Interface Spin-Orbit Coupling in a Non-centrosymmetric Thin-(4)

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).