M Froehlich b S Tanaka c K Kouznetsov and John Clarke Department of Physics University of California Berkeley California 94720 and Materials Sciences Division Lawrence Berkeley National Laboratory Berkeley California 94720 Z Lu V Matijasevic and K C ID: 24661
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Currentaddress:TRWElectronicsSystemsandTechnologyDivision,OneSpacePark,RedondoBeach,CA90278.Currentaddress:DepartmentofEcologicalEngineering,ToyohashiUni-versityofTechnology,Tempaku-cho,Toyohashi441,Japan. FIG.1.Schematicofthegradiometer,consistingofanasymmetric¯uxtransformercoupledtoadirectlycoupledmagnetometer;andtionofthe¯uxtransformerinductivelycoupledtothemagnetometershadedsquare1712Appl.Phys.Lett.(12),22September19970003-6951/97/71(12)/1712/3/$10.001997AmericanInstituteofPhysics tothemagnetometerloopandinputlooponly.Thecurrentinducedinthepickuploopofthemagnetometeris,whererepresentsthescreeningeffectofthe¯uxtransformer.Asweshallsee,withappropriatedesignisonlyslightlylessthanunitysothatthesensitivityofthemagnetometeritselfisnotsigni®cantlyreducedbythepresenceofthe¯uxtransformer.Totestthisconcept,wefabricatedagradiometerinthecon®gurationofFig.1.Thesingle-layer,directlycoupledmagnetometerwaspatternedbyphotolithographyandArionmillingina150nmthick®lmofYBCOlaserdepositedona10mmbicrystal.Theouterandinnerdimen-sionsofthemagnetometerloopare10and2mm,respec-tively,yieldinganestimatedinductanceof4nHandanestimatedareaof20mmWeestimatetheSQUIDinductancetobe50pH,includingcontributionsfromthetwomwidejunctions.Thecriticalcurrentandresistanceperjunctionare200Aand1.2,respectively.The¯uxtrans-formerwasfabricatedfroma260nmthickYBCO®lmco-evaporatedatConductusona100mm-planesapphirewa-fer,bufferedwithCeO,andpatternedbyphotolithographyandetchingina0.05%aqueoussolutionofHNO.Weesti-matetheinductanceandareaoftheinputcoiltobe10nHand36mm,andofthepickuplooptobe5nH,includinga13nHcontributionfromthestrip-line,and411mm.FromEq.,theseestimatedvaluesleadto0.04,andfromEq.0.95;thus,thepresenceofthe¯uxtransformerreducestheintrinsicsen-sitivityofthemagnetometerbyonly5%.Thegradiometerbaseline,givenbytheseparationofthemidpointsoftheinputandpickuploops,isapproximately48mm.Wemountedthemagnetometerand¯uxtransformerfacetoface,separatedbya2.5mthickmylarsheetandaftersomeexperimentationseverallayersof50mthickTe¯ontape.Themagnetometerwasattachedtoa®berglassmountwhilethe¯uxtransformerwasattachedtoadelrinmount,thepositionofwhichwecouldadjustinthetionfromoutsidethecryostatbymeansofascrew.Inthisway,wecouldvaryinsitutoobtainthebalanceconditionofEq.;thepositionofthe¯uxtransformercouldbead-justedtoabout2.5m.Thegradiometerwasimmersedinliquidnitrogenwiththeaxisverticalandthemagnetometeratthelowerend.Therewasnomagneticshielding.TheSQUIDwas¯uxmodulatedat100kHzandoperatedina¯ux-lockedloop.Toassessthebalanceofthegradiometer,weplaceditatthecenterofa1.2mdiamHelmholtzpair,withtheaxisofthecoilsperpendiculartotheplaneofthegradiometer.Weinjecteda100Hzcurrentintothecoilsandaveragedtheoutputfromthe¯ux-lockedloop200±400times,usingaspectrumanalyzer.Theoutputofthemagnetometerata®xed100Hzmag-netic®eldversusthepositionofthe¯uxtransformerisplot-tedinFig.2;at0,thepositionoftheinputloopisentirelyoutsidethecentralholeofthemagnetometerpickuploop,andthecouplingbetweenthemissmall.Asweslidetheinputlooptowardstheopeninginthemagnetometerloop,theoutputfromthe¯ux-lockedloopprogressivelydecreases,dippingsharplynear4.3mm,andthenincreasesagain.Observationsonanoscilloscopeshowthatthephaseoftheoutputsignalrelativetothedriving®eldchangedsignacrosstheminimum.Theminimumrepresentstheoptimumbalancepointofthegradiometer,andcorrespondstoareductionintheresponsetotheappliedmagnetic®eldofapproximately2930.Thisvaluemayormaynotrepresenttheintrinsicbal-ancelimit;itisentirelypossiblethatgradientsintroducedintothe100Hzmagnetic®eldbynearbysteelobjectswerethelimitingfactor.Thebalanceremainsstableat77K,butrequiresreadjustmentafterthegradiometerhasbeenther-mallycycled.Animportantcriterionforausefulgradiometeristhattheresponseto®eldsappliedintheplaneofthegradiometershouldalsobelow.Toevaluatetheresponseinthetion,we®rstrotatedthedewarbyapproximately90Éwiththegradiometerunbalanced(0)tolocatetheprecise,atwhichtheminimumresponsetothe100Hzoccurred.Werestoredthedewartoitsoriginalposition,bal-ancedthegradiometer,andthenrotatedthedewarbackto.Thisprocedureyieldedanaveragerejectioninthedirectionofabout1400.Asbefore,wewereunabletodeter-minewhetherthisresidualresponsewasintrinsictothegra-diometerorameasureofthenonuniformityofthe100HzAsademonstrationofthereductioninambientnoise,inFig.3weshowtheoutputofthemagnetometerfortheun-balanced(0)andoptimallybalancedcases,withthesig-nalfromtheHelmholtzpairswitchedoff.The60Hzpeakisreducedbyafactorof1600.Thisreductionisconsistentwiththebalancewehavebeenabletoachieve,butitispossiblethattheresidualsignalarosefromagradientinthe60Hz®eld.Thepeaksat40and80Hzareofunknownorigin;peaksatlowerfrequenciesareduetomicrophonics.Finally,wemeasuredtheresponseofthebalancedgra-diometertoagradient®eldbypassinga100Hzcurrentthroughalongwireinthedirectionplacedverti-callybelowthegradiometer,paralleltoitsplane.Thesepa-rationofthewirefromthemidpointofthebaselinewaschangedprogressivelyfrom0.5±0.75m,distancessub-stantiallygreaterthanthebaseline.Thegradiometerre-sponseversusdistanceisshownintheinsetinFig.3.Theleast-squares-®ttedslopeonthislog±logplot,0.05,isclosetotheexpectedvalueof2.Wenotethat FIG.2.Amplitudeofthesignalfromthe¯ux-lockedloopforauniform100Hzmagnetic®eldappliedatrightanglestothegradiometervsthepositionoftheinputlooprelativetothemagnetometer.Right-handordinateisthebalancefactor.InsetshowsexpandedAppl.Phys.Lett.,Vol.71,No.12,22September1997Dantskeretal. distortionsintheappliedgradientduetonearbyconductingobjectsand,particularly,aslightresidualresponsetoauni-formmagnetic®eld,willcausedeviationsfromtheidealThisapproachtoplanargradiometershasseveraladvan-tages.The¯uxtransformerinvolvesonlyasinglelayerofYBCO,anditslengthcouldreadilybeextended,to,say,100mm,therebyincreasingitsbaseline.Furthermore,itshouldnotbenecessarytouseparticularlyhighquality®lms:wehaveshownpreviouslythatrelativelyhighlevelsofintrin-noiseduetothemotionof¯uxvorticesina¯uxtransformerwitharelativelylargeareaandinductancedonotcontributesigni®cantlytotheoverallnoise.Thus,itmaybepossibletousesinteredYBCO®lmsoninexpensivepolycrystallinesubstrates.Thefactthattheintrinsicmagnetic-®eldsensitivityofthemagnetometerisreducedbyonlyafewpercentbythepresenceofthetrans-formerisparticularlyappealingforhigh-devices,inwhichresolutionisatapremium.Needlesstosay,onecouldusehigh-magnetometersthataremoresensitivethanthedirectlycoupledmagnetometerusedinthisdemonstration,forexample,amultilayer,multiturn¯uxtransformercoupledtoaSQUID.Theasymmetric¯uxtransformercouldbeusedequallywellwithrfSQUIDs,anditssimplicitymakesitworthyofconsiderationforlow-gradiometers.Thegen-eralprinciplecouldbeextendedtootherderivatives.Forexample,theadditionofasecond,identicalpickuplooptothetransformerontheoppositesideoftheinputloopwouldproduceasecondderivativegradiometermeasuring.Inprinciple,axialgradiometersarealsopossible,forexample,usingYBCOsinteredonatube,butitmaybedif®culttoachieveahighrejectionof®eldsperpendiculartotheaxis.Ourasymmetricgradiometerhasabaselineof48mmandhasachievedameasuredbalanceofabout1partin3000withrespecttomagnetic®eldsperpendiculartoitsplane.Directmeasurementsandtheobservedreductionintheam-bient60Hznoiseindicateanin-planerejectionofbetterthan1partin1000.Thiscombinationofbalanceandrelativelylongbaseline,togetherwiththeminimalreductioninthesensitivityofthemagnetometer,makethishigh-etereminentlysuitableformultichannelarraysforbiomag-neticmeasurements.Onecouldsubtractsignalsamongthegradiometerstoachievehigher-ordergradientsandusemag-netometersmeasuringtoreducethepickupofthein-planenoise.However,insucharrays,itwouldbeimprac-ticabletobalancethegradiometersmechanicallyinthewaywehavedescribed,notleastbecauseoftheneedtorepeattheprocedureafterthermalcycling.Amorepracticableap-proachmightbetocouplethe¯uxtransformerpermanentlytothemagnetometerina¯ip-chiparrangementandtoachievethe®nalbalancebylasertrimmingaspeciallyde-signedregionofthetransformer.ThisworkwassupportedbytheDirector,Of®ceofEn-ergyResearch,Of®ceofBasicEnergySciences,MaterialsSciencesDivisionoftheU.S.DepartmentofEnergyunderContractNo.DE-AC03-76SF00098.ThisletterisdedicatedtothememoryofOliverM.Froehlich.J.Zimmerman,J.Appl.Phys.,702Forareview,seeJ.Vrba,inSQUIDSensors:Fundamentals,FabricationandApplications,NATOASISeries,editedbyH.WeinstockAcademic,Dordrecht,1996,p.117.M.B.Ketchen,W.M.Goubau,J.Clarke,andG.B.Donaldson,J.Appl.,4111D.Drung,IEEETrans.Appl.Supercond.,2112R.H.Koch,J.R.Rozen,J.Z.Sun,andW.J.Gallagher,Appl.Phys.Lett.,403Forexample,W.Eidelloth,B.Oh,R.P.Robertazzi,W.J.Gallagher,andR.H.Koch,Appl.Phys.Lett.,3473;V.Zakosarenko,F.Schmidl,H.Schneidewind,L.Dorrer,andP.Seidel,,779V.Schultze,R.Stolz,R.Ijsselsteijn,V.Zakosarenko,L.Fritzsch,F.Thrum,E.Ilõchev,andH.-G.Meyer,IEEETrans.Appl.Supercond.;M.I.Faley,U.Poppe,K.Urban,H.-J.Krause,H.Soltner,R.Hohmann,D.Lomparski,R.Kutzner,R.Wordenweber,H.Bousack,A.I.Braginski,V.Y.Slobodchikov,A.V.Gapelyuk,V.V.Khanin,andY.V.,3702;G.M.Daalmans,Appl.Supercond.Y.Tavrin,Y.Zhang,M.Muck,A.I.Braginski,andC.Heiden,Appl.Phys.Lett.,1824H.J.M.terBrake,W.A.M.Aarnink,P.J.vandenBosch,H.J.Holland,J.Flokstra,O.Dossel,andH.Rogalla,Proceedingsofthe2ndworkshoponHTSApplicationsandNewMaterials,UniversityofTwente,En-schede,TheNetherlands,May8±10,1995,p.154;B.O.David,O.Dosel,V.Doorman,R.Eckart,W.Hoppe,J.Kruger,H.Laudan,andG.Rabe,IEEETrans.Appl.Supercond.,3267A.N.Matlashov,V.P.Koshelets,P.V.Kalashnikov,Yu.E.Zhuravlev,V.Yu.Slobodchikov,S.A.Kovtonyuk,andL.V.Filippenko,IEEETrans.Magn.,2963M.B.KetchenandJ.M.Jaycox,Appl.Phys.Lett.,736M.B.Ketchen,W.J.Gallagher,A.W.Kleinsasser,S.Murphy,andJohnR.Clem,ProceedingsofSQUID'85,editedbyH.D.HahlbohmandH.WalterdeGruyter,Berlin,Germany,1985,p.865.D.Koelle,A.H.Miklich,E.Dantsker,F.Ludwig,D.T.Nemeth,JohnClarke,W.Ruby,andK.Char,Appl.Phys.Lett.,3630T.W.Button,N.McN.Alford,F.Wellhofer,F.Shields,T.C.Abell,andF.S.Day,IEEETrans.Magn.,1434 FIG.3.Outputofthe¯ux-lockedloopfortheunshieldedgradiometeratoptimalbalancelowertraceandwith¯uxtransformerat0.Insetshowsthesignalfromthe¯ux-lockedloopfortheoptimallybalancedgradiometervsthedistanceofawirecarrying100Hzcurrentbelowthecenterlineofthegradiometer.1714Appl.Phys.Lett.,Vol.71,No.12,22September1997Dantskeretal.