Interface Spin-Orbit Coupling in a Non-centrosymmetric Thin-(2)

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.