Annihilation and Control of Chiral Domain Walls with Magnetic Fields - Karna et al. - 2021 - Unknown

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ThisisanopenaccessarticlepublishedunderaCreativeCommonsAttribution(CC-BY)License,whichpermitsunrestricteduse,distributionandreproductioninanymedium,providedtheauthorandsourcearecited.pubs.acs.org/NanoLettLetterAnnihilationandControlofChiralDomainWallswithMagneticFieldsSunilK.Karna,*MadalynnMarshall,WeiweiXie,LisaDeBeer-Schmitt,DavidP.Young,IlyaVekhter,WilliamA.Shelton,AndrasKovacs,MichalisCharilaou,andJohnF.DiTusá*CiteThis:NanoLett.2021,21,1205−1212ReadOnlineACCESSMetrics&MoreArticleRecommendations*sıSupportingInformationABSTRACT:Thecontrolofdomainwallsiscentraltonearlyallmagnetictechnologies,particularlyforinformationstorageandspintronics.Creativeattemptstoincreasestoragedensityneedtoovercomevolatilityduetothermalfluctuationsofnanoscopicdomainsandheatinglimitations.Topologicaldefects,suchassolitons,skyrmions,andmerons,maybemuchlesssusceptibletofluctuations,owingtotopologicalconstraints,whilealsobeingcontrollablewithlowcurrentdensities.Here,wepresentthefirstevidenceforsoliton/solitonandsoliton/antisolitondomainwallsinthehexagonalchiralmagnetMn1/3NbS2thatrespondasymmetricallytomagneticfieldsandexhibitpair-annihilation.Thisisimportantbecauseitsuggeststhepossibilityofcontrollingtheoccurrenceofsolitonpairsandtheuseofsmallfieldsorsmallcurrentstocontrolnanoscopicmagneticdomains.Specifically,ourdatasuggestthateithersoliton/solitonorsoliton/antisolitonpairscanbestabilizedbytuningthebalancebetweenintrinsicexchangeinteractionsandlong-rangemagnetostaticsinrestrictedgeometries.KEYWORDS:Solitonpairdynamics,Nanoscopicchiraldomainwalls,Dzyaloshinskii−Moriyainteraction,Chiralmagnets,andShapeanisotropy4,18,19Adramaticincreaseininvestigationsofmagnetisminwalls(DW).Howthispicturechangeswithvariationsinmaterialshavingachiralcrystalstructurefollowedthethephysicalparametersthatcontrolthesizeandcharacterofdiscoveryofregulararraysofskyrmions,whirlsofthelocal20DWhasyettobefullyexplored.magnetizationallwiththesamechirality(handedness)Oneroutetowardproducinghexagonalchiralmagnetshas1−7Downloadedvia42.153.129.17onMay14,2021at10:01:16(UTC).arrangedinalattice,inMnSi.Thesesuggestedanewbeentointercalatetransitionmetalelementsbetweentheroutetowardovercomingdomainwallvolatility,therandomhexagonallayersofvanderWaalscompounds.4,12−23Here,weswitchingofsmallmagneticdomainsduetothermalintercalatethe3dtransitionmetalMnintoNbS2(Figure1a),8−15fluctuations,whichmaybeenhancedinlow-dimensionalformingamagnetwithacrystalstructurethatlacksbothstructureswithmagneticanisotropyandwheretheinterplayofinversionandmirrorsymmetries.ThemagneticpropertiesareSeehttps://pubs.acs.org/sharingguidelinesforoptionsonhowtolegitimatelysharepublishedarticles.topologyandthermalnucleationhaslongbeenrealized.16exploredthroughmagnetometry,small-angleneutronscatter-FurtherexplorationofMnSimadeclearthattheunderlyinging(SANS),andFresnelimaginginLorentztransmissioncrystalsymmetryplaysadominantroleindeterminingtheelectronmicroscopy(LTEM).Wecomparethesedatawithmagneticstatesthatemergeinthisandsimilarcubiccrystals1,3,7predictionsofmodelsandmicromagneticsimulationsthatwiththeB20symmetry.ThesmallcrystallineanisotropycorroboratethediscoveryofalinearsolitonlatticeandtheandcubicsymmetryoftheB20’sareessentialtotheformationobservationofsoliton−antisolitonannihilationbyanexternalofhelicaldomainsinthegroundstate,aswellastheconical5magneticfield,confirmingtheoreticalpredictions.Here,aandskyrmionlatticestatesthatappearwithsmallrotational-solitonwithopposite-handedmodulationisreferredtoasansymmetry-breakingmagneticfields.Incontrast,thereducedantisolitontodistinguishfromthehomochiralcase.symmetryandrelatedcrystallineanisotropyfoundinhexagonalchiralmagnetsresultinaverydifferentsetofmagneticstates.7,17Here,thehelicalpitchinthemagneticallyorderedReceived:August6,2020stateisconfinedtothecrystallographicc-axisevenwhenRevised:January17,2021exposedtoamagneticfield,H.Thus,forHlyingperpendicularPublished:January25,2021tothec-axis,skyrmionlatticesarenotfound.Instead,experimentsindicateadistortedhelicalstructureallowingthepossibilityoftheformationofchiralmagneticsolitondomain©2021TheAuthors.PublishedbyAmericanChemicalSocietyhttps://dx.doi.org/10.1021/acs.nanolett.0c031991205NanoLett.2021,21,1205−1212

1NanoLetterspubs.acs.org/NanoLettLetterFigure1.CrystalstructureandmagneticmicrostructureofMn1/3NbS2.(a)Crystalstructure:theintercalatedMnatomsoccupytheoctahedralinterstitialholes(2csite)betweentrigonalprismaticlayersof2H-NbS2intheidealcase.(b)DefocusedFresnelimagesforan∼230nmthickregionofsample1recordedat12K.Aseriesofalternatingbrightlines(domainwalls)separatedbygrayregionsthatarenotstrictlyperiodicareobserved.(c)Lineprofileoftheintensityshownin(b)integratedalongthe(12̅0)directionforthewhite-boxedregionshownin(b).(d)Fresnelimageforan∼130nmthickregionofsample1recordedat12K.Aseriesofalternatingbrightanddarklinesperpendiculartothec-axisofthecrystalareobservedthatlackastrictperiodicity.(e)Lineprofileoftheintensityshownin(d)integratedalongthe(12̅0)directionforthewhite-boxedregionshownin(b).(f−k)Fresnelimagesofsample2ofthickness∼160nminzeroandappliedmagneticfields(identifiedinthefigure)recordedat14K.Arrowsindicatethepositionofalternatingbright(whitearrows)anddark(blackarrows)linesofcontrast.Schematicsofthemagneticstructureatthetopofpanels(b,f)aresuggestedbyourmicromagneticsimulations.WhileourpreviousinvestigationsofMn1/3NbS2revealedmomentslyingintheplanenormaltotheelectronbeam(i.e.,momentslyingalongtheNbS2planesforminganearlythelamellaplane),thecontrastpatterninFigure1bimpliesa21,2324ferromagneticstatebelowTc=45K,Fresneldefocusedrotationofthemagnetizationwithinthehexagonalab-planeofimagestakenonthinlamella(Figure1)displayferromagneticthecrystalashighlightedbythesharpbrightstripes.Thisdomainsofhundredsofnanometersinsizewithchiral(Bloch)imageisconsistentwithadistortedhelicalmagneticstructureDW.TheDWpropagatealongthecrystallographicc-axiswithwheremagneticmomentstendtolieintheplaneofthelamellaarotationintheNbS2plane(Figure1b,c).TheseFresnelmodifyingthiseasy-planesystemtowardaneffectiveeasy-axismicrographsofMn1/3NbS2differsignificantlyfromwhatwasone.TheappearanceofalternatingdarkandbrightstripesinfoundinisostructuralCr1/3NbS2whereasimplehelimagneticthethinnersamples(Figure1d,f)separatedbylargerregionsofstatewithequallyspacedbrightanddarkstripeswasobservedslowlyvaryingornearlyconstantcontrastissubstantially4inLTEMforathinlamella.Furthermore,Figure1b,d,fdifferentfromthatseeninthethickersample(Figure1b)orin4demonstratesadramaticchangewithareductionoftheCr1/3NbS2requiringadifferentinterpretation.thickness,t,ofthelamella.Fortherelativelythickspecimens,tPerhapsmoreintriguingistheresponseofthecontrast=230nm(Figure1b,c),anearlyperiodicsequenceofbrightpatterntosmallHorientedparalleltotheelectronbeam,linesinterspacedbetweendarkerregionsatdistancesof∼250Figure1g−k(andatseveralotherfieldsinFiguresS1−S3)).nmalongthec-axisappearedwhenimagesweretakenat12K.Forfieldsofonesign(definedpositivehere),darkstripesareThesemicrographschangesignificantlyforthinnerlamella,t∼seentotranslaterightwardandbrightstripesleftwarduntil130nmFigure1dandt∼160nmFigure1f,wherealternatingtheyapproacheachotherabove30mTformingdark/brightbrightanddarkstripesareseparatedbygrayregionsofroughlypairs.ForlargerH(Figure1i),theybegintoannihilateeach1μmalongthec-axis.Again,strictperiodicityisnotobserved.otherwithvestigesofthepairsapparentattheedgeoftheForthethreesamplesthatwehavemeasured,warmingabovesamplesothatthecontrastpersistsattheupperedge.The25Kcausesalossofcontrast,andsubsequentcoolingresultscontrastlinesthatpersistmergeatadistanceofafewhundredinasimilarpatternofstripes,albeitatadifferentlocationnanometersfromtheedgewherethecontrastislost.withinthefieldofview[seeVideoS1inSupportingSignificanthysteresisisapparentasHdecreases(FigureS1j)Information(SI)].Thissuggestsamagneticoriginfortheuntilthedirectionswitches(negativeH),causingthecontrast,aconclusionstrengthenedbythesensitivityofthereappearanceofalternatingdarkandbrightstripes.ThesecontrastpatterntosmallfieldasdemonstratedinFigure1g−k.stripesmoveinanoppositedirectionastheHisincreasedinKeepinginmindthatLTEMisonlysensitivetomagneticthenegativesense,formingtightbright/darkpairs(FigureS1k1206https://dx.doi.org/10.1021/acs.nanolett.0c03199NanoLett.2021,21,1205−1212

2NanoLetterspubs.acs.org/NanoLettLetterFigure2.Linearsolitonlattice.Snapshotsfromthemicromagneticsimulationsshowing(a)acontourplotofthea-componentofthemagnetizationatzeroexternalfieldforathicksampleexhibitingalinearsolitonlatticeintheformofrepeatingdomain-wallpairs.(b)Schematicdemonstratingthegeneralizedparametrizationofthemagnetizationvectorforthecontourshownin(a).Here,eachdomainwallinthepairhasoppositepolarity,buttheyallhavethesamehandedness,whichisdeterminedbythesignoftheDMI.(c)Contourplotofthea-componentofthemagnetizationforathicksampleinafield,H=0.1T,exhibitingamagneticsolitonlatticestate.(d)Schematichighlightinga2πright-handedchiraldomainwall.Ifthesampleisthinner,however,magnetostaticinteractionsplayadominantroleanddomain-wallpairswiththesamepolarityandopposinghandednessoccur,asshownin(e).(f)Withtheapplicationofamagneticfield,athinsamplelacksmuchofthetopologicalprotectionenjoyedbythethickersampleduetotheproximityofchiraldomainwallsofoppositehandedness.Generalizedparametrizationofthemagnetizationvectorfora(g)right-handed(region1)and(h)left-handed(region2)π-domainwall.(i)Schematicdemonstrationofapairofhomochiraldomainwallpairs(region3).andFigureS2).Thisunusualasymmetryinthemotionofmakeanalyticprogress,wereplacethedemagnetizationtermchiralDWisnotyetunderstood.However,itislikelyawiththeeffectivein-planeanisotropy,K̃,thatincreaseswithconsequenceoftheDzyaloshinskii−Moriyainteraction(DMI)decreasingthicknessofthesampleandfavorsspinsintheplaneonDWandinteractionsbetweenthemsimilartothatobservedofthelamellae,thatis,withthetermK̃sin2ϕ.Thisapproachinferromagneticfilmswithperpendicularmagneticaniso-neglectsedgeeffectsthatarecapturedbythefullsimulations25tropy.Alternatively,itmaybeaconsequenceofthevariationbutisadequateforclassifyingthephasesofthemodel.ofsamplethicknessalongthelamella.Undertheseassumptions,forfieldintheeasyplanebutInsightintotheseresultsaremadebyconsideringamodelnormaltothelamellae,thephaseϕ(z)satisfiesthedoublewherethetotalenergydensitycontainscontributionsfromthesine-Gordon(dSG)equation,2Aϕzz−K̃sin2ϕ+Hcosϕ=0.exchangestiffness,A,easy-planeanisotropyK,DMI,D,TheenergyofthesolutionsismodifiedbytheDMI,whichcouplingtotheexternalmagneticfield,H,andthedipole−distinguishesthisproblemfromotherphysicalcontextswhere26,27dipoleinteractionsviaalocaldemagnetizingfieldHdmthedSGappears.ForK̃=H=0,werecoverthewell-knownhelicalstate,ϕ(z)=q0zwithq0∼D/2A.Amuch22I=∇+AK()()mmmc+·∇D(×−m)μ0MsH·mlongerpitchofthehelixinMn1/3NbS2comparedtoCr1/3NbS221281(∼250nmversus48nm)indicatesasmallerDMIstrength−·μ0MsdHmm.(1)andthereforegreaterroleofthedipolar-drivenanisotropy.For2K̃≠0,H=0,thespinsprefertobeintheplaneofthelamellae,Here,m=M/MsisthemagnetizationunitvectorwithMsasϕ=0,π,andthesetwoclassicalconfigurationsareconnectedthesaturationmagnetization.WeusethismodelbothtobyBlochDW,whicharethesolutionsofthesine-Gordonperformthefullmicromagneticsimulations(seeMethods)andequationsforthephaseϕ(z).TheDMIinteractionlowerstounderstandthemainfeaturesoftheexperimentallyobserved(raises)theenergyoftheseDWtobeEAsK±∼2K̃±Dstructureusingasimplifiedcontinuumdescription.Inthelatterdependingonthechirality(windingnumber,approach,wetakeKtobelargeenoughsothatthespinsare1+∞w==∫ϕd1z±).Therefore,foranisotropies0

3NanoLetterspubs.acs.org/NanoLettLetterFigure3.Magneticproperties.(a)ProposedmagneticphasediagramofMn1/3NbS2asafunctionoftemperature,T,andmagneticfield,H,appliedperpendiculartothecrystallographicc-axis.PhaseIisahelicalmagneticphaselackingstrictperiodicity,phaseIIisanearlyferromagneticphasethatisnotfullycharacterized,whereasphasesIIIandIII′arenearlyfullypolarizedmagneticphases,andtheregionabove45K(labeledPM)isparamagnetic.Theregionnearthecriticaltemperature,Tc=45K,ischaracterizedbyapeakintheTdependenceoftherealpartoftheacsusceptibility,χ′(T),atfiniteH(panelc)andFigureS5b(denotedasT1)andplottedinthephasediagramassolidbluestars.AtlowerT,weobservetwodistinctmaximaintheimaginarypartoftheacsusceptibility,χ″(T)(paneldandFigureS5d)thataredesignatedinpanelaasopenredtriangles(T2)andopengreensquares(T3).T2andT3arewellcorrelatedwithfeaturesintheHdependenceoftherealpartofχ′(paneleandFigureS5a),whereH1(solidgreensquaresin(a))denotesthelowfieldminimumandH2(solidredtrianglesin(a))denotesthemaximumatslightlyhigherH.SolidpinkcirclesindicateH3,themaximainχ″(H)(panelf)andFigureS5a),whichappeartotrackT2andH2atslightlyhigherH.H3alsotracksthesaturationfieldinthemagnetization,M(H),(panelbanddesignatedbypurplediamondsinpanela)butatasomewhatsmallerH.Atlowertemperatures,thereisahysteresisobservedinM(H)(panelb)witharangeindicatedbythedottedlinesinpanela.Theuppertemperaturelimitofthehystereticregioncorrelateswelloverarangeofthephasediagramwiththemaximuminthederivativeofχ″(T)withrespecttoT(dχ″/dT)(panelfandtheinsettoFigureS5c),whichisindictedinpanelaassolidbluepentagons(T4).Insettopanelf:Tdependenceofthemagnitudeofthemaximuminχ″(H)shownin(f).Blochπ-DW.ThisagreeswiththeresultsofsimulationsSmall(large)kinkshavephasevaryingintheregions(ϕ0,π−presentedinFigure2a,bandlikelycorrespondstotheLTEM31ϕ0)and(−π−ϕ0,ϕ0)respectively.SimilarphenomenadatainFigure1b,c.Theoriginofthisstateissimilartothat(withoutDMI)havebeenpredictedandanalyzedintheB-appearingforK̃=0underafinitefield,wheretheenergyof2πphaseof3He.32,33Abovethecriticalfield,spinsarepolarized,solitons(versusπDW)isEAsh±∼±2HD,sothatachiralsmallkinksvanish,andtheenergyofthelargekinks229continuouslytransformsintothatofthe2πsolitonknownsolitonlatticeisstabilizedforH≤Hc∼D/2A.Thislattice30hasbeenobservedinCr1/3NbS2.fromK̃=0.ThisisconfirmedbythesimulationsforathickForhigheranisotropy(thinnersamples),theDWareeithersample,Figure2c,d,(aswellasVideoS2)showingthechiralthermallygeneratedorpinnedbytheboundaries,andthepatternsimilartothatobservedinref4.DMI-induceddifferenceintheenergiesofDWofdifferentSmallkinkshavespinsnearlyalignedwiththefield,hencewindingissmallcomparedtothedomain-wallenergy.Then,theyhavelowerenergyandhigherdensityatmoderatefields,thefieldatthelateraledgesofthelamellaisessential,andtheasisclearfromsimulations(Figure2f:):thelightredregionsdescriptionofdipolarinteractionsasleadingtoaneffective(momentstiltedtowardthefield)aremostlyseparatedbyuniaxialanisotropyisinsufficient.Insimulations,atH=0webrightredregions(momentsalongthefield).Importantly,findwideregionsofspinstiltedslightlyawayfromtheplane,becausethedSGequationisnotexactlyintegrable,thesekinksseparatedbytheDWwithspinsnormaltothelamellaintheinteractastheyarenotexacteigenstatesofthesystematanyoppositedirection,seeFigure2e,g,h.Thetotalwinding31,34,35field.StudiesintheabsenceoftheDMIdemonstratednumberisdeterminedbytheboundaryconditions,andfortrappingofkink−antikinkpairsintolong-livedquasi-boundtopologicallytrivialboundariesDWappearmostlyinpairs34,3536statesequivalenttonontopologicalmagneticbions.addinguptow=0.Asequenceofredstripes(magneticExperimentalobservationofpairsofbrightanddarklinesinmomentspointingupateachoftheDW)inFigure2eLTEMpatternsunderamagneticfield,Figure1h,k,suggestsindicatesswitchingchiralitybetweensequentialdomains,seeFigure2g,h,anabsenceofnetwinding,andhencenon-thattheDMIinteractionmayhelpstabilizethesepairs.topologicalnatureofthemagneticorder.ThisshouldbeVanishingofthesignalathigherfields,oncethelinesapproachcontrastedwiththequasiperiodicred/bluepatterninFigure2aeachother,indicatesthattheseareobjectswithoppositecharacteristicofthechiralstate.windingnumbers,sothattheglobalstateisnontopological.WhenthefieldH

4NanoLetterspubs.acs.org/NanoLettLetterFigure4.SANSmeasurementofMn1/3NbS2at(a)3K,(b)17K,and(c)42Kwiththewavevector,Q,paralleltothe(001)reflectionalongthehorizontal.Thesignalat55K(paneld)wasconsideredasbackgroundandsubtractedfromthedatacollectedatlowertemperatures.Datawereobtainedwiththeincidentneutronbeamperpendiculartothec-axis.(e)Variationoftheintegratedintensity,I,obtainedfromtheareadesignatedbythewhitelinesinpanelsa−cversusQattheindicatedtemperatures.TheshadedregioncorrespondstotheQ-rangeexpectedfortheperiodicitiesfoundintheLorentzTEMstudies(seeFigure1).theDMinteraction,notaccountedforinthatanalysis,needstoatthesehigherH,wehesitatetorefertothisregionasfullybefullyelucidatedtheoretically.fieldpolarized.ToplacetheseimagesandcalculationsincontextandtoFurtherinsightintothemagneticstructurewasaccom-betterestablishthemagneticstateofthesystemfromwhichplishedthroughsmall-angleneutronscattering(SANS)thedomainstructuresimagedinFigure1derive,wehavemeasurements(Figure4).Thegeometryofthemeasurementmeasuredthemagneticpropertiesofbulksinglecrystalsaddinghasthecrystallographicc-axisnearlyhorizontalintheplaneofmoreunderstandingtopreviousresults.21,23,38Theseestab-thedetector,whiletheneutronbeamliesalongtheab-plane.lishedamagneticphasetransitiontoanearlyferromagneticForT32K.ThesedatashowninFigure3a,wherewehighlightadistinctchangeinarepresentedingraphicalforminFigure4e,wherethebehaviorbelow∼25K(phaseI).Theresponseofthissystemintensityafterintegrationbetweenazimuthalangles,χaz,lyingtomagneticfieldsasobservedinthemagnetization,M(H),andwithinthewhite,wedged-shapedregionsinFigure4a−cistheacsusceptibility,revealschangesnotcommonlyobservedplottedasafunctionofQandinFigureS7.Thevariationsweobservewithcoolingarelikelyrelatedtotheevolutionoftheinsimplemagnets.Forexample,M(H)withHorientedacsusceptibilitythatmotivatedthephasediagramofFigure3a.perpendiculartothec-axisisdisplayedinFigure3bwhereaThisscatteringstreaksignalsadisorderedmagneticstructurehysteresisisapparentforT<25KonlyfornonzeroH,consistingofeitherferromagneticdomainsoranonsinusoidalillustratedinFigure3abydottedlines.Themaximumhelicalmagneticstructure.Whetherthedisorderisintrinsictotemperaturewherethishysteresisisfound,T∼25K,21correspondswithdistinctchangesintheT-andH-dependentMn1/3NbS2,oraresultofMnsitedefects,orthepossiblepresenceofstackingfaultsalongthec-axisevidentinX-rayacsusceptibilityshowninFigure3c−f.Mostdramaticisthediffractionoflargercrystalsisnotyetknown.However,areductionintheimaginarypartoftheacsusceptibility,χ″,atallsimpledisorderedferromagneticstateisnotlikelysincetheHforT<25K(Figure3d,f).Thus,phaseIischaracterizedbywidthofmagneticscatteringalongthec-axiswouldresemblethehysteresisinHandthesmallχ″,correspondingwellwiththatfoundinthenuclearBraggscattering.ThecrystallographictheTandHregionwherelinesofcontrastwereobservedindisorderapparentinourpreviousneutrondiffractionmeasure-theFresnelimages.Theimplicationisthatthereisadistinct21mentsandoursingleandpowdercrystalX-raycharacter-changeinthemagneticdomainstructureanddynamicsattheizationisnotcompatiblewiththemosaicityrequiredbytheboundaryofphaseIwithphasesIIandIIIsincetherangeofHSANSdataforadisorderedferromagneticstate.Inaddition,spanningthepurportedphaseItypicallycorrespondstohighresolutionelectronmicrographsofourLTEMspecimensmesoscopic-sizedfeatures.Thisconclusionissupportedbythedisplayminimaldisorder,withnoindicationofstackingfaultsvariationofthefrequencydependenceofχ′andχ″asonthescaleoftheimages,andnoindicationofandisplayedinFigureS4.incommensurateorder(FigureS6).Instead,theSANSdataTheotherregionsofthephasediagramarecategorizedbyindicateanonperiodicstripephase,aconclusiondrivenbythetheresponseobservedinχ′andχ″includingforT>Tc,whereFresnelimageswhichdemonstratealackofstrictperiodicityasmallχ′andχ″areconsistentwithaparamagneticstate.Forresultinginasetofhelicalpitchlengthscorrespondingtothetemperaturesbetween24and45KandH<40mT(phaseIIshadedregioninFigure4e.ThisissupportedbyrecentSANSinFigure3a),theresponseischaracterizedbyahighlyH-measurementsofisostructuralCr1/3NbS2wheresmallsitedependentχ′andalargeχ″thatismaximumnearfieldswhendisorderresultsinhigherorderpeaks.WeconcludethattheM(H)approachessaturation.Finally,forH>40mTthe21Mnsitedisordercontributessignificantlytothewidthofsystemisnearlysaturated.However,sinceapeakinχ′persists39scatteringinFigure4.atthetransitionbetweenphaseIIIandthePMstate(T1)atHTheimportanceoftheDMIinthissystemismadeclearbywellabovetheapparentsaturation,andχ″continuestoevolvethepresenceofspintexturesthatarebothnonperiodicand1209https://dx.doi.org/10.1021/acs.nanolett.0c03199NanoLett.2021,21,1205−1212

5NanoLetterspubs.acs.org/NanoLettLetterthicknessdependent.Interestingly,magneticcontrastinHAADFSTEMimagesofMn1/3NbS2;wavevectorandFresnelimagesonlyappearsatT<25K

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