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

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)