplementaryInformationS2.

The temperature dependence of the WTe2/Fe3GaTe2 heterostructureresistanceisdepictedinFig.S4inSupplementaryInformation.Byanalyzingthetemperature-dependentresistivities,ρWandρF, ofWTe2andFe3GaTe2devicesunderH=9T,wedeterminethecurrent distributionratioIF/IWbetweenFe3GaTe2andWTe2layerswithinthe heterostructure.TheIF/IWratioexhibitsaminimumof~12ataround 60K. Below this temperature, IF/IW increases with decreasing temperature,approaching14at5K,suggestingthatthemajorityofthe currentflowsthroughtheFe3GaTe2layer.

Figure2bpresentsthenonsaturatingMRinbothWTe2andWTe2/ Fe3GaTe2heterostructureat5K.NonsaturatingMRcanoriginatefrom severalmechanisms,includingcharge-carriercompensation,open-orbit transport,orothereffectsrelatedtoFermisurfacetopology41–43.Among these,charge-carriercompensation,inwhichnearlyequalvolumesof electronandholepocketsleadtoacontinuousincreaseofresistance withmagneticfield,hasbeenidentifiedasthedominantmechanismin systemssuchasWTe217,LaSb44,ReO345,andGdBi46.IntheWTe2,thehole-electroncompensationisconfirmedbytwo-bandmodelfitting18(SupplementaryInformationS5).UpontheintegrationofFe3GaTe2,thefield-induced growth of MR becomes less pronounced at high magnetic fields.Nevertheless,asubstantialnonsaturatingMRpersistsupto9T, suggesting that the hole-electron resonance remains active, albeit potentially modified by the magnetic interface. To elucidate this interplay, we examined the angular dependence of the longitudinal resistance,asshowninFig.2c.GiventhatUAMRprovidesamathematical framework encompassing all possible angular dependencies of magnetoresistance,weadoptthetermUAMRtodescribetheangular-dependent magnetoresistance (ADMR) measured in our experiments. Below80K,Rxxvariesstronglywiththeangleβbetweenthemagnetic fieldandthez-axisintheyz-plane,producingapronouncedUAMR.Its amplitudeisdefinedas UAMR = (Rxx,⊥ - Rxx,∥)/Rxx,∥ ×100%,whereRxx,∥andRxx,⊥denote the longitudinal resistance with the magnetic field applied in the ab-planeandalongthec-axis,respectively.ThisUAMRisalsoobservedin isolatedWTe2andFe3GaTe2,asshowninFig.2d,e,respectively.The formerisattributedtothehole-electronresonanceinWTe2,whilethe latterislikelyrelatedtointerfacialfieldsin2Dlayeredsystems33–36.

Bycomparingthesethreedevices,itisevidentthattheUAMRin theWTe2/Fe3GaTe2devicedistinctlydiffersfromthatintheWTe2and Fe3GaTe2devices. Although WTe2 itself exhibits appreciable UAMR below80K,itisnotdirectlycorrelatedwiththemagneticmomentsand followsacos2βangulardependence,asindicatedbydashedfittinglines in Fig. 2c, d, e. In contrast, the angular dependence in the WTe2/ Fe3GaTe2 device deviates significantly from cos2β,exhibiting a sharp peaknearH⊥c,reminiscentofthebehaviorobservedintheFe3GaTe2 device.Thismayarisefromthestrongperpendicularmagneticanisotropy (PMA) competing with the Zeeman energy, leading to a misalignment between the magnetic moment orientation and the magneticfielddirection39,47.However,contrarytotheWTe2/Fe3GaTe2 device,Fe3GaTe2deviceshowsamuchlowerUAMRwhenthemagnetic fieldisalongthec-axiscomparedtowhenitisperpendicular.Wefurther compare the WTe2/hBN/Fe3GaTe2 device, as presented in SupplementaryInformationS6.WiththeinsertionofanhBNspacer,the interfacial coupling between magnetization and charge carriers is effectively suppressed. Under this condition, the observed UAMR recovers a cos2β dependence, characteristic of the bulk response of WTe2.ThiscomparisonindicatesthattheUAMRintheWTe2/Fe3GaTe2 heterostructure incorporates contributions from both WTe2 and Fe3GaTe2 yetcannotberegardedasasimplesuperpositionofthetwo. Whilethebulkeffectsassociatedwithhole–electronresonanceandthe FermisurfaceofWTe2makeanimportantcontribution,theinterfacial interplaybetweenmagnetizationsandbothelectronandholecarriers intheWTe2/Fe3GaTe2heterostructureconstitutesthedecisivefactorin shapingtheUAMR(SupplementaryInformationS10).Thisbehaviorin theWTe2/Fe3GaTe2heterostructurehasbeenconsistentlyreproduced acrossmultipledevices(SupplementaryInformationS11).

Magneticorientationdependence
TofurtherclarifythecontributionofmagneticmomentstotheUAMR intheWTe2/Fe3GaTe2device,weperformacorrectionontheorientationsbetweenthemagnetizationmandtheappliedmagneticfieldH usingtheFe3GaTe2device.Thiscorrectionisbasedonthefactthatthe anomalousHalleffect(AHE)signaloftheFe3GaTe2deviceispositively correlatedwiththez-componentofitsmagneticmoments.Figure3a showsthetransversemagnetoresistanceRxyoftheFe3GaTe2deviceas a functionofβ.ThenormalizedpolarplotisshowninFig.3b.From these results, it is evident that the magnetic moments prefer to maintainanorientationnearthec-axisratherthanfullyaligningwith theappliedmagneticfield,asillustratedintheinsetofFig.3c.WhenH is applied atan angle β, the actualangleβm between the magnetic momentsandthez-directioncanbeexpressedas39,47
βm=arccos(Rxy(β)/Rxy(β=0)) (1)

TheresultingrelationshipbetweenβmandβisshowninFig.3c.It isclearthatmandHarenearlycollinearnearthec-axis,whilethereisa significant deviation when approaching the ab-plane, particularly at low temperatures. We introduced the corrected βm into the WTe2/ Fe3GaTe2 device,andtheresultsareshowninFig.3d.Itisevidentthat theUAMRoftheWTe2/Fe3GaTe2devicenowalignsmorecloselywith the cos2β angular dependence. Some deviations from the cos2β dependenceremainafterthecorrectionisduetothehighsensitivityof thePMAofFe3GaTe2tothickness,makingitchallengingtoachievea perfectmatchbetweenthecorrectedanglesintheparalleldeviceand thoseintheheterostructuredevice.Thisindicatesthatthemagnetization in Fe3GaTe2 plays a crucial role in the UAMR of the WTe2/ Fe3GaTe2 device.Additionally,theUAMRoftheWTe2/Fe3GaTe2 device atlowtemperaturescanalsobefittedusinghigher-ordertermsrelatedtom(greencurveinFig.3d),whichisalsoacharacteristicfeatureof non-collinearitybetweenthemagnetizationandthemagneticfield,as discussedintheSupplementaryInformationS7.

RelationshipbetweentheUAMRandthehole-electron resonance
Next,weexaminetherelationshipbetweentheUAMRandthehole-electron resonance by analyzing its temperature dependence. The UAMRofWTe2/Fe3GaTe2exhibitssimilartemperaturetrendaspristine WTe2,asshowninFig.4a.AlthoughthecurrentflowinginFe3GaTe2 layerismuchlargerthanthatinWTe2layer,theheterostructuredevice exhibitsanexceptionallyhighUAMRof288.78%.Thislargevaluemay includebulkcontributionsfromindividualWTe2andFe3GaTe2layers, whichcanbeestimatedtobe~31.48%basedonaparallel-circuitmodel. The estimated contributions of this bulk effect in WTe2/Fe3GaTe2 deviceatdifferenttemperaturesareshownasthegreendashedlinein Fig.4a,whicharefarsmallerthantheUAMRobservedhere.Furthermore, control experiments reveal that the UAMR is significantly reducedwhentheinterfaceisdisruptedorweakened,forinstanceby inserting an hBN spacer (Supplementary Information S6) or by increasing the thickness of the heterostructure (Supplementary InformationS11),indicatingtheimportantroleofthemagnetic interface.

The inset of Fig. 4a shows the ratio of electron to hole carrier densities(ne/nh)inWTe2(SupplementaryInformationS5).BycorrelatingthisratiowiththetemperatureevolutionofUAMR,wefindthat higherUAMRvaluesoccurinthetemperaturerangewheretheelectronandholecarrierdensitiesarenearlybalanced.Asthetemperature increases,theUAMRgraduallydecreases.Oncethesystemmovesout ofthehole-electroncompensationregime,itapproachesthemagnitude of UAMR typically observed in magnetic heterostructures (TableS2intheSupplementaryInformation).Athighertemperatures, thermal fluctuations increasingly suppress the long-range magnetic orderinFe3GaTe2,leadingtotheattenuationofinterfacialinteraction-related magnetoresistance48. Consequently, the UAMR in WTe2/ Fe3GaTe2 convergestowardthatoftheFe3GaTe2device,asshownin Fig. 4b. The temperature-dependent UAMR in both WTe2/Fe3GaTe2 andpristineWTe2devicescanbewelldescribedbyanempiricalgeneralizedlogisticfunction,UAMR(T)=U2+(U1-U2)/(1+(T/T0)p),which,whilenot directlyderivedfromamicroscopictheory,providesanaccuratedescription oftheobservedtemperaturedependence(solidlinesinFig.4a).Here, U1andU2representthelow-andhigh-temperaturelimitsofUAMR,respectively,T0characterizestheapproximatetransitiontemperature, andpdeterminesthesharpnessofthetemperaturedependence.For WTe2/Fe3GaTe2(WTe2),theextractedparametersareU1=288.62 (491.97)%,U2=-0.62(0.65)%,T0=27.54(27.35)K,p=2.68(2.64).By contrast, Fe3GaTe2 exhibits only a small negative UAMR (not exceeding–1.1%)acrossitsentiremagneticallyorderedregime,makingthelogisticdescriptioninapplicable.

We further analyze the possible physical sources of the large UAMRinWTe2/Fe3GaTe2.First,weanalyzethedatawithintheframeworkofthe SMRmodel32, with the results shown in Fig. S11. In the hole–electron resonance regime, the conventional SMR framework fails to capture the experimental data, as it leads to an unphysical negativespin-mixingconductance.Incontrast,ataround150K,where electron–hole compensation is lifted while Fe3GaTe2 still maintains long-rangemagneticorder,theSMRmodelprovidesareasonablefit, giving a spin-mixing conductance on the order of 1014Ω−1m−2. This valueisconsistentwithtypicalexperimentalreportsinconventional systems49,50. Second,weperform the ADMR measurements in other planesarepresentedintheSupplementaryInformationS13,whereRxx fortheyz-andxz-planesisfoundtobecomparableandsignificantly largerthanthatforthexy-plane.Theseangulardependenciescanbe generallydescribedbythetwovectorMRtheory,whichpositsthatthe ADMRisdeterminedbytherelationshipsamongvectorsincludingthe charge current, magnetization, and the interfacial electric field33–36. According to the two-vector MR theory, the sum of the expansion coefficientsofRxxfortheyz-andxz-planesiscomparableandcanbe much larger than that for the xy-plane, consistent with our experimentalobservations.Ingeneral,thesedifferentphysicalmechanisms maycoexistin our system. However, the key point hereis thatthe UAMRformalismitselfisavector-basedanalyticalframeworkrather thanadescriptionoftheactualmicroscopicorigin.Inourcase,the carrierandthemagneticinterface,whichcanbeadyadically included withinthe two-vectorMR frameworkand warrants further investigation.

Basedontheseobservations,weproposethatthelargeUAMRin the WTe2/Fe3GaTe2 device is closely associated with the interplay between the magnetic interface and charge carriers under hole–electronbalancecondition.Specifically,underthehole-electron resonancestate,electronsandholesshiftandaccumulatetooneside underthemagneticfieldduetotheLorentzforce.Thissuppressesthe formation of a built-in electric field that balance the transverse migrationofcarriers.Therefore,thetransversescatteringcontinuesto increase,thelongitudinalcarriermeanfreepathdecreases,ultimately leadingtoahuge,unsaturatedlongitudinalresistance.Whenamagneticinterfaceispresent,thesustainedinteractionbetweencarriers andthemagneticinterfaceallowsthegenerationoflargeUAMR.This interaction has often been neglected in prior studies of magnetoelectrictransport,butourresultshighlightitscriticalsignificance.Itis thereforeessentialtoreevaluatetheroleofholecarrierswithinthe existingtheoreticalframeworksofspintransport,particularlytheSHE andSOT14,15,51,52.Webelievethistobeahighlysignificantandurgently needed direction for theoretical development, as it emphasizes the profoundinfluence ofholecarrierson spin-relatedphenomena and challengesthecurrentparadigmsofspintransport.

Evolutionoftransversemagnetoelectrictransport
Wenowdirectourattentiontothetransversetransportcharacteristics inWTe2/Fe3GaTe2heterostructure.Figure5a,bdisplaythetransverse magnetoresistanceRxyasafunctionofthemagneticfieldangleinthe yz-planeatvarioustemperatures.ItisimportanttonotethattheRxy signalmaycontaincontributionsfromthelongitudinalresistanceRxx. Weattemptedtoantisymmetrizethedatawithrespecttothemagnetic fielddirection(seeSupplementaryInformationS12fordetails).How- ever,intheWTe2/Fe3GaTe2bilayer,theevencomponentofRxy does not correspond to the even part ofthe measured Rxx, and the odd component of Rxx fails to reproduce the odd part of Rxy. This discrepancyindicatesthattheevencontributioninRxycannotbeattributed solely to longitudinal mixing, but instead reflects intrinsic interfacialeffects.Accordingly,weretainedtherawdatawithoutperformingantisymmetrization.At5K,withthemagneticfieldHaligned alongthec-axis,RxyencompassescontributionsfromboththeAHEin theFe3GaTe2layerandtheordinaryHalleffectintheWTe2layer,as showninFig.5c.Analysisusingthetwo-bandmodel(Supplementary Information S5) indicates that electron and hole carriers remain comparableatlowtemperatures,highlightingthecriticalroleofhole carriersinthisregime18,21,22.Figure5dshowstheRxy-Hloopobtainedin theab-plane.Theenhancedcoercivityforthein-planefieldarisesfrom thecomplexmagnetizationswitchinginFe3GaTe2,resultingfromthe interplay of strong PMA, thermal fluctuations, and domain dynamics47,53,54. Previous studies have reported in-plane topological Halleffect(THE)-likesignalsinFe3GaTe2andFe3GeTe255–57,whichbear someresemblancetothehump-likeanomalyaround~3Tobservedin Fig. 5d. However, given that the heterostructure may host multiple non-topological contributions, such as the planer Hall effect in Fe3GaTe2,andthemultibandtransportinWTe2,thepresenceofatrue THEinthissystemremainstobeestablished.

TorevealtheintrinsicsymmetryofRxy,weisolatethetargetsignal in the WTe2/Fe3GaTe2 device using a linear least-squares method, whichremovesthespuriouscontributionfromRxxwhilepreserving thepotentialeven-symmetriccomponentinRxy(seeSupplementary Information S12 for details). The resulting Rxy is plotted in polar coordinatesaftertakingitsabsolutevalue,asshowninFig.5eandFig. S22. With increasing temperature, the angular dependence of Rxy undergoes three characteristic transformations: (a) In the low-temperatureregimebelow80K,correspondingtothehole-electron resonanceregionofWTe2,Rxyexhibitsacomplexangulardependence that deviates from the conventional symmetric trigonometric relationships. It breaksthemirrorsymmetrywithrespecttotheab-plane, revealingthechiralnatureofthetransversecurrent,whichisdistinct fromthatobservedinconventionalelectron-dominantmagneticheterostructuresorinisolatedFe3GaTe2andWTe2(seeFig.3andFig.S16). (b)Intheintermediatetemperatureregimearound150K,referredto as the competition region, additional extrema in Rxy emerge near angles~20°awayfromthey-axis,incontrasttoconventionalsystems where Rxy extrema typically occur at 0° and 180°, indicating a significantchangeinthespatialsymmetryoftransversetransport.(c)In high-temperatureregimenear300K,knownastheelectron-dominant regime,RxyresemblesthatobservedinFig.3forFe3GaTe2,dominated bytheconventionalAHEwithacosβrelationship.ThedetailedevolutionoftheRxysymmetryispresentedinFig.S22.

In order to gain deeper insights into the interfacial coupling between hole-electron resonance and magnetic moments, we performed first-principles calculations to map the SOC distribution in WTe258–61. The calculated band structure with projecting different orbitals for the W and Te atoms in reciprocal space are shown in Fig.6a,b,respectively.TheseresultsrevealthattheSOCinWTe2 primarilyarisesfromthehybridizationbetweenthed-orbitalofWandthe p-orbitalofTe.Notably,neartheFermilevel,theSOCassociatedwith W d-orbitals exhibits pronounced anisotropy in momentum space, givingrisetoaspatiallyinhomogeneousSOClandscape.ThisanisotropicSOCdistributioncanmodulatetheinterfacialinteractionswith adjacent FM layers, influencing spin-dependent scattering and the coupling between hole-electron resonance and magnetic moments. Such modulation provides a plausible mechanism for the observed chiraltransversetransport.

Consideringthedecisiveroleofcrystalsymmetryindetermining theband structureand therebythe spin transport, we performed a symmetry-based quantitative analysis. The constructed WTe2/ Fe3GaTe2 interfacestructureisshowninFig.6c.Beyondtheintrinsic symmetry breaking of WTe2, the Fe3GaTe2 interface further enhances the spatial asymmetry, placing the system in the point group C3v(No. 156), characterized by a threefold rotational axis and three mirror planes.Accordingtopointgroupanalysis,theHallcurrentalongthey directioncanbeexpressedas
jyH=p1cosβ+p3cos3β+p5cos5β+q1sinβ+q3sin3β+q5sin5β (2)
wherepnandqn(n=1,3,5)arecoefficientsdeterminedbythecrystal structureandintrinsicpropertiesofthematerials.Inadditiontothe conventionalcosβterm,higher-orderharmonicsandsinetermsare symmetry-allowed.Thesinetermsareevenfunctionswithrespectto theabplane,whilethecosinetermsareodd.Theircoexistenceyields jy(m)≠-jy(-m),indicatingthattheHallcurrentintrinsicallyreflects the broken ab-plane symmetry62. The first-order terms are mainly associatedwiththedipolemoment(netmagnetization),whereasthe higher-order terms primarily originate from multipole moments contributing to the Hall current63,64. Details are provided in Supplementary Information S14. Around 150K, fitting results reveal that higher-order coefficients increase significantly relative to the first-order terms. This enhancement is likely driven by temperature-dependent variations in carrier concentration. In this regime, the electroncarrierdensityrisesrapidlywhiletheholefractiondecreases sharply(seeinsetofFig.4a),accompaniedbyevolvingphononand magnonscattering.ThesechangesaltertheBerrycurvature,thereby enhancing the multipole effectand accounting for the pronounced contributiontotheHallresistance63.

Inconclusion,wehavedemonstratedasignificantUAMR(~289%) and the chiral transverse transport properties inanall-vdW heterostructure WTe2/Fe3GaTe2, enabled by the interplay of hole-electron resonance and FM interface. The UAMR observed in the WTe2/ Fe3GaTe2 heterostructureisnotablyinfluencedbythemagnetization orientationoftheFe3GaTe2layer.Despitethecurrentmainlypassing throughFe3GaTe2,theUAMRshowsaWTe2-liketemperaturedependence, highlighting the crucial carrier-magnetization interaction enhancedatthehole-electronresonance.Furthermore,whenholeand electron carriers are nearly balanced, chiral transverse transport is clearlyobserved.Intheintermediateregime,whereelectronsgraduallydominatebutholecarriersremainactive,higher-ordersymmetry componentsoftheHallresistivityemerge.Theoreticalanalysesindicate that these unconventional transport responses originate from interfacialsymmetrybreaking,whichpermitschiralHallcurrentsand higher-ordersymmetryterms.Thebrokensymmetryalsoinducesan inhomogeneousSOCdistribution,furthermodulatingthesymmetry of the magnetoresistance. These findings underscore the potential limitations of previous magnetic-electric transport models that have primarily considered electron carriers, suggesting the urgency of expanding theoretical frameworks that incorporate hole carriers in spintronics.

Methods
Singlecrystalsgrowth
SinglecrystalsofFe3GaTe2aregrownbythestandardhigh-temperature self-fluxtechnique.Amixtureofiron(Fe,99.98%),gallium(Ga,99.99%), andtellurium(Te,99.99%)powdersinamolarratioof1:1:2isplacedin analuminacrucible,andanotheremptyaluminacrucibleiskeptontop ofitwithquartzwoolseparation.Thewholecrucibleassemblyissealed inanevacuatedquartzampouleafterafewpurgeswithAr.Theampoule isfirstheatedto1273Kandheldatthistemperaturefor24htoobtaina homogeneous solution. Subsequently, the temperature is rapidly decreasedto1153Kwithin1h,followedbyaslowcoolingprocessto 1053Kin100handremainedfor12hat1053Kfortheannealingofthe crystals. The ampoule is then quickly taken out of the furnace and centrifugedtoseparatethecrystalsfromthefluxes.WTe2singlecrystals arepreparedbychemicalvaportransportmethodusingBrastransport agent.High-puritytungsten(W,99.999%)andtellurium(Te,99.999%) powdersarepreciselyweighedinstoichiometricratioandplacedintoa quartzampoulewithtransportagentBr(3mg/mlvolume).Thesealed ampoulewasplacedinatwo-zonefurnacewithatemperaturegradient. Thesourcezoneisgraduallyheatedto1093K,whilethegrowthzoneis maintainedat993K,heldatthistemperaturefor7–10days.Afterthe growthprocess,thefurnaceisslowlycooledtoroomtemperature.

Devicefabrication
First, a six-electrode Hall bar is prepatterned on a SiO2 (285nm)/Si substrateusingelectron-beamlithography,withTi/Au(5/15nm)electrodes deposited by thermal evaporation. Then, thin flakes of Fe3GaTe2 and WTe2 are mechanically exfoliated from bulk crystals usingadhesivetape.Theexfoliatedflakesaretransferredontopolydimethylsiloxanestamps,whichareadheredtoaglassslide.Finally, underopticalmicroscope,theFe3GaTe2flakewithappropriatethicknessandshapeischosenandtransferredontotheelectrodes.Using thesamemethod,aWTe2flakeispreciselystackedontotheFe3GaTe2 toformtheWTe2/Fe3GaTe2heterostructure.Topreventoxidation,the heterostructureisencapsulatedwithanhBNlayer.Bothmechanical exfoliation and transfer process are operated inside an argon-filled glovebox maintaining oxygen and water levels below 0.1 ppm. The obtainedWTe2/Fe3GaTe2heterostructuredeviceisbakedat120°Cfor 10mintoenhanceinterfacialcontact.

Measurements
The accurate thickness of each flake is determined by an AFM in a tapping mode. Magnetic and electricaltransportmeasurements are performed using a Physical Property Measurement System (PPMS DynaCool, Quantum Design, USA). During the measurements, an excitationcurrentof10μAisappliedalongthex-directionwithinthe ab-planeofWTe2andFe3GaTe2.ADMRmeasurementsareperformed by rotating a 9T magnetic field within the yz-plane while simultaneously recording the longitudinal resistance (Rxx) and transverse resistance(Rxy)asfunctionsofthefieldorientation.

Peer review rounds
[{"round": 1, "reviewer_comments": {"reviewer_1": "The authors studied unusual anisotropic magnetoresistance (UAMR) of WTe2(9nm)/Fe3GaTe2(26 nm) heterostructure. The\nmain finding is the observation of an exceptionally huge UAMR of 289% at 5K when the magnetic field rotates in the yz-\nplane (perpendicular to the current). Below 60K, more current (up to 90%) flows in Fe3GaTe2 layer. Significant UAMR was\nobserved below 100K. From the first-principles calculations, the authors showed a large spin-orbit coupling (SOC) exists in\nWTe2 with the hybridization of W d-orbits and Te p-orbits. In addition, authors show the temperature-dependence of UAMR\nfollows a generalized logistic function. Large MR is a crucial quantity in spintronics that is important for magnetic sensing\nand data storage. Thus, the topic is of great importance in the field of spintronics. I find the results also very interesting and\nuseful for the general readers of NC. However, I need to resolve some puzzles before making my formal assessment.\n1) Large UAMR in WTe2 was already observed in Refs. 17-22. For example, even bigger UAMR was reported in Ref. 20. Is\nnot it nature to have large UAMR of WTe2(9 nm)/Fe3GaTe2(26 nm) heterostructure?\n2) Huge MR in WTe2 was also attributed to the exact balance between electrons and holes in Ref. 17, the same as here in\naddition to the SOC in WTe2. Other than SOC which I will also discuss below, I do not see the fundamental difference\nbetween two mechanisms.\n3) In terms of the role of SOC, I do not see how can it lead to large MR in general and UAMR in particular. Can authors\nprovide a convincing argument? I believe that it is important.\n4) In Ref. 20, UAMR in WTe2 was claimed to be absolute cosine(\\beta) not square of it although the data are similar. Authors\nshould compare their fitting and data against those in Ref. 20. It can help readers to have better understanding of the\nsystems.\n5) It is also unclear to me how exact balance of electrons and holes and SOC leads to the specific expression of UAMR. A\nquantitative sketch like what was done in Ref. 17 about large quadratic B dependence of MR from two carrier model.\nAlthough two carrier model cannot really explain the linear MR reported in Ref. 20 and UAMR, it at least provides a possible\nscenario for unsaturated quadratic B phenomenon. The manuscript will surely make a contribution to the field and the topic if\nauthors can do so.\n6) It is not clear to me why Fig. 5d has the contribution from topological Hall effect (THE). THE is proportional to skyrmion\nnumbers. Can authors show the existence of skyrmions in their samples?", "reviewer_2": "In this study, the authors reported a giant, unusual anisotropic magnetoresistance (UAMR up to 289% in WTe2/Fe3GaTe2\nheterostructure. In contradistinction to conventional magnetoresistance mechanisms, the authors claimed that the UAMR is\nthe result of a distinctive interplay between charge compensation and magnetisation dynamics at the interface, thereby\nfacilitating Coulomb-unconstrained spin angular momentum transfer. Authors justified further that the WTe2 layer,\ndistinguished by its near-perfect balance of hole and electron carriers, dynamically neutralises internal electric fields under\nmagnetic field application, resulting in persistent nonequilibrium scattering and large, non-saturating MR. The observed\nangular and temperature-dependent UAMR deviates significantly from the classical cos^2θ behavior, especially below 80 K,\nwhere hole-electron resonance is most active. The main issue is that the origin of UAMR is not very clear due to following\nreasons.\n- Unsaturated MR can arise from different sources. How authors make sure such MR in their device is from e-h\ncompensation.\n- Without the e-h compensation, several materials show UAMR.\n- MR in WTe2 itself is very asymmetric and only B|| to c shows giant value., and other directions are either negligible or very\nlow, identifying the role of anisotropic Fermi surface rather than e-h compensation.\nThe comments above make it very clear that the behaviour of electrons and holes, which is related to their Fermi surfaces, is\nmore important than the spins of electrons and holes in this study. So, what the authors say is very premature.", "reviewer_4": "The transition metal dichalcogenide (TMD), WTe2, has attracted a lot of attention as an ‘anomalous’ semimetal that exhibits\na striking linear magnetoresistance up to very high magnetic field. Various studies of the electronic states and electrical\ntransport in this material suggest that ‘electron-hole resonance’ (nearly balanced electron and hole populations) may be\nresponsible for the observed magnetotransport. The present manuscript aims to explore the effect of this\nelectron-hole resonance on spin transport. The motivation is not based on a rigorous theoretical prediction but rather relies on the intuitive\nnotion that spin transport under conditions of electron-hole resonance should yield interesting phenomena. There is a\nreasonable rationale for this since all prior spintronics platforms have centered on materials wherein one carrier type\ndominates. Thus, the theoretical analyses and fundamental understanding of spin scattering, spin\ndiffusion, spin accumulation etc. has generally been confined to the regime of single carrier types — or at best uncorrelated, single particle\nphysics of two carrier transport. Thus, the approach undertaken in this manuscript potentially offers an opportunity to open up a\nnew area for spintronics.\nThe key claim made here is the observation of a “giant” or “exceptionally large” and “unusual” anisotropic magneto-\nresistance (AMR) in WTe2/Fe3GaTe2 hybrid heterostructures in the temperature window where electron-hole resonance\noccurs. The authors draw this conclusion by measuring electrical transport as a function of magnetic field (orientation,\nmagnitude) and temperature. I would urge the authors to be cautious about the excessive use of such superlatives unless\nthe data clearly warrant it. For example, a reader of this manuscript will look at the data shown in Fig. 2 and wonder what (if\nanything) is remarkable about the AMR of the hybrid WTe2/FGT devices when the control devices of purely WTe2 and FGT\nshow almost the same behavior. It is certainly true that there are qualitative differences in the dependence of the AMR on\nmagnetic field orientation (angle with current and sample plane), but the ‘large’ effect of “289%” is only revealed after\nsubtracting other contributions. The authors are to be commended for doing a careful job of analyzing the data and teasing\nout the hidden physics. However, this does not warrant the use of hyperbole to describe the observations… If one aims to\nexploit the claimed discovery of an “unusual” and “giant” AMR in this material system, the raw signal would need to have the\nenhanced attributes. Even though there may be some very interesting physics lurking in the data shown here, the\nobservations do not show much chance of making any technological impact unless the phenomenon can stand on its own.\nThe authors also report the observation of chiral transverse transport in the hole-dominated regime. This is also (in principle)\nquite interesting from a fundamental aspect and the authors accompany their observations with a DFT calculation that\npotentially provides a foundation for understanding the phenomenon. The authors attribute ‘chirality’ to the interfacial\ncoupling between hole-electron resonance and magnetic moments or spin texture formation due to DMI. The authors also\nmention that the chiral transport originates from the hybridization between the d-orbital of W and the p-orbital of Te, which\ninduces spatial symmetry breaking in the spin-orbit coupling (SOC) strength. However, this entire discussion is not very\nclear or rigorous (e.g/ “This anisotropic SOC distribution could mediate anisotropic interactions ….” In the absence of a more\nrigorous calculations, the use of illustrations or cartoons (in the supplementary) would be helpful.\nOverall, the work presented here provides a first glimpse of spin transport and spin-charge interconversion in a previously\nunexplored regime that combines several interesting factors arising from the presence of electron-hole resonance in a a\nstrongly spin-orbit coupled 2D material interfaced with a 2D ferromagnet. In principle, this could elicit broad interest because\nof the potential implications for spintronics with 2D materials. The manuscript in its current form falls somewhat short of\nachieving this goal. Drawing potentially impactful insights into spin transport in this interesting materials combination is\nespecially tricky since the claimed behavior does not really stand out in its own right but is rather subtly cloaked by other\ntransport contributions that are dominant even in the individual WTe2 and FGT. The authors would be well advised to stick\nto clearly highlighting the novel aspects of the physics they are trying to reveal and avoid unnecessary hype with claims of\n‘large’ effects without context. There should also be a high threshold to inventing new technical jargon such as “unusual\nAMR” or UAMR. The term AMR is well understood by the spintronics community and the term “UAMR” as coined here is\nimprecise and not particularly meaningful. There are also several detailed questions that need to be addressed before this\nmanuscript could be suitable for publication in Nature Communications. These are listed below. A major global concern is\nthat the conclusions drawn in this manuscript are based upon data on a single device (with measurements also shown on\ntwo control devices). Were additional hybrid devices measured to make sure the observed unusual aspects of AMR are\nreproducible? It is hard to imagine a paper such as this being published just based on results from a single device… Finally,\nit would be helpful if the authors were to get the manuscript carefully proofed for typos, style, and language clarity. For\nexample, the grammatically incorrect use of the phrase “electron-dominate” in several figures (a better phrase “electron-\ndominant” is used in the text in a couple of places; perhaps ‘electron-dominated” might be worth using instead). There are\nother places where words are randomly capitalized. As it stands, the manuscript is very hard to read because of such\nlanguage issues and would not be suitable for Nature Communications without significant rewriting.\n1. The specifications (dimensions) of the measured device are not explicitly provided. These should be mentioned\nsomewhere.\n2. The measurement conditions mention a ‘small current’ of 10 microamps. Why is this current considered “small”? It would\nbe more meaningful to mention the current density and characterize its magnitude in the context of potential Joule heating.\nIs there any Joule heating contribution to the observed AMR? (Nat. Commun. 9, 111 (2018))?3. As mentioned above, this work\nexplores a potentially new regime where spin-dependent transport is explored in the presence of electron-hole resonance.\nHowever, it would be helpful if the authors could more precisely compare the quantitative and qualitative aspects of the AMR\nfound here compared to earlier work involving the same materials, specifically WTe2/CGT (Nature Materials 24, 1049–1057\n(2025)) or other spin orbit coupled materials like topological insulators where an analogous effect, SMR, has also been\nstudied.\n4. Both WTe2 and FGT are conducting, and most of the current flows through FGT presumably since this is about 3 times as\nthick as the WTe2. (It would be helpful to have a comparison of the resistivity of the individual layers to estimate this current\ndistribution better.) How will the properties of the interface be decoupled from the bulk in the presence of these parallel\nchannels? The authors also conclude the AMR of the WTe2/FGT hybrid device contains features of both the individual\ncomponents. Since both components are conducting, shouldn’t this be expected? Similarly, if most of the current flows\nthrough FGT, why would the observed AMR be absent in the hybrid device above 150K if it is present in the FGT?\n5. What is the thickness of the control samples? Is it the same as that of the individual layers in the hybrid device? This does\nnot seem to be explicitly mentioned.\n6. The temperature dependence of the AMR in the hybrid device resembles that of WTe2 even though most of the current\nflows through FGT. This is perhaps worth dwelling on more deeply in the analysis and interpretation of the data. The abrupt\nincrease in the unusual component of AMR for WTe2/FGT below 150 K compared to only WTe2 below 80 K is striking. This\nleads the authors to hypothesize that magnetic interactions have some influence on the charge carriers. This is a\nreasonable conjecture but it would be useful to guide the reader toward ways in which this\nhypothesis could be tested. Are magnetic interactions the only possible scenario? If so, what sets\nthe energy scale corresponding to 150 K where the effect turns on. It would also be useful to show\nthe T-dependent Rxx vs B data for the hybrid device.\n7. Measurements of the Hall effect (Rxy) are always tricky because of unavoidable mixing of Rxx contributions into Rxy. The\nusual approach is to antisymmetrize the data with respect to the magnetic field direction. The authors need to explain how\nthey accounted for any possible mixing of Rxx into Rxy. This could play an important role in interpreting signatures\nassociated with chirality.\n8. It would be useful to extract the carrier type and density from the Hall data for some temperatures for the hybrid and control\nsamples.\n9. The authors use Fig. 5 (c) to conclude that hole carriers predominantly contribute to the ordinary Hall effect. However, the\nRxy vs B is non-linear. Have the authors made a two carrier fit to extract information about multiple carrier contributions?\nCould they provide estimates of the relevant characteristics (carrier density, mobility)? Given the parallel conduction\nchannels in this heterostructure, this is of course likely to be difficult to interpret but would be useful to know.\n10. The authors refer to a ‘topological Hall effect’ with reference to Fig. 5 (d). However, this is far from clear: what aspects of\nthis data might lead the authors to claim the presence of a topological Hall effect? The most obvious signature of the\ntopological Hall effect is an excess Hall voltage above the anomalous and ordinary Hall effects. This has to be carefully\nextracted and is not obviously present, even to an experienced eye. To make this attribution requires many more elaborate\ntests.\n11. The experimental section on the symmetry of Rxy needs to be more clearly written and needs more references. For\nexample, why are the experimental observations evidence of “chirality”? This is not at all clear. Also, what do the authors\nmean by “higher order symmetry” in this context?", "reviewer_5": "I co-reviewed this manuscript with one of the reviewers who provided the listed reports. This is part of the Nature Communications initiative to facilitate training in peer review and to provide appropriate recognition for Early Career Researchers who co-review manuscripts."}, "author_response": "We sincerely appreciate the positive evaluations and constructive feedback from all five\nreferees. In response to these valuable comments, we have carefully revised both the main\nmanuscript and the supplementary materials. We believe that all concerns raised by the referees\nhave been fully addressed. Below, we summarize the major revisions and provide detailed,\npoint-by-point responses. Specifically, the responses to referee #1 are presented on pages 2-9,\nreferee #2 on pages 10-16, referee #3 on pages 17-26, referee #4 on pages 27-47, and referee #5\non page 48.\nList of Major Revisions:\n1.Updated control sample: The bulk WTe control sample has been replaced with a thin WTe\n2 2\nflake whose thickness is comparable to that of the WTe layer in the WTe /Fe GaTe\n2 2 3 2\nheterostructure. Accordingly, the control data of WTe in Figs. 2 and Fig. 4 have been updated\n2\nwith the results from the thin-flake devices. The current distribution in the heterostructure has also\nbeen re-estimated based on the resistivity of the thin WTe layer (Supplementary Materials S4).\n2\n2.Additional control experiment: A new control device, WTe /hBN/Fe GaTe , has been\n2 3 2\nfabricated and characterized to isolate the magnetic interface contribution (Supplementary\nMaterials S6).\n3.Two-band model analysis: We added magnetic dependent Hall resistance measurements at\ndifferent temperatures. The carrier concentrations and mobilities of electrons and holes have been\ncalculated using the two-band model (Supplementary Materials S5). The temperature dependence\nof the carrier concentration ratio is now presented in the inset of Fig. 4(a).\n4.Expanded discussion on the origin of large UAMR: The mechanism responsible for the large\nUAMR in the WTe /Fe GaTe heterostructure has been further analyzed and discussed,\n2 3 2\nhighlighting the critical role of carrier-magnetic interfacial interactions.\n5.Refined theoretical analysis: Additional theoretical calculations have been performed to\nelucidate the origin of chiral transverse transport from the perspective of interfacial symmetry in\nthe WTe /Fe GaTe heterostructure.\n2 3 2\n1\n-----------------------------------\nReply to the Reviewer 1\n-----------------------------------\n[...]"}, {"round": 2, "reviewer_comments": {"reviewer_2": "Thank to the authors for revising the manuscript, which is much clearer than the previous version. My main concern was the\norigin and clarification of the UAMR in WTe₂/FGT heterostructures. The authors have addressed this issue by adding a\ndiscussion of the two-band model and presenting data from an additional device to isolate the magnetic contribution. They\nhave also expanded the discussion of the UAMR. In my view, the current version of the manuscript is now suitable for\npublication in Nature Communications.", "reviewer_3": "This referee is satisfied with the additional data/discussions added according to the previous comments. Therefore, with\nsufficient novelty in such an interesting system studied, the paper may still be worth publishing in Nature Communications", "reviewer_4": "The authors have responded satisfactorily to the concerns that were raised in the first report by significantly revising relevant\nparts of the manuscript and adding more data, particularly from additional samples/devices. In general, we believe that the\nmanuscript now conveys, with appropriate caveats, the introduction of a potentially interesting experimental platform for\nstudying spin transport effects in the presence of electron-hole resonance.\nA primary concern raised in the first report still stands, namely, the continued emphasis on highlighting the large value of\nUAMR at low temperature. Although this UAMR reaches 289%, this value is achieved only at 5 K, and it is not really\nexceptional when placed in context of other MR effects in topological materials. For instance Cd₃As₂ exhibits spin Hall\nmagnetoresistance (SMR) of 68% at low temperatures (Phys. Rev. B 97, 201110(R), 2018), ZrTe₅ shows 43% (Phys. Rev. B\n98, 121108(R), 2018), β-Ag₂Te shows 40% at room temperature (Nat. Commun. 15, 1259, 2024). These are smaller, no\ndoubt, than the UAMR observed here but still significant. In any case, the emphasis on large values in terms of percentage is\nnot particularly meaning full without some context... The primary advance that ought to be highlighted is suggested by the\nsentences in the abstract: \"Here, we propose utilizing the hole-electron resonance in WTe2 to achieve Coulomb force-\nunconstrained spin angular momentum transfer across the magnetic heterojunction interface, offering a novel platform for\nexploring unconventional spin transport phenomena. Within this framework, a large unusual anisotropic magnetoresistance\n(UAMR) of 289% is observed in the plane perpendicular to 16 the charge current, far exceeding conventional spin Hall\nmagnetoresistance (SMR) and cannot be explained by standard spin absorption or scattering models.\" The authors would\nbe advised to revise this section in the abstract as follows: \"Here, we propose utilizing the hole-electron resonance in WTe2\nto achieve Coulomb force-unconstrained spin angular momentum transfer across the magnetic heterojunction interface,\noffering a novel platform for exploring unconventional spin transport phenomena. A clear signature of this mechanism is the\nobservation of an unusual anisotropic magnetoresistance (UAMR) of 289% in the plane perpendicular to the charge current.\nThe value of this UAMR far exceeds conventional spin Hall magnetoresistance (SMR) and cannot be explained by standard\nspin absorption or scattering models.\" We believe this more precisely conveys the true scientific advance made in this\nmanuscript.\nIn addition, there are a couple of important issues that remain to be addressed.\n1. The authors now show I–V characteristics in Fig. S3(a). This is useful but raises a new concern: the data is restricted to\nthe current range of 5 μA to 20 μA, and notably, does not intersect with the origin. This strongly suggests that the contacts\nmay be non-ohmic, which could significantly influence the interpretation of the transport measurements. It would be\nimportant to clarify whether this behavior arises from contact resistance or some other mechanism.\n2. The temperature dependence of UAMR has been fitted using a “generalized logistic function.” It would be helpful to\nprovide a physical justification for using this specific functional form. Is the choice of this model based on an underlying\ntheoretical framework, or is it purely empirical? Clarifying this point would strengthen the interpretation of the temperature-\ndependent behavior.", "reviewer_5": "I co-reviewed this manuscript with one of the reviewers who provided the listed reports. This is part of the Nature Communications initiative to facilitate training in peer review and to provide appropriate recognition for Early Career Researchers who co-review manuscripts."}, "author_response": "Response letter\n[...]"}, {"round": 3, "reviewer_comments": {"reviewer_4": "I am satisfied that the authors have addressed all my concerns and recommend the paper for publication in Nature\nCommunications.", "reviewer_5": "I co-reviewed this manuscript with one of the reviewers who provided the listed reports. This is part of the Nature Communications initiative to facilitate training in peer review and to provide appropriate recognition for Early Career Researchers who co-review manuscripts."}, "author_response": ""}]

Decision letter