Interface Spin-Orbit Coupling in a Non-centrosymmetric Thin-Film Superconductor

We present a detailed study of the effects of interface spin-orbit coupling (ISOC) on the critical field behavior of non-centrosymmetric (NCS), ultra-thin superconducting Be/Au bilayers. Parallel field measurements were made in bilayers with Be thicknesses

InterfaceSpin-OrbitCouplinginaNon-centrosymmetricThin-FilmSuperconductor

X.S.WuandP.W.Adams

DepartmentofPhysicsandAstronomy

LouisianaStateUniversity

BatonRouge,Louisiana,70803

arXiv:cond-mat/0509385v2 [cond-mat.supr-con] 19 Sep 2005Y.YangandR.L.McCarleyDepartmentofChemistryandtheCenterforBiomodularMulti-scaleSystemsLouisianaStateUniversityBatonRouge,LA,70803(Dated:February2,2008)Wepresentadetailedstudyofthee ectsofinterfacespin-orbitcoupling(ISOC)onthecritical eldbehaviorofnon-centrosymmetric(NCS),ultra-thinsuperconductingBe/Aubilayers.Parallel eldmeasurementsweremadeinbilayerswithBethicknessesintherangeofd=2 30nmandAucoveragesof0.5nm.ThoughtheAuhadnosigni cante ectonthesuperconductinggap,itproducedprofoundchangesinthespinstatesofthesystem.Inparticular,theparallelcritical eldexceededtheClogstonlimitbyanorderofmagnitudeinthethinnest lmsstudied.Inaddition,theparallelcritical eldunexpectedlyscaledasHc||/ o∝1/dsuggestingthatthespin-orbitcouplingenergywasproportionalto o/d2.Tilted eldmeasurementsshowedthatcontrarytorecenttheory,theISOCinducesalargein-planesuperconductingsusceptibilitybutonlyaverysmalltransversesusceptibility.PACSnumbers:74.20.Rp,74.78.Db,73.40.JnOneofthemostfundamentalcharacteristicsofasuperconductoristhesymmetryofitscondensatewavefunction.Indeed,thishasproventobeacentralissueinthedescriptionofanumberofnon-conventionalsuperconductorssuchashigh-TcsystemsandtheruthenatesInconventionalBCSsuperconductivitythecondensateistimereversalinvariantandisformedfromCooperpairsconsistingofelectronsofoppositemomentumandoppositespinInnon-conventionalsuperconductors,however,thissimplesymmetrycanbemodi edbytheunderlyingcrystalstructureand/orthesymmetryofthepairinginteraction.AcompellingexampleoftheformeristherecentlydiscoveredheavyfermionsuperconductorCePt3Si,whosecrystalstructurelacksinversionsymmetryCePt3Siexhibitsalinenodegapstructure7,whichisbelievedtobe,inpart,aconsequenceofstrongspin-orbit(SO)couplinginanon-centrosymmetric(NCS)crystalsymmetry9,10].Thishasstimulatedrenewedinterestinthepossibilityofrealizingnon-conventionalpairingstatesfromtheconvolutionofbrokeninversionsymmetryandspinorbitcoupling,neitherofwhichviolatetimereversalinvariance.Recenttheoreticalworkontheproblemhassuggestedthatabilayercon guration,which,byde nition,lacksinversionsymmetry,consistingofalowatomicmassthin- lmsuperconductorcoatedwithahighatomicmassnon-superconductingelementsuchasAuorPtwouldbeamodelsystemforstudyingthee ectsofSOcouplinginaNCSsuperconductorInthepresentLetter,wepresentastudyofinterfaceSOcouplinginthinBe lmscoatedwith0.5nmofAuviacriticalmagnetic eldmeasurements.Contrarytorecenttheoreticalpredictions,we ndthattheSOinducedin-planesuperconductingspinsusceptibilityissigni cantlylargerthanthecorrespondingperpendicularsusceptibility.Furthermore,theSOcouplingcannotbedescribedintermsofAbrikosov-Gorkovimpurityformalism[4]inthatitappearstobeafunctionofthesuperconductinggap.Intheexperimentsdescribedbelowweusecritical eldmeasurementstodeterminetheSOcouplingstrengthinBe/Au lmsofvaryingBethickness.TheMakiequation15]isausefultoolforextractingthespinresponseofthesuperconductorfromtheorbitalresponse,particularlywhenthe lmisnotinthethin- lmlimitand/orthe eldisnotparalleltothe lmsurface.Ingeneralthecritical eldofathin lmisafunctionofthesuperconductinggap

o,the lmthicknessd,theelectrondi usivityD,andthespinorbitcouplingparameterb.Thecritical eldHcisdeterminedbytheimplicitfunction[15]:

Tα+ +2α 1ln (1)+ψ222γ4πkBT

where

21/2α±=b±γ,γ=(b2 µ2,BHc)

We present a detailed study of the effects of interface spin-orbit coupling (ISOC) on the critical field behavior of non-centrosymmetric (NCS), ultra-thin superconducting Be/Au bilayers. Parallel field measurements were made in bilayers with Be thicknesses

Tcisthecriticaltemperature,andψisthedigammafunction. isafunctionoftheanglebetweentheplaneofthe lmandthemagnetic eld,

(θ)=D[2eHcsin(θ)+1

o≈√

3b/ ob/ o

≥1,(3)whereEq.(2)isthefamiliarClogstonspin-paramagneticcritical eld[16,17,18].NotethatfromEq.(3)thecritical eldcanbearbitrarilyhighwithincreasingb.Incontrast,iftheZeemancouplingisneglectedthen,atany nitethicknessd<ξ,theparallelcritical eldislimitedbytheorbitalterm,

2µBHc||3 3

d(4)

Numerousstudiesofthespin-paramagnetictransitioninultra-thinAlandBe lmshaveshownthatthesetwolightelementshaveaverylowintrinsicSOscatteringrate[19,20,21]andaretruespin-singletsuperconductors.Consequently,theymakeidealcandidatesforsystematicstudiesofthee ectsofISOCinducedbyimpuritycoatings

[11,22].Notonlydoesthisbilayercon gurationbreakinversionsymmetry,butonecantreattheISOCasaboundaryconditiononthespincomponentofthesuperconductingwavefunction.Earlymeasurementsofthecritical eldbehaviorofAl lmscoatedwithlessthan0.2nmofPtrevealedthatthePt-inducedISOCcanproducesigni cantenhancementsoftheparallelcritical eldwithvirtuallynoe ectonthetransitiontemperature[19].ThoughthetemperatureandangulardependenciesoftheAl/Ptcritical eldswereinreasonableagreementwiththeMakiformula,theoverallmagnitudeofHc||wastypically～10 30%higherthancouldbeaccountedforbyreasonableestimatesofb.

Recentanalysisofthespinstatesoftwo-dimensionalNCSsuperconductors,and,inparticular,superconducting-normalmetalbilayers,predictsthatISOCwillintroduceananisotropicspintripletcomponentintosuperconductinggroundstate[12,13].Thetripletcomponentismostdirectlymanifestinthespinsusceptibilityofthesuperconductorχs.Ofcourse,conventionalspin-singletBSCsuperconductorshaveχs～0atT=0,butISOCisexpectedtoliftnsnsthespindegeneracy,andinthestrongcouplingl:χs ～χ/2,χ⊥～χ,whereχ isthein-planesuperconductingsusceptibilityandχnisthenormalstatesusceptibility.TheClogstoncritical eldgivenbyEq.(2)isderivedbyequatingthemagneticfreeenergydi erencebetweennormalandsuperconductingstateswiththecondensationenergyofthesuperconductingstate.Ifχs=0thenEq.(2)canbegeneralized,√2µBHc=1 χs/χn.(5)Thiswouldimplythattheparallelcritical eldofabilayer,suchastheAl/PtsamplesofRef.19,wouldneverbelargerthanHc||= o/µB.However,thecritical eldenhancementsobservedinthoseearlyexperimentsweresigni cantlygreaterthanthisupperlimit.Sincethelate1970’sverylittleworkhasbeendoneonSOcouplinginthin lmsuperconductors,thoughseveralfundamentalquestionsremainunanswered.Forinstance,theAl/PtmeasurementsweremadeatasingleAlthicknessandoveraverynarrowrangeofgapvalues.Clearly,onewouldliketodeterminethedepthtowhichtheISOCpenetratesintothesuperconducting lmandhowthespincomponentofcritical eldbehaviorscaleswith lmthicknessandgapmagnitude.Anotherimportantissueiswhetherornottheanisotropyinχsisobservableintheangulardependenceofthecritical eld.

Be/Aubilayer lmsofvaryingBethicknesswerepreparedbye-beamevaporationinainitialvacuumof～0.2µTorr.Allofthedepositionsweremadeon repolishedglasssubstratesheldat84K.FirstalayerofBe lmwiththicknessintherange2. 30.0nmwasdepositedatarateof0.14nm/s,thena0.5nmAu lmwasdepositedat0.01nm/swithoutbreakingthevacuum.BoththeBeandBe/Au lmswerefoundtobeverysmoothandhomogenous,withnoevidenceofislandingorgranularity,seeFig.1.The lmsweresubsequentlytrimmedinordertoeliminateedgee ects.Resistivemeasurementsweremadeinadilutionrefrigeratorwithabasetemperature50mKbyastandardfour-probelock-inmethod.The lmswerealignedwiththemagnetic eldviaaninsitumechanicalrotator.Inthedatapresentedbelowthetransitiontemperatureswerede nedbythetemperatureatwhichtheresistancefellto10%ofitsnormalstatevalueandthecritical eldwasdeterminedbythemidpointoftheresistivetransition.

We present a detailed study of the effects of interface spin-orbit coupling (ISOC) on the critical field behavior of non-centrosymmetric (NCS), ultra-thin superconducting Be/Au bilayers. Parallel field measurements were made in bilayers with Be thicknesses

ThetransitiontemperatureofthehomogeneouslydisorderedBe/Au lmsusedinthisstudyareplottedasafunctionofBethicknessinFig.2.Filmswithd<2nmareknowntodisplayanon-perturbativezerobiasanomalyintheirtunnelingdensityofstates,whichisassociatedwiththeemergenceoftheCoulombgap[23].AscanbeseeninFig.2,thisisalsothecriticalthicknessbelowwhichthezerotemperaturesuperconductingphaseislostandtheelectrondi usivitygoestozero.InordertomakeuseofEq.(1)itwasnecessaryto tthethicknessdependenceofTcandDwithanempiricalfunctionalform.Inparticular,thesolidlinesinthemainpanelandtheinsetofFig.2arethefunctions:

Tc(d)=Tcotanh[(d 1.35)/1.29)]

D(d)=Dotanh[d2/23.3],(6)(7)

whereTco=0.68KandDo～3 /m.Dowasdeterminedfrom lmswithd>10nmusingtherelation1/R=2e2ν0Dod,whereRisthesheetresistanceandν0isthedensityofstatesperspinofBe.TheBCScoherencelengthforaBe lmwithTc～0.7Kisξo～4µm.Fortherangeofdi usivitiesplottedintheinsetofFig.√2themeanfreepathisalwayslo<1nmandthecorrespondingPippardcoherencelengthsareintherangeξ=0.85

We present a detailed study of the effects of interface spin-orbit coupling (ISOC) on the critical field behavior of non-centrosymmetric (NCS), ultra-thin superconducting Be/Au bilayers. Parallel field measurements were made in bilayers with Be thicknesses

critical eldsofthetwo lms.Thisre ectsthefactthatitisalmostindistinguishablefromwhatonewouldobtainusingthephenomenologicalTinkhamformula[4,15]whichonlyinvolvesHc||andHc2.Incontrast,thedashedlinedepictsthesolutiontoEq.(1)assuminganexponentiallyattenuatedSOparameterb=1.85exp( θ/θo)mV,withacharacteristicangleθo=2.5 .ThedashedlinecapturesthedipstructureinthedatawhichindicatesthattheZeemancomponentofthecritical eldisangledependent.Thedipstructureisconsistentwithananisotropicsuperconductingsusceptibilityconsistingofalargein-planecomponent(oftheorderofthenormalstatesusceptibility)andasmalltransversecomponent.Thesenseofthisanisotropyisoftheoppositesignofthatcalculatedfornon-disordered2DNCSsuperconductors,wherethein-planecomponentisexpectedtobehalfthatofthetransversecomponent.Nevertheless,thefactthatISOCinducesapreferentiallylargein-planesusceptibilitywouldalsoaccountforearlierreportsofanomalouslyhighparallelcritical eldsinAl/Ptbilayers[19].

Insummary,wehaveusedcritical eldmeasurementstoprobethee ectsofinterfacespin-orbitcouplingonthespinstatesofsuperconductingBe lms.We ndthata～1monolayercoatingofAuontheBesurfaceproducesalarge,anisotropicenhancementtotheZeemancomponentofthecritical eld.Thenormalizedparallelcritical eldHc||/ oofBe/AubilayersscalesastheinverseoftheBethicknessandcanexceedtheClogstonlimitbyasmuchasanorderofmagnitude.Thecritical eldscalingwasobservedoverawiderangeof owhichisinconsistentwiththestandardimpurityscatteringmodelofSOcoupling.Webelievethatthescalingis,infact,amanifestationofthesuperconductor’sattempttoreconcileamixed-spinboundaryconditionattheAuinterfacewiththeintrinsicspin-singletgroundstateofBe.Naively,onewouldexpectthattheISOChealinglengthwouldbeoftheorderofξ,butitmaybesigni cantlyshorterinthepresenceofdisorder.Nevertheless,theanisotropicspinsusceptibilityisclearlyevidentinthetilted elddata.Ahigh eldstudyofthelocaltunnelingdensityofstatesattheBe/AuandtheBe/substrateinterfaces,respectively,shouldprovideanimportantlocalprobeoftheextentofspin-mixingatthetwoboundaries.

WegratefullyacknowledgeenlighteningdiscussionswithVictorEdelstein,GianluigiCatelani,IlyaVekhter,DanaBrowne,andDavidYoung.ThisworkwassupportedbytheNationalScienceFoundationunderGrantDMR02-04871.

[1]

[2]

[3]

[4]

[5]

[6]

[7]

[8]

[9]

[10]

[11]

[12]

[13]

[14]

[15]

[16]

[17]

[18]

[19]

[20]

[21]

[22]

[23]

[24]

[25]C.C.TsueiandJ.R.Kirtley,Rev.Mod.Phys.72,969(2000).A.P.MackenzieandY.Maeno,Rev.Mod.Phys.75,657(2003).K.D.Nelson,Z.Q.Mao,Y.Maeno,andY.Liu,Science306,1151(2004).M.Tinkham,IntroductiontoSuperconductivity(McGraw-Hill,NewYork,1996).E.Bauer,G.Hilscher,H.Michor,C.Paul,E.W.Scheidt,A.Gribanov,Y.Seropegin,H.Noel,M.Sigrist,andP.Rogl,Phys.Rev.Lett.92,027003(2004).K.Izawa,Y.Kasahara,K.Matsuda,Y.andBehnia,T.Yasuda,R.Settai,andY.Onuki,Phys.Rev.Lett.94,197002(2005).I.Bonalde,W.Bramer-Escamilla,andE.Bauer,Phys.Rev.Lett.94,207002(2005).D.P.Young,M.Moldovan,X.S.Wu,P.W.Adams,andJ.Y.Chan,Phys.Rev.Lett.94,107001(2005).P.A.Frigeri,D.F.Agterberg,A.Koga,andM.Sigrist,Phys.Rev.Lett.92,097001(2004).K.Samokhin,E.Zijlstra,andS.Bose,Phys.Rev.B69,094514(2004).V.M.Edelstein,Phys.Rev.B67,020505(2003).L.P.Gor’kovandE.I.Rashba,Phys.Rev.Lett.8703,037004(2001).S.K.Yip,Phys.Rev.B65,144508(2002).K.Maki,Phys.Rev.148,362(1966).K.Aoi,R.Meservey,andP.M.Tedrow,Phys.Rev.B9,875(1974).A.M.Clogston,Phys.Rev.Lett.9,266(1962).B.S.Chandrasekhar,Appl.Phys.Lett.1,7(1962).Theb=0solutionoftheMakiequationactuallyrepresentsthesupercoolingcritical eldofanintrinsicallyhysteretic rst-orderphasetransition.P.M.TedrowandR.Meservey,Phys.Rev.Lett.43,384(1979).P.W.Adams,Phys.Rev.Lett.92,067003(2004).P.W.Adams,P.Herron,andE.I.Meletis,Phys.Rev.B58,R2952(1998).P.M.TedrowandR.Meservey,Phys.Rev.B25,171(1982).V.Y.Butko,J.F.DiTusa,andP.W.Adams,Phys.Rev.Lett.84,1543(2000).G.BergmannandC.Horriaresser,Phys.Rev.B31,1161(1985).G.Bergmann,Phys.Rev.B6319,193101(2001).

We present a detailed study of the effects of interface spin-orbit coupling (ISOC) on the critical field behavior of non-centrosymmetric (NCS), ultra-thin superconducting Be/Au bilayers. Parallel field measurements were made in bilayers with Be thicknesses

Figures

FIG.1:A)0.1x0.1µmatomicforcemicrographofa6nmthickBe lmevaporatedontoglassat84K.B)MicrographofaBe lmcoatedwith0.5nmofAu.

We present a detailed study of the effects of interface spin-orbit coupling (ISOC) on the critical field behavior of non-centrosymmetric (NCS), ultra-thin superconducting Be/Au bilayers. Parallel field measurements were made in bilayers with Be thicknesses

FIG.2:TransitiontemperatureofBe/AubilayersasafunctionofBethickness.TheAuthicknesswas0.5nmineachsample.Thesolidlineisabest ttothedatausingtheempiricalformofEq.(6).Inset:relativedi usivityofBe/AubilayersasafunctionofBethickness.Thesolidlineisa ttoEq.(7).

We present a detailed study of the effects of interface spin-orbit coupling (ISOC) on the critical field behavior of non-centrosymmetric (NCS), ultra-thin superconducting Be/Au bilayers. Parallel field measurements were made in bilayers with Be thicknesses

FIG.3:Normalizedparallelcritical eldsasafunctionofBethicknessforBe/Aubilayers(circles),Be/Pb(crossedbox),pureBe lms(triangles).Thelongdashedlinerepresentsthetheoreticalorbitallylimitedcritical eldgivenbyEq.(4).Thesolidlineisalinearleast ttothebilayerdata.ThehorizontaldashedlinerepresentstheClogstoncritical eld.

We present a detailed study of the effects of interface spin-orbit coupling (ISOC) on the critical field behavior of non-centrosymmetric (NCS), ultra-thin superconducting Be/Au bilayers. Parallel field measurements were made in bilayers with Be thicknesses

FIG.4:Ratioofthecritical eldofBe/AubilayersandBe lmsofequalBethicknessasafunctionoftiltangle,θ=0correspondstoparallel eld.triangles:d=7.4nm,circles:d=5.4nm,diamonds:d=2.9nm.Thesolidlinesareaguidetotheeye.

We present a detailed study of the effects of interface spin-orbit coupling (ISOC) on the critical field behavior of non-centrosymmetric (NCS), ultra-thin superconducting Be/Au bilayers. Parallel field measurements were made in bilayers with Be thicknesses

FIG.5:Ratioofthecritical eldofa5.4nmBe/Aubilayer(Tc=0.68K,Hc2=0.137T,R=240 )and5.4nmBe lm(Tc=0.505K,Hc2=0.048T,R=162 )asafunctionoftiltangle.SolidlineisthesolutionofEq.(1)assuminganisotropicSOcouplingparameterofb=1.85mVfortheBe/Aubilayerandb=0.0132mVfortheBe lm.ThedashedlineisthesolutionofEq.(1)assumingthattheBe/AuSOparameterisexponentiallyattenuatedwithincreasingtiltangle.Leftinset:FitofEq.(1)totheBe lmdata.Rightinset:Solidlineisa tofEq.(1)totheBe/Audatawithaconstantb.Thedashedlineisasomewhatbetter tusinganexponentiallyformb=boexp( θ/θo).

本文来源：https://www.bwwdw.com/article/b414.html