Experimental Studies on Magnetic Nano Structures and Anti-Ferromagnetic Thin Films

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Experimental Studies on Magnetic Nano Structures and Anti-Ferromagnetic Thin Films
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english
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Ghosh, Siddhartha
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University of Florida
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Doctorate ( Ph.D.)
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University of Florida
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Physics
Committee Chair:
Hebard, Arthur F
Committee Members:
Muttalib, Khandker A
Biswas, Amlan
Tanner, David B
Arnold, David

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physics
Physics -- Dissertations, Academic -- UF
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Physics thesis, Ph.D.
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Abstract:
Magnetic materials restricted in nano-scale gives rise to extremely fascinating behavior which is both important due to their potential applications as well as for their interesting fundamental science involved. Magnetic nano-structures are highly used in many different areas of modern daily life ranging from high density magnetic data storage devices, sensors, bio-medical engineering (contrast agents in MRI, drug delivery, treating hyperthemia) and many more potential future applications. In this document we presented and discussed the physics of magnetic nano-structures. In the first two chapters a broad overview on magnetism and magnetic nano-structure is given. Then one after one we discussed different magnetic nano-structures in reduced dimension i.e. magnetic multilayer, superlattice, magnetic QD etc. In the second part of this document we have discussed the transport studies on ultra-thin films of anti-ferromagnetic metals i.e. Chromium and Manganese. In this part we present results of experimental in-situ magneto-transport studies on thin anti-ferromagnetic films for a range of disorder values, characterized by the sheet resistance at 5K.
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by Siddhartha Ghosh.
Thesis:
Thesis (Ph.D.)--University of Florida, 2012.
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Adviser: Hebard, Arthur F.
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RESTRICTED TO UF STUDENTS, STAFF, FACULTY, AND ON-CAMPUS USE UNTIL 2013-12-31

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EXPERIMENTALSTUDIESONMAGNETICNANOSTRUCTURESANDANTI-FERROMAGNETICTHINFILMSBySIDDHARTHAGHOSHADISSERTATIONPRESENTEDTOTHEGRADUATESCHOOLOFTHEUNIVERSITYOFFLORIDAINPARTIALFULFILLMENTOFTHEREQUIREMENTSFORTHEDEGREEOFDOCTOROFPHILOSOPHYUNIVERSITYOFFLORIDA2012

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2012SiddharthaGhosh 2

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Idedicatethistomyparentsandfamilyfortheiractivesupportandunderstanding. 3

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ACKNOWLEDGMENTS FirstIamreallythankfultomyresearchadvisorProf.A.F.Hebardforgivingmetheopportunitytoworkinhislab.Prof.Hebardisakindheartedenthusiasticpersonwhoisalwayswillingtolearnnewthings.Hispersonalsupportandguidancecoupledwithhisresource-fulllaboratorycreatedanamazingPh.D.experienceforme.Alongwithhiselegantbutsimpleapproachtophysics,IhavealsodeeplyappreciatedthefreedomIenjoyedduringmystayinhislab.Iwouldliketothankallthepresentandformerlabmembersfortheirhelps.IamspeciallythankfultoDr.RajivMisraforpatientlyteachingmealltheopartingproceduresofthecomplicatedinstrumentSHIVA,andtoDr.RiteshDasforhelpingmeoutwithmagneticmeasurements.hankstoSanalBuvaevduringthenishingmonthsofmyPh.D.lifeforlearningSHIVAquicklyandcorrectlyandforhelpingmeoutwithvaroiusmeasurementswhenIwasbusywritingthisthesis.ThankstoallthelabmembersPatrick,Sef,Xiaochang,KaraandSimafortheirhelp,supportandencouragement.IwouldalsoliketoacknowledgePete,Larry,RobfromelectronicshopandEd,Marc,Bill,John,Skip,Mikefrommachineshop.SpeciallyIwouldliketothankcryogenicpeople,GregandJohn,fortheirconstantsupplyofliquidHeandN2throughouttheyear.AndalotofthankstopumpshopguyJayHorton&departmentelectricianTimNolandforhelpingmeoutwithallmycryo-pumpandcompressorproblems.Iwouldliketothankallofmycommitteemembers,Prof.AmlanBiswas,Prof.DavidTanner,Prof.KhandkarMuttalibandProf.DavidArnold.SpeciallyIwouldliketothankProf.Biswasforhisguidanceanddiscussionswhichhelpedmealottonishmydegree.IamalsothankfultoProf.D.Norton&hisstudentsDr.JoeCianfroneandDr.Kyeong-WonKimforthewonderfulcollaborationinmultiferroics.AlotofthankstoProf.B.MudgilandhisstudentDr.AjaysahafortheircollaborationinmagneticQDproject.Iammostdeeplygratefultomyparentsforalltheirsacrice,supportandunconditionallovethroughoutmywholelifewithoutwhichnothingwouldhavebeen 4

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possible.Alsoalotofthankstomyin-lawsforalltheirsupportandpatienceandfortrustingmewiththeirdaughter.Andnallyit'stimetothankmylovingwifeMoumitawhowastheonlyfamilymember,standingbymeforlast4yearsofmylengthyPh.D.lifeandinspiringmeineverysituation. 5

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TABLEOFCONTENTS page ACKNOWLEDGMENTS .................................. 4 LISTOFTABLES ...................................... 9 LISTOFFIGURES ..................................... 10 ABSTRACT ......................................... 13 CHAPTER 1INTRODUCTION ................................... 14 2MAGNETICNANOSTRUCTURESANDMAGNETIZATIONATNANOSCALE 20 2.1ReviewOnRelevantNano-Structures .................... 21 2.1.1Particles ................................. 21 2.1.2ThinFilms ................................ 24 2.2MagnetizationDynamicsAtNano-Scale ................... 26 2.2.1TheoreticalBackground ........................ 26 2.2.2DomainsAndDomainWalls ...................... 27 2.2.3MagneticHysteresis .......................... 29 2.2.4TemperatureDependenceOfMagnetism ............... 32 3EXISTENCEOFFERROMAGNETISMINBIMODALQUANTUMDOTS .... 35 3.1MagneticAndFluorescentQuantumDots .................. 35 3.2ExperimentalDetails .............................. 36 3.2.1Synthesis ................................ 36 3.2.2Characterization ............................ 38 3.3ResultsAndDiscussion ............................ 39 3.3.1OpticalMeasurements ......................... 39 3.3.2TEM,XRDAndEDSStudy ...................... 39 3.3.3MagneticMeasurements ........................ 42 3.4Conclusions ................................... 48 4FERROMAGNETISMINBILAYERSOFPALLADIUM/C60 ............ 50 4.1MagnetismOfPalladium ............................ 50 4.2ExperimentalAndTheoreticalDetails .................... 52 4.3ResultsAndDiscussion ............................ 54 4.4ComputationalStudy .............................. 59 4.5Conclusions ................................... 63 5INSEARCHOFTWO-PHASESUPERLATTICEMULTIFERROICS ....... 65 5.1Multiferroics ................................... 65 6

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5.2MultiferroicPropertiesOfBaFeO3-KTa0.47Nb0.53O3Superlattices ..... 66 5.2.1SynthesisAndCharacterization .................... 66 5.2.2ResultsAndDiscussion ........................ 71 5.2.3Conclusions ............................... 74 5.3StudiesOnBa2FeMoO6-BaTiO3Sueperlattices ............... 75 5.3.1ExperimentalDetails .......................... 76 5.3.2ResultsAndDiscussion ........................ 77 5.3.3Conclusions ............................... 84 6QUANTUMCORRECTIONSINDISORDEREDMETAL ............. 87 6.1WeakLocalization(WL) ............................ 87 6.1.1ConductivityCorrectionByWL .................... 88 6.1.2MagnetoresistanceCorrectionByWL ................ 90 6.1.3HallEffectCorrectionByWL ..................... 91 6.2Electron-ElectronInteraction(EEI) ...................... 92 6.2.1ConductivityCorrectionByEEI .................... 95 6.2.2MagnetoresistanceCorrectionByEEI ................ 95 6.2.3HallEffectCorrectionByEEI ..................... 96 6.3AnomalousHallCorrectionInMagneticMetal ................ 96 6.3.1QuantumCorrectionsFromElectron-ElectronInteractions ..... 97 6.3.2QuantumCorrectionsFromWeakLocalization ........... 97 7EXPERIMENTALSTUDIESONCHROMIUMTHINFILMS ............ 99 7.1ExperimentalDetail .............................. 99 7.1.1ThinFilmDeposition .......................... 101 7.1.2MeasurementTechnique ........................ 102 7.2PreviousStudyOf3DMetal-InsulatorTransitionInGadolinium ...... 102 7.3StudiesOnChromiumThinFilm ....................... 105 7.3.1Temperature-DependentConductivityOfWeaklyDisorderedCr .. 106 7.3.2Temperature-DependentConductivityOfHigherDisorderedCr .. 110 7.3.3Temperature-DependentConductivityOfUltra-HighDisorderedCr 112 7.3.4W-PlotForChromium ......................... 114 7.4Conclusion ................................... 116 8EXPERIMENTALSTUDIESONDISORDEREDMANGANESETHINFILMS .. 117 8.1ExperimentalDetail .............................. 117 8.2Power-LawTemperatureDependenceInIntermediate-DisorderMn .... 118 8.3ExponentialHoppingBehaviorInHighlyDisorderedMn .......... 125 8.4W-PlotStudyForManganese ......................... 126 8.5ConclusionsOnManganese ......................... 128 9SUMMARY ...................................... 130 REFERENCES ....................................... 132 7

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BIOGRAPHICALSKETCH ................................ 140 8

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LISTOFTABLES Table page 3-1EDSandICPanalysisoftheFe-dopedquantumdots .............. 42 3-2SaturationmagnetizationvaluesforindicatednanoparticlesandFeridexI.V. .. 45 7-1Growthparametersforchromiumlms ....................... 101 9

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LISTOFFIGURES Figure page 1-1Magneticorderingofdifferentmagneticsystems ................. 15 1-2SchematicrepresentationoftheSHIVAapparatus ................ 18 2-1Schematicrepresentationofdifferentnanostructuregeometries ......... 21 2-2Variationofcoerciveeldwithparticlediameter .................. 22 2-3Magneticdomainsanddomainwallstructure ................... 27 2-4Differenttypesofdomainwallsinmagneticnanostructures ........... 28 2-5Hysteresismechanismbycoherentspinrotationinsingledomain(SD)systems 30 2-6Hysteresismechanismbydomainwallmotioninmultidomain(MD)systems 32 2-7TemperaturedependenceofmagnetizationofaCdTeFeSquantum-dotsample 33 3-1Preparationow-chartofCdTeFeSQDbyhydro-synthesis ............ 37 3-2AbsorbanceandPLemissionpeaksforFedopedCdTeSQDs ......... 40 3-3TEMimageofFedopedCdTeSQDsemittingat730nm ............. 41 3-4XRDofFedopedandundopedCdTeSQDs .................... 41 3-5EDSspectrafortheFe-dopedCdTeSemittingat740nm ............ 42 3-6XPSspectraforCd,Fe,TeandSinFe-dopedQD710 .............. 43 3-7HysteresisloopsmeasuredfortheQDswithdifferentemissionpeaks ..... 44 3-8Comparisonofmagnetizationofdifferentquantumdotsmeasuredat10K ... 45 3-9HysteresisloopandtemperaturedependenceofmagnetismonFeridexNPs 46 3-10MvsTmeasuredonquantumdotswithdifferentemissionpeaks ........ 47 4-1SchematicillustrationofPd/C60system ...................... 53 4-2StudyofsurfacecontaminationinPd/C60system ................. 55 4-3RelativepresenceofcarbonandPdconcentrationsinPd/C60system ..... 56 4-4MagnetichysteresisloopmeasurementonPd/C60 ................ 57 4-5TemperaturedependenceofthemagnetizationofPd/C60system ........ 58 4-6DifferentsituationsaccordingtoDFTinPd/C60multilayersystem ........ 62 10

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5-1LatticestructureofPerovskiteanddoublePerovskitesystems .......... 66 5-2XRDscanofa24x24BaFeO3-KTa0.47Nb0.53O3(BFO-KTN)Superlattice(SL) 67 5-3XPSdataforannealed6x6BaFeO3-KTa0.47Nb0.53O3(BFO-KTN)SL ...... 68 5-4TEMdataonanannealed24x24BaFeO3-KTa0.47Nb0.53O3(BFO-KTN)SL ... 69 5-5EDSmeasurementforanannealed24x24BFO-KTNSL ............. 70 5-6MvsHmeasurementshowseffectofannealingonBFO-KTNSLs ....... 71 5-7HysteresisloopsofBFO-KTNSLs&BaFeO3thinlms .............. 72 5-8ComparisonofmagneticpropertiesofBFO-KTNSLs&BaFeO3thin-lms ... 73 5-9MvsTmeasurementofannealedBFO-KTNSLs ................. 74 5-10XRDscanofaBa2FeMoO6-BaTiO3SL ...................... 77 5-11-2XRDscanofaBa2FeMoO6thin-lmgrownonaSrTiO3substrate ..... 78 5-12ComparisonofmagneticpropertiesofBa2FeMoO6thin-lms. .......... 80 5-13MvsTofBa2FeMoO6thin-lmsgrownatdifferenttemperatures ........ 80 5-14TransportpropertiesofBa2FeMoO6thin-lms ................... 82 5-15DetailedstructureofBa2FeMoO6basedsuperlatticeandbilayer ........ 83 5-16MagnetizationcurvesofBa2FeMoO6basedSLsandbi-layers .......... 84 5-17MvsTmeasurementonBa2FeMoO6basedSLstructures ........... 85 7-1Pre-depositedcontactpadstructure ........................ 100 7-2Shadowmaskgeometryalongwithitsaspectratios ............... 101 7-3TypicalDCmeasurementcircuitusedduringmeasurements ........... 103 7-4Previousstudyonhighly-disorderedgadolinium .................. 104 7-5Temperaturedependenceofnormalizedconductivityinweakly-disorderedCr 107 7-6Comparisonofpowerlawandlogarithmicttingforweakly-disorderedCr ... 108 7-7VariationofttingparametersA,Bandpofchromium .............. 109 7-8Previousstudiesonweaklydisorderedgadolinium ................ 109 7-9Temperaturedependenceofnormalizedconductivityinhighly-disorderedCr 111 7-10PlotofnumericalprefactorARvsR0forhighly-disorderedCr .......... 112 11

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7-11Temperaturedependenceofnormalizedconductivityinultra-highdisorderedCr 113 7-12PlotofWandRxxasafunctionoftemperatureforCr ............... 115 8-1(2D)=L0vsTofweaklydisorderedMnfor6k
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AbstractofDissertationPresentedtotheGraduateSchooloftheUniversityofFloridainPartialFulllmentoftheRequirementsfortheDegreeofDoctorofPhilosophyEXPERIMENTALSTUDIESONMAGNETICNANOSTRUCTURESANDANTI-FERROMAGNETICTHINFILMSBySiddharthaGhoshDecember2012Chair:ArthurFHebardMajor:PhysicsMagneticmaterialsrestrictedinnanoscalegiverisetoextremelyfascinatingbehaviorwhichisbothimportantduetotheirpotentialapplicationsaswellasfortheirinterestingfundamentalscienceinvolved.Magneticnanostructuresarehighlyusedinmanydifferentareasofmoderndailyliferangingfromhighdensitymagneticdatastoragedevices,sensors,bio-medicalengineering(contrastagentsinMRI,drugdelivery,treatinghyperthemia)andmanymorepotentialfutureapplications.Inthisdocumentwepresentanddiscussthephysicsofmagneticnanostructures.Inthersttwochaptersabroadoverviewonmagnetismandmagneticnanostructureisgiven.Thenwediscussdifferentmagneticnanostructuresinreduceddimensioni.e.magneticmultilayers,superlattices,magneticquantumdotsetc.Inthesecondpartofthisdocumentwehavediscussedthetransportstudiesonultra-thinlmsoftheanti-ferromagneticmetalsi.e.chromiumandmanganese.Wesubsequentlyinvestigatethemagneticpropertiesasafunctionofdisorderstrengthcharacterizedbythesheetresistanceatlowtemperature(5K). 13

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CHAPTER1INTRODUCTIONMagnetism,theoldestscienticdisciplinetohavebeencontinuouslystudiedsince6thcenturyBC,stilloffersinterestinggroundforscienticinnovationtoday.Afterbeingdiscoveredbytheminingofmagnetite(loadstone)severalmilleniumago,magnetismhasstimulatedprogressinscienceandtechnologyforlastseveralcenturies.Magneticmaterialsinbulkcanbeclassiedinto5maincategories,namelydiamagnetic,paramagnetic,ferromagnetic,anti-ferromagneticandferrimagnetic.Diamagnetism:Diamagnetismemergesinallmaterialsandisthepropensityofamaterialtoshowanegativemagnetism.Materials,whoseelectronstructurescreateaclosedshell,likemonoatomicraregases(e.g.He,He,Aretc.),polyatomicgases(H2,N2etc.),covalentelements(e.g.C,Si,Geetc.)andmostorganiccompoundsshowdiamagneticproperties.Eventhoughdiamagneticmaterialsaremadeofatomswithoutanynetmagneticmoment,theyreactinawaysothattheygetrepelledbyanexternalmagneticeld.Whenasingleelectronorbitisexposedtoanexternalmagneticeld,ittriestodecreasetheeffectivecurrentoftheorbit,andsoproducesamagneticmomentopposingtheappliedeld(Lenz'sLaw).Ifweconsiderabulkmaterialismadeofbillionsofelctronicorbitsthenitisobviousthatwholematerialwillshowasmallnegativemagnetism.Thevaluescalculatedaccordingtothistheoreticalunderstandingarequalitativelytruebutdonotquantitativelyagreewithexperimentalvalues.Thisdiscripancycallsforaquantum-mechanicaltheory,whichisbeyondthescopeofthisdissertation.Paramagnetism:Substanceswithincompleteelectronshellstructuresshowparamagneticbehavior.Particularlymaterialswithincompleteinnershellsexhibitstrongparamagneticbehaviorlikemetals(tungsten,cesium,aluminium,lithium,magnesium,sodiumetc.),rare-earthmaterials(neodymium,samariumetc.)andsomemetal-oxidesandsalts(e.g.KCr(SO4)212H2O).ThePauliexclusionprincipleforcesthepaired 14

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Figure1-1. Magneticorderingof(a)Paramagnetic,(b)Ferromagnetic,(c)Antiferromageticand(d)Ferrimagneticmaterials electronstohavetheirintrinsic(`spin')magneticmomentspointinginoppositedirections,causingtheirmagneticeldstocancelout.Butanunpairedelectronisfreetoalignitsmagneticmomentinanydirection.Whenanexternalmagneticeldisapplied,thesemagneticmomentswilltendtoalignthemselvesinthesamedirectionastheappliedeldandtherebyshowapositivemagneticresponse.Butwheneverthisexternalmagneticeldisremoved,intrinsicmagneticmomentswithinparamagnetbecomerandomly(Fig 1-1 (a))orientedbecauseoftemperatureuctuations.Ferromagnetism:Aferromagnetisalsoamaterialwithunpairedelectrons.However,unlikeparamagneticmaterials,thesesubstanceshaveatendencytoalignitsintrinsicmoments(magnetic)paralleltoeachotherinordertomaintainalowered-energystate(Fig 1-1 (b)).Thus,evenwhentheappliedeldisremoved,theelectronsinthematerialmaintainaparallelorientation.Everyferromagneticsubstancehasanuniquetemperature(calledtheCurietemperature)abovewhichitdoesnotkeepitsferromagneticproperties,andbecomesparamagnetic.Highertemperatureincreasesthermaldisordereffectwhichoverwhelmstheenergy-loweringduetoferromagnetic 15

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order.Somewell-knownferromagneticmaterialsaretransitionsmetallikenickel,iron,cobalt,gadoliniumandtheiralloys(Fe2O3,FeOFe2O3,NiOFe2O3,CrO2).Antiferromagnetism:Anantiferromagnetisasubstancewhichhasthetendencytoaligntheintrinsicmagneticmomentsofneighboringvalenceelectronsinoppositedirections(Fig 1-1 (c)).Antiferromagnetshavetwoferromagneticsublattices[blueandredspinsin(Fig 1-1 (c))]whicharearrangedanti-parallelly.AntiferromagnetshaveazeronetmagneticmomentandonlyscatteringtechniquesusingX-rayorneutron[whichinteractwitheachferromagneticsublattice]canhelpinstudyingthestructureofantiferromagnets.Antiferromagnetsalsohaveanuniquetemperaturelikeferromagneticmaterials,abovewhichtheybecomeparamagnets.ThistemperatureiscalledNeeltemperatureafterLouisNeel,whorstidentiedantiferromagneticordering.Antiferromagneticmaterialsusuallyshowdiamagneticandferrimagneticpropertiesdependingonthetemperature.MainexamplesofantiferromagneticmaterialsaretransitionmetalslikeManganese(-Mn),Chromuim(Cr),theircompounds(e.g.FeMn)andsometransitionmetaloxides(NiO).Ferrimagnetism:Alongwithferromagnets,ferrimagnetsareanotherkindofmagneticmaterailwhichretaintheirmagnetizationintheabsenceofanexternalmagneticeld.Butatomic-structurewiseferrimagnets'magneticorderingissimilartoantiferromagnets(Fig 1-1 (d))andalsohastwoferromagneticsublattices[greenandredspinsin(Fig 1-1 (d))]whicharealignedanti-parallelly.Butunlikeantiferromagnets,thesematerialshavetwoferromagneticsublatticeswithunequalstrengthsotheyhaveanetmagneticmoment.Magneticpropertiesofferrimagnetsaremoreorlesslikeferromagnets.TheimportantclassesofferrimagneticmaterialsareYIG(yttriumirongarnet)andferritescomposedofironoxidesandotherelementssuchasaluminum,cobalt,nickel,manganeseandzinc.Allthesemagneticpropertiesinbulkmaterialsmentionedabovecanbeessentiallyexplainedthroughatomic-scalemagneticphenomena,suchasquantum-mechanical 16

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exchange[ 1 2 ],relativisticspinorbitcoupling[ 3 ],crystaleldinteraction[ 4 ]etc.Buttherecentadvancementinnanotechnologyshowsthatnitesizenano-scalematerialshavecompletelydifferentmagneticpropertiescomparedtobulkmaterials[ 5 ].AccordingtoSkomski[ 5 ],thescienticandtechnologicalimportanceofnanoscalemagnetismcanbesummedupinthethreefollowingcategories:1.Atremendousvarietyofmagneticnano-structuresarepresentwithinterestingphysicalproperties,rangingfromnaturallyoccurringnanomagnetsandcomparativelyeasy-to-producebulknanocompositestodemandingarticialnanostructures.2.Theinvolvementofnanoscaleeffectsintheexplanationandimprovementofthepropertiesofadvancedmagneticmaterials,likethe`metamaterials'whereasoftphaseandhardphaseisaddedinasuitablenanostructuretoimprovethepermanentmagnetperformanceoftheexistingintermetallics(e.g.SmCo5,Sm2Co17andNd2Fe14Betc).3.Nanomagnetismhasopenedthedoorforcompletelynewtechnologies,includingbutnotlimitedtoultra-highdensitymagneticrecording[ 6 7 ],spintronics[ 8 9 ],giant-magneto-resistancephenomena[ 10 11 ],improvednanocompositepermanentmagnetmaterials[ 12 ],biogenicnano-magnets&bio-medicalapplications[ 13 14 ].Inthisdissertation,wearegoingtofocusontransport,magneto-transportandmagneticpropertiesofdifferenttypesofmagneticnano-structuresrangingfrommultilayerstoquantumdotstoultra-thinlms.Mostofthesenano-structuresweregrowninauniquehome-madehighvacuumsystemdesignedforinsitucharacterizationofairsensitivelms.ThisinstrumentiscalledSHIVA(SampleHandlinginVAcuum)whichisschematicallyshowninFig. 1-2 .SHIVAisanexclusivedesignthatcombinesacustom-madegrowthchamber,aCryofabcryostatandaloadlockintoonesinglevacuumsystemwithbasepressureatalow10)]TJ /F2 7.97 Tf 6.59 0 Td[(9Torr.Ithasmagneticallycoupledmechanicalarms(A1,A2,A3)whichmovethesampleholderfromloadlock(LLin 17

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Figure1-2. SchematicrepresentationoftheSHIVAapparatusandablowup(incolor)ofthereceiverplatformshowinghowapuckcanbelocked-inwiththehelpofthruster.LL:Loadlock;A1,A2,A3:transferarmswiththrustermountedateachend;V1,V2:gatevalvesseparatingthegrowthchamberfromloadlockandloadlockfromcryostatrespectively;S1,S2:RF&DCsputteringgun;T1:Thermalevaporationgun Fig. 1-2 )togrowthchamberandthenfromgrowthchambertocryostat.Twogatevalves(V1andV2inFig. 1-2 )separategrowthchamberandcyostatfromtheloadlock.Samplesareusuallygrownusingshadowmasksonasetofpre-depositedelectrodesmadeofthicklmsofpalladiumgrownonthesapphiresubstrates.Theseultrathinsamplescanbegrowneitherbysputteringorthermalevaporationtechniquesandmeasuredusingquartzcrystaloscillatorrmlyattachedonthereceiverstageclosetothesample.Thisultra-highvacuum(pressure210)]TJ /F2 7.97 Tf 6.58 0 Td[(9Torr)hastwoAJAmagnetronsputterguns(S1andS2inFig. 1-2 ),aRADAKthermalevaporationfurnace(T1inFig. 1-2 )andanionbeamgunforionmilling.Thesampleholderismountedonthestagewhichisconnectedtoanotherarm(manipulatorinFig. 1-2 ),thisarmallowsustorotatethesubstratesothatitfacestheproperdepositionsource.Afterthesampleisgrown,itistransportedtoaCRYOFABliquidheliumdewarwithaliquidnitrogenouterjacket.Thishighvacuum(10)]TJ /F2 7.97 Tf 6.59 0 Td[(8Torr)cryostathasanAMIsuperconducting 18

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magnet,whichallowsmagnetotransportmeasurementattemperaturesdownto4.5Kandmagneticeldupto7T.Thehighlysensitive(1/100thofKelvin)temperaturecontrolsystemcomprisesaLakeshore332temperaturecontrollerconnectedtoCernoxthermometerandresistiveheatermountedonthesamplereceiverstage.Thesampleholderandholderreceiverstage(bothingrowthchamberandcryostat)areelctricallyconnectedthroughspringloadedcontacts.Wiresemergefromthereceiverstageviavacuumfeed-throughstoabreak-outpaneloutsidethevacuumsystem.Sowhensampleholderisengagedproperlyinthereceiver,eachoftheelectrodesonthesubstrateiselectricallyaccessibleoutsidethevacuumsystematthebreakoutpanel.Thisfacilityenablesustoin-situmeasurementofsampleresistancebothduringgrowthandinsidethecryostat. 19

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CHAPTER2MAGNETICNANOSTRUCTURESANDMAGNETIZATIONATNANOSCALEInthischapterwewillpresentanoverviewonsomeoftherelevantmagneticnano-structureslikenano-particlesandthinlmsandthendiscussimportantmagnetizationdynamicsatnano-scale.Inthefollowingchapterswewilldiscussmagneticstructuresstartingwithnano-particlesthenproceedtomultilayerandthennallytomagneticthinlms.Soindetail,thenextchapter(3)illustratesmagneticmeasurementsonhydro-synthesizedCdTeFeSquantumdotsalongwithopticalandMRIstudiesdonebycollaboratorsDr.A.K.SahaandDr.P.SharmaunderthesupervisionofProf.B.M.Moudgil.Chapter4stressesonthemagneticpropertiesofPdnanoparticlesembeddedinC60alongwithdensityfunctionaltheory(DFT)calculationstosupportourexperiment.DFTcalculationswereperformedbyourcollaboratorsDr.HasanSahinandProf.F.M.Peeters.Inthenextsectionofthethesis(Ch.5)westudiedmagnetic,transportandmagneto-transportpropertiesofseveraltwo-phasemultiferroics,whereferroelectricanddouble-perovskiteferromagneticmaterialsweregrownsequentiallytoachieveamultiferroicsuper-latticestructure.InthiscollaborativestudysampleswerepreparedbyDr.J.Cianfrone&Dr.K.W.KimfromProf.DavidNortons'lab,whilethetransportandmagneto-transportmeasurementswereperformedbySanalBuvaev.Finallyinthelastthreechapters(i.e.Ch.6,7&8),wehavediscussedtheoreticalbackgroundofdisorderedmagneticthin-lmsandexperimentalstudiesonantiferromagneticthinlmsofCrandMn.Theearliestevidenceofmagneticnanostructuresarefoundinmothernatureintheformsofmagnetite(Fe3O4)nanoparticlesprecipitatedinbacteria,molluscs,insectsandhigheranimals.Longchainsofmagnetiteparticles(40to100nm)havebeendiscoveredwithinthemagnetostaticbacteriathatliveindarkenvironments[ 15 ].Magnetiteparticleshavebeenalsofoundinthebrainsofbees,pigeonsandtuna,whichmayserveassensorsformigration[ 16 ]ingeo-magneticelds.Magnetiteandother 20

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Figure2-1. Typicalnanostructuregeometries:(a)chainofneparticles,(b)stripednanowire,(c)cylindricalnanowire,(d)nanojunction,(e)vicinalsurfacestep,(f)nanodots,(g)antidotsand(h)particulatemedium.ThegureisreproducedfromRef.[ 5 ] oxideparticlesarealsoresponsibleforrockmagnetism,wherevolcanicrockscontainingmagneticoxideparticlesshowmagnetismrangingfrom1Tto100T.Thisexistenceofrockmagnetismcanbeveryusefulinarchaeomagneticdatingandformonitoringchangesintheearthsmagneticeld[ 17 ].Magneticnanoparticlesarealsofoundinsuperparamagneticsystems[ 18 ],ferrouids[ 19 ]andmeteorites[ 20 ]. 2.1ReviewOnRelevantNano-StructuresAdvancedmagneticnanostructurescanbeclassiedintoagreatdiversityofgeometries,rangingfromquantumdotstonanowirestonano-composites.Inthissectionwe'lldiscusstwogeometriesrelevanttothisthesis,namelynano-particlesandthinlms. 2.1.1ParticlesMagneticnanoparticlesareoneofthemostwidelystudiedsystems,whichexistinthenaturalenvironmentorcanbeproducedarticially.Magneticnano-particlescanbeclassiedintotwomaintypes,singledomain(SD)particlesandmulti-domain(MD)particles.ThelengthscalewhichseparatesSDandMDparticlesiscalledthecritical 21

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Figure2-2. Variationofcoerciveeldwithparticlediameterformagneticnanoparticles.ThegureisreproducedfromChapter11ofRef.[ 24 ]. singledomainradius(RSD),(denedinEqn. 2 ).Themagnetizationdynamicsinsingledomain(SD)nanoparticleswasrstexplainedbyStonerandWohlfarth[ 21 ]intheirpioneeringworkonSD-particles,whichassumescoherentspinrotation(CSR)asthemainmagnetizationphenomena.ThisCSRassumptionallowsexactsolutionfortheoristsbutnotgenerallyobservedbyexperimentalists,whichcalledforadditionalmodelswithincoherentspinreversalmechanisms[ 22 23 ].Coercivity:Inthestudyofnanoparticles,coercivityisthemostinterestingpropertywhichhasastrikingdependenceontheparticlesize.AsshownintheFig. 2-2 therearethreedistinctregionsinparticlediametervscoercivitycurve.Initiallywhentheparticlediameterisdecreasedinthemultidomainregion,coercivityisincreasedfollowingtheequationHC=a+b D,wherea&bareconstantsandDistheparticlediameter.Butafterreachingamaximum,HCstartstodecreasewhenparticlediameterisfurtherreduced.ThisisthesingledomainregionwherecoercivityfollowstheequationHC=p)]TJ /F5 7.97 Tf 19.73 5.03 Td[(q D3=2,whenp&qareconstantsandDistheparticlediameter.FinallybelowacriticaldiameterDpthecoercivityiszero,andtheseparticlesarecalledsuperparamagnetic. 22

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MagneticAnisotropy:Anotherpropertysensitivetosizeofthenanoparticleisthemagneticanisotropyenergy.Inbulk,crystalanisotropyistheprimarysourceofmagneticanisotropy.Butinnano-scaleparticlesothersourcesofanisotropyhavebeenidentiedlikestrainanisotropy,exchangeanisotropyandshapeanisotropy[ 25 ].Forthisreasonmagneticanisotropyinnanoparticlescanbetwo-ordersofmagnitudehigherthanbulk.Forsphericalnano-structuresmagneticanisotropycanbeexpressedbythefollowingequation, K=KC+6KS D(2)whereKCisthecrystalanisotropy,KSthesurfaceanisotropyandDistheparticlediameter.BlockingTemperature:Theblockingtemperature(TB)ofnano-particlescanbewrittenas: TB=KD3=k ln(m=0)(2)whereKisthemagneticanisotropyenergy,Distheparticlediameter,misthecharacteristicmeasurementtimeoftheexperimentand0isthecharacteristicattempttimeofspinreversal(oftheorderof10)]TJ /F2 7.97 Tf 6.59 0 Td[(9to10)]TJ /F2 7.97 Tf 6.59 0 Td[(12sec[ 26 ]).ButthediameterdependenceofTBisnotsimplycubicbecauseKisalsoafunctionofdiameter(Eqn. 2 ).Sofromthiseqn. 2 wendthatblockingtemperatureinnanoparticlesisnotintrinsicbutisanexperimentaltechniquedependentparameter.MagneticnanoparticlescanbeusefulforadvancedmagneticrecordingusingESD's(elongatedsingle-domainparticles)[ 27 ],magneto-resistivesensorsandinspinelectronicsusingtheirGMR(giantmagnetoresistance)properties[ 10 11 ].Thesenano-particlescanalsobeutilizedformonitoringmagneticeldsanddomaincongurationsusingferrouids(stablecolloidalsuspensionsofferromagneticnanoparticlesinorganicsolvents)[ 19 ].Anotheremergingareaisbiomedicalapplicationsusingmagneticnanoparticles,whichincludesmagneticseparationofcells,proteins 23

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andDNAfragments,bio-imaging,magneticresonanceimaging(MRI)enhancement,targeteddrugdeliveryandhyperthermiacancertherapy[ 13 14 ]. 2.1.2ThinFilmsMagneticthinlmsarewidelystudiednanostructureswhichmakeimportantcontributionstotheunderstandingofthefundamentalphysicsofmagnetism.Thin-lmstructuresexhibitanumberofinterestingpropertieslikeanisotropiesofidealandvicinalsurfaces,anisotropiesofinterfaces[ 28 ],momentmodicationsatsurfacesandinterfaces,thickness-dependentdomain-wallandcoercivephenomena,interlayerexchangecouplingandtemperaturedependenceofmagneticordering[ 29 30 ].Earlyresearchonmagneticthinlmshadalreadystartedin1930sbyBloch'srecognitionthatwithinHeisenbergmodel,magnetismin2Dlmwillbeunstableatnitetemperatureduetouctuations[ 31 ].ThisfamoushypothesiswaslaterrigorouslystudiedanddevelopedbyMerminandWagner[ 32 ].Buthighqualityresearchin1960and70swasoftenrestrainedbypoorvacuumsystems.Howeverthissituationchangedinmid1980swhenimprovementsinvacuumandcharacterizationtechnologyledtoanexplosionintheresearchofmagneticthinlms.Inthisperiodmagnetizationofultra-thinFe/Ag(001)wasrstexperimentallyfoundtolieperpendiculartotheplaneofthelm[ 33 ],whichisaresultofhighsurfacemagneticanisotropyenergy.Followingthisexperiment,ananisotropyintheperpendicularmagnetizationwasreportedonNiFe(111)/Cu(111)systembyGradmannandMuller[ 34 ],whichwasthenidentiedinmanyothermagneticthinlms[ 35 ].Thencamethegiant-magnetoresistance(GMR)effectin1988,whichwasrstidentiedinFe/CrtrilayersandmultilayersbyFertandGrunberg[ 10 11 ](ForwhichtheywereawardedtheNoblePrizeinPhysicsin2007).GMRisthephenomenawhichdescribesasignicantchangeintheelectricalresistancedependingonwhetherthemagnetizationofadjacentferromagneticlayersareinaparalleloranantiparallelalignment.Afterthesestructureorientedresearchactivities,surfaceandinterfacerelatedresearchbecameanewdirectioninmagneticthinlm 24

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study.Recentresearchhasshownthattinyamountsofnon-magneticsurfactantscandramaticallyalterthepropertiesoftheultra-thinmagneticlms[ 36 ].Furthernewimpetusinthethinlmresearchcamefromnewcharacterizationtechniques,likeSTM(scanningtunnelingmicroscopy),AFM,MFM(atomicandmagneticforcemicroscopy),XMCD(X-raymagneticcirculardichroism),PEEM(photoemissionelectronmicroscopy),PNR(polarizedneutronreection),SEMPA(scanningelectronmicroscopywithpolarizationanalysis),tonameafew.Coupledwithadvancednanolithography,thesenewcharacterizationtechniquesenabledscientiststofabricateandcharacterizenewmagneticnanostructuresbasedonultrathinlms.Inthelastfewyearsthereisanemergenceofanotherexcitingneweldofthin-lmresearchwhichiscalledspintronics.Spintronicsistheeldofresearchwhichtriestocombinetheelectronchargedegreeoffreedomwiththatoftheelectronspin.Ifpossible,thiswillenablenewwaysofnon-volatileinformationstorageandprocessingathigherspeed,higherdensitiesandlowerpowerconsumption[ 37 38 ].Magneticthinlmshavehugepresent-dayandpotentialapplicationsintheeldofmagneticdatastorageindustry.Therstcommerciallyavailableharddiskdrive(HDD)[introducedin1956]hadarecordingdensityofabout2kbin)]TJ /F2 7.97 Tf 6.59 0 Td[(2,whichreachedrecordingdensitiesof200Gbin)]TJ /F2 7.97 Tf 6.59 0 Td[(2in2007.Thistremendousincreaseof108timesinmagneticrecordingdensityinthelast51years(anannualgrowthrateof40%)wouldnothavebeenachievedwithoutthefundamentalresearchonmagneticthinlms.AlthoughtheGMR[ 10 11 ]effectwasmostwidelyusedbythedatastorageindustry,manyothertechniques(liketunnelmagnetoresistance(TMR)[ 39 ],current-inducedmagneticswitching[ 40 ],current-induceddomainwalldisplacement[ 41 ])werealsoextensivelyusedinmagneticstoragedevices.OtherthanthemostlyusedHDD(harddiskdrive)therearemanyothertypesofstoragedeviceslike,DRAM(dynamicrandomaccessmemories),MRAM(magnetoresistiverandomaccessmemory)andHAMR(heat 25

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assistedmagneticrecording).Magneticthin-lmsarealsohighlyusedintheresearcheldsofspintronics[ 8 9 ]andmultiferroics[ 42 43 ]. 2.2MagnetizationDynamicsAtNano-Scale 2.2.1TheoreticalBackgroundFromatheoreticalpointofview,nanostructuralphenomenaareoftendescribedbydifferentialequationsofthetype: r2)]TJ /F4 11.955 Tf 11.95 0 Td[(2=f(r);)]TJ /F2 7.97 Tf 6.59 0 Td[(1:interactionlength(2)ThisisunlikeinhomogeneousLaplace(orPoisson)equationr2=f(r)whichimplieslong-rangeinteractionsandelectro/magneto-staticphenomena.Thisinteractionlength()]TJ /F2 7.97 Tf 6.59 0 Td[(1),isdenedbythecompetitionbetweenkineticenergyofelectron(hopping)andelectrostaticenergies(Coulombinteractionandexchange).Inclassicallimit)]TJ /F2 7.97 Tf 6.59 0 Td[(1scalestokFora0,whereasinrelativisticlimit,interactionlengthincreasestol0=a0/,when=40e2=~1/137(Sommerfeldsne-structureconstant)[ 12 ].Animportantquestionarisesastothequanticationoftheboundarybetweennano-scaleandmacro-scale.Andhowmanyatomsarenecessarytomakeananostructuredifferentfrombothatomicandbulkmagnet?Wehavetoaddressthesequestionsseparatelyforintrinsicandextrinsicmagneticproperties.Intrinsicmagneticproperties(spontaneousmagnetization,therstuniaxialanisotropyconstant,theexchangestiffnessetc.)areseenonlengthscalesoffewinteratomicdistancesandusuallytendtoapproachtheirbulkvalueswithinalengthscaleof1nm,althoughthereareafewexceptionslikeCurietemperatureofmultiphasemagneticnanostructures[ 12 44 ].Buttheextrinsicpropertieslikeremnantmagnetization(Mr),coerciveeld(HC)etc.arenon-equilibriumpropertiesandhighlydependentonthegeometricalstructureandshowinterestingphenomenalikerandom-anisotropyscaling,Mrenhancement,micro-magneticlocalization,bulging-typenucleationmodesandavarietyofgrainboundaryandexchange-couplingeffects[ 44 46 ]. 26

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Figure2-3. MagneticDomainsanddomainwallstructure.ThegureisinspiredbyagurefromChapter9ofRef.[ 24 ]. 2.2.2DomainsAndDomainWallsAmagnetic-domainisdenedbythelengthoverwhichthespinsretaintheircollinearity(Fig. 2-3 )[ 47 ],sowithinasinglemagneticdomainthemagnetizationisuniform.However,inthebulkmaterialtheseindividualdomainsreorientthemselvestominimizethetotalmagneticenergy.Thetotalmagneticenergyisacombinationoflong-rangemagnetostaticenergy(Emag)andtheshort-rangeexchangeenergy(Eex).Forsphericalnanostructuresthemagnetostaticenergycanbewrittenas: Emag=0M2SV=12(2)where0isthefreespacepermeability,MSisthesaturationmagnetizationandVisthevolumeoftheparticle.Nowtheexchangeenergy(energyrequiredtoformaBlochdomainwall)isgivenby Eex=4p AKR2(2) 27

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Figure2-4. Differenttypesofdomainwallsinmagneticnanostructures(a)Blochwallsand(b)Neelwall.ThegureisreproducedfromChapter9ofRef.[ 24 ]. whereKistheanisotropyconstant,AistheexchangestiffnessandRistheradiusoftheparticle.ItisclearfromtheseequationsthatmultipledomainswillbeenergeticallyfavorableforlargerparticleswhenEmaggrowsasR3andEex/EdwgrowsasR2.Equatingtheenergies(Emag=Edw)wegetthemaximumlimitofsingledomaininsphericalparticles(RSD).Thisiscalledthecriticalsingledomainradius[ 47 ]: RSD=36p AK=0M2S(2)wherethetransitionfromsingledomain(SD)tomultidomain(MD)occurs.Magneticdomainwallsaredenedastheinterfacialregionbetweentwomagneticdomains(Fig. 2-3 ),atorwithinwhichthemagnetizationmustchangedirectionfromoneeasycrystallographicdirectiontoanother.ItisevidentfromtheFig. 2-3 that,domainwallrotationhappensinaplaneperpendiculartotheplaneofthedomain,i.e.whenthespinsofthedomainslieinxyplanethedomainwallrotationhappensinyzplane.ThiskindofdomainwalliscalledaBlochwall,whichwasrsttheoreticallypredictedbyF.Blochin1932[ 48 ].(Fig. 2-4 (a)).Butincaseofnanostructuresandmagneticthinlmsaninterestingthinghappenswhenthesamplethicknessbecomescomparabletothethicknessofthedomainwall.Inthesedomainwalls,spinrotationhappensinthesame 28

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planeofthedomainsasevidentfromFig. 2-4 (b).TheistypeofdomainwalliscalledaNeelwall. 2.2.3MagneticHysteresisThemostimportantmagnetizationphenomenaismagnetichysteresis,whichreferstotheirreversiblepathdependentbehaviorofthemagnetizationasafunctionoftheexternalmagneticeldinferromagneticsystems.Hysteresisisacomplexnonlinear,nonequilibriumandnonlocalphenomena.Inmagneticnanostructures,thephysicsofhysteresisisdramaticallydifferentforSD(singledomain)andMD(multidomain)particles.ForSDsystems,themagnetizationreversalinhysteresishappensbyspinrotationonlywhereasforMDstructuresmagnetizationreversalhappensbybothspinrotationanddomainwallmotion.Rotationofspinswithinmagneticmaterialscanbeoftwotypesnamelya)coherentandb)incoherent.Itisclearfromthenamesthatincoherentrotationallthespinsrotatesimultaneouslyandinincoherent,theydonot.Theexchangelength: lex=s A 0M2S(2)isthedistanceoverwhichtheatomicexchangeinteractionsdominateandallspinsrotatecoherently.Usuallylex>RSDinmostofthematerials,sowecansaythatinmostsoftferromagnetsthemechanismofhysteresisisdominatedbyeithercoherentrotationorbydomainwallmotion.HysteresisbyCoherentRotationinSDSystems:IncaseofcoherentrotationwecanassumethewholeSDparticleasagiantspinofmagnetizationM=MSV,Visthevolumeoftheparticle.Nowwhenanexternalmagneticeld(H)isappliedalongtheeasyaxisofmagnetization,thetotalenergyoftheparticlecanbewrittenas: E(H)=KVsin2)]TJ /F7 11.955 Tf 11.95 0 Td[(MSVHcos(2)Hereistheanglebetweentheappliedeldanddirectionofmagnetization.TherstterminEq. 2 comesfromtheanisotropyenergyandthesecondtermfromthe 29

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Figure2-5. Hysteresismechanismbycoherentspinrotationinsingledomain(SD)systems Zeemanenergy.ItisevidentfromthisequationthatE(H)hastwoenergyminimaat=0and=,separatedbytheenergymaximaat=/2.Physicallythe=0(=)correspondstothemagnetizationalong(opposite)theappliedmagneticeld.Thisenergybarrierisdependentontheappliedmagneticeldbythefollowingequationas[ 21 ]: E(H)=KV1H H02(2)whereE+(H)[E)]TJ /F3 11.955 Tf 7.08 1.8 Td[((H)]istheenergybarrierheightforup[down]spins,andH0=2K/MS.TheentirehysteresisloopinSDparticlescanbeexplainedintermsofthistwostateenergyproblem.NowinFig. 2-5 thehysteresisloopisshownwhenthemagneticeldissweptfromalargepositivevaluetoalargenegativevalueandagainfromanegativetopositivevalue.Whenthemagneticeldislarge,(situation(a)inFig. 2-5 )theenergybarrierfordown-spinissmallerthanthethermalenergy,soallspinsmovetoup-spinstateandwehavethepositivesaturationmagnetisation.Insituation(b)ofFig. 2-5 the 30

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magneticeldiszero,soenergybarrierisKV(settingH=0inEqn. 2 )forbothupanddownspinsandmagnetizationislockedatM=MRasenergybarrierislargerthantheavailablethermalenergy.Nowinthesituation(c)(ofFig. 2-5 )HisnegativesoE)]TJ /F3 11.955 Tf 7.08 1.79 Td[((H)willbereduced(Eqn. 2 ),butstilltheenergybarrierforupspinsishigherthantheaveragethermalenergy.Butnowsomeupspins(whoseenergyishigherthanaverageenergykT)canmovetodownspinstatesonetmagnetizationislittlelessthanMR.Theninsituation(d)atH=HCenergybarrierforup-spinsisfurtherreducedandnowthermalenergyequalsenergybarrierandthesamenumberofspinsarepresentinspinupandspindownstates,sothenetmagnetizationiszero.Finallyinsituation(e)ofFig. 2-5 H=-Hmaxandenergybarrierforup-spinsismuchsmallerthanavailablethermalenergy.Soallupspinsmovefromup-spinstatetodown-spinstateandnegativesaturationmagnetizationisachieved.HysteresisbyDomainWallMotioninMDSystems:Inmulti-domainsystemshysteresisoccursbyacombinationofbothcoherentspinrotationandthedomainwallmotion.HerewearetryingtoexplainthehysteresisinMDsystemsbyonlyconsideringthedomainwallmotion.Figure. 2-6 showsthedomainwallmovementsduringthehysteresiscycle.AtthebeginningwhenthemagneticeldisH=+Hmax(situation(a)inFig. 2-6 )allthespinsinthesystemareparalleltoexternalappliedeldwhichgivesrisetopositivesaturationmagnetization(MS).Inthissituationthesamplehasonlyonedomain.Nowinsituation(b)inFig. 2-6 whenthemagneticeldiszeroadomainwallisformedinthesample.Butthisdomainwallisimmobilizedbytheimperfectionsinthesampleandsotheup-spindomainislargerthanthedown-spindomainandthenetmagnetizationisequaltoremanentmagnetization(MR).Thenanegativeexternaleldisappliedandthedomainwallstartstomoveright(situation(c)inFig. 2-6 )andspin-downdomainincreaseswhilespin-updomaindecreasesresultinginanetmagnetizationthatislessthanMR.Insituation(d)inFig. 2-6 ,thenegativemagneticeldequalsthecoerciveeldandtheupanddowndomainnowhavesamesizeso 31

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Figure2-6. Hysteresismechanismbydomainwallmotioninmultidomain(MD)systems thenetmagnetizationiszero.FinallywhenthemagneticeldisdecreasedtoH=-Hmaxthedomainwallhasmovedallthewaytotherightmakingallspinsalignedalongthemagneticeld(situation(e)inFig. 2-6 )andnowthenetmagnetizationequalsthenegativesaturationmagnetization. 2.2.4TemperatureDependenceOfMagnetismInthissectionwearegoingtodiscusshowmagnetizationchangesoverarangeoftemperature.Therearetwomajorwaysofcoolingdownmagneticsample,describedasthezeroeldcooled(ZFC)andtheeldcooled(FC)protocol.IntheZFCprotocol,thesampleiscooleddowntoalowtemperaturewithoutanyappliedmagneticeldandthenasmallmagneticeldisappliedandmagnetizationismeasuredduringwarmup.IntheFCmode,thesampleiscooledinthepresenceofsameexternalmagneticeldandthenmagnetizationismeasuredduringwarmingup.Thetemperature-dependent 32

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Figure2-7. TemperaturedependenceofmagnetizationofaCdTeFeSquantum-dotsamplecomprisingparticlesof4.6nmdiameter curvesofbothFCandZFCmodesareshowninFig. 2-7 foraCdFeTeSquantumdotatanappliedeldof100Oe.ThepointwhereFCandZFCcurvesmergeiscalledtheirreversibletemperature(Tirr).FormostmagneticnanoparticlesTirrissameastheblockingtemeprature(TB).TheFCmagnetizationcanbeeasilyunderstoodsincecoolingthesampleinpresenceofmagneticeldlocksthemagnetizedstate.Afterthatwhensampleiswarmedup,thethermaldisorderinitiatesamix-upbetweenspin-upanddownstateswhichgraduallydecreasesthemagnetizationastemperatureincreases.ButtheZFCmagnetizationcurveneedsalittlemoreattentiontoexplain.Attheatomiclevelmagneticsystemscanbetreatedasatwo-statesystemofspin-upandspin-downstatesseparatedbyanenergybarrier.Asspinupanddownstatesareequallypopulatedathightemperature,spontaneousmagnetizationwillbezerowithoutanyexternalappliedeld.Nowwhenasmallmagneticeldisapplied,smallenergybarrierswill 33

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becrossedbyspin-downtospin-upstateandasmallmagnetizationwillbeachieved.Theniftemperatureisfurtherincreased,theprobabilityofovercomingthelargerbarriersincreasesandmagnetizationincreasesuptoanirreversibilitytemperatureTirr.Butatirreversibletemperaturetheprobabilitiestoovercomethebarrierforspinupanddownbecomenearlyequal.Atthispointspinmixingstartswhichcausesadecreaseinmagnetizationwithfurtherincreaseintemperature. 34

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CHAPTER3EXISTENCEOFFERROMAGNETISMINBIMODALQUANTUMDOTS 3.1MagneticAndFluorescentQuantumDotsTherecentprogressinthesynthesisofcolloidalquantumdots(QDs)hascreatedentirelynewformsofdilutedmagneticsemiconductors,whichcanbeusedinmanybio-medicalapplicationsrangingfrommagneticseparationofcells,proteinsandDNAfragments,bio-imaging,magneticresonanceimaging(MRI)enhancement,targeteddrugdeliveryandhyperthermiacancertherapy[ 13 14 ].Thequantumdotswithcoexistingpropertiesofmagnetismanduorescencecanbeparticularlyveryuseful,asmagnetismenablescontrolofinvivomoleculardistributionthroughMRI,PET,CTorXRDanduorescenceallowsopticalimagingwithdetailedsubcellularinformation.Ontheopticalpart,QD'scanhavepotentialapplicationsduetotheiruniquepropertieslike,easilytunablenarrowemissionspectra,highphotostabilityandbroadexcitationfrequency.EspeciallytheNIR(nearinfrared)QDs(emittingwithin650-900nm)arehighlyinterestingfortheirlowabsorptionandautouorescencefrommostanimaltissuesinthisregion[ 49 50 ].Onthemagneticpart,super-paramagneticnanoparticlesofironoxide(SPIO)arelargelyusedinclinicalimagingasanFDAapprovedMRIcontrastagent[ 51 ].Variousstrategieshavebeenusedtocombineuorescenceandmagnetismincluding,incorporationofmagneticanduorescentnanoparticlesintosilicaorpolystyrenebeads,dopingQDswithparamagneticions,encapsulatingQDswithSPIOparticlesetc[ 52 53 ].OnemajorproblemofmultimodalQDisretainingtheirperformanceforallthemodalities,whichneedscarefuldesign,correctsynthesismethodology[ 54 ],chemicalstabilityandmethodstopreventsubsequentaggregation.Althoughfewstudiesexistonquantumnano-structureswithbothuorescenceandmagneticproperties[ 55 56 ],mostofthesequantumdotsweresynthesizedbyusingorganometallicsolvents.Butforbio-medicalapplicationsitisdesirabletohaveQDsfabricatedinaqueoussystemswhichemitin 35

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theNIRwavelengthregimeandalsoretaintheirmagneticproperties.TherehavebeensomepreviousstudieswithQDsthatemitinthevisibleregime[ 57 ].Inthissectionwewilldiscussthesynthesis,magneticmeasurementalongwithopticalandMRIstudiesofhighquality,vis-NIRemitting,magneticandwaterdispersibleFedopedQDsusingahydrothermalsynthesistechnique[ 58 ].InthiscollaborativestudysynthesisoftheQDsalongwiththeiropticalmeasurementsweredonebyDr.A.K.SahaandDr.P.SharmawithProf.B.M.Moudgil.HydrothermalsynthesisisanefcienttechniqueofmakingwatersolubleQDswheretheyarepreparedusingwaterintheautoclavesatahightemperature.AftergrowingtheseQDs,theyarecoatedwithanon-toxicN-Acetyl-Cysteine(NAC)stabilizerwhichbio-chemicallyattractedtoward-COOHgroupandhelpsinbioconjugationfortargeteddelivery.ThismethodallowsthesynthesisofmagneticNIRquantumdotswithoutusingthetoxicsurfactantsusedintheorganometallicsynthesisprocedures.Tothebestofourknowledgethisisthersttimewater-dispersiblebi-modal(magneticanduorescent)QDshavebeensynthesizedbyhydrothermaltechniqueforbioimagingapplications.TheseQDsemitinthe560-740nmwavelengthregimeswithauorescenceefciencyof40-60%.Itispossibletosynthesizestablequantumdotsupto750nmusingthishydrothermaltechnique. 3.2ExperimentalDetailsThefollowingmaterialswereusedtomakethisbi-modalquantumdot:CdCl2(99.7%Fisher),FeCl24H2O,N-Acetyl-Cysteine(NAC)(99%Sigma),telluriumpowder(200mesh,99%Acros),sodiumborohydride(99%Acros)andsodiumhydroxide(99%Fisher). 3.2.1SynthesisThesynthesisprocessperformedintheMoudgillab,isshowninaow-chartinthefollowingFig. 3-1 .Initiallythesodiumhydrogentelluride(NaHTe)waspreparedfromNaBH4andtelluriumpowder(withamolarratio2:1)inArgonpurgeddistilled(DI)water.ThenthisNaBH4/Tesolutionwasagedinrefrigeratorformorethan8hrs(at4C)for 36

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Figure3-1. Preparationow-chartofCdTeFeSQDbyhydro-synthesis thereactiontobecompleted.Inaseparate250mlroundbottomaskCdCl2(30mM)solutionof100mlDIwasprepared.N-Acetyl-Cysteine(NAC)andFeCl24H2OwereaddedtothesolutionsothatCd:NACandCd:Femolarratioswere1:2.5and8.5:1respectively.ThissolutionwasthenbubbledwithpureArgongasformorethan30minwhilesubsequentlyaddingNaHTewhichmakesthecolorofthewholesolutionwinered.ThepHofthissolutionwasadjustedto(8.0-8.4)byusing2MNaOHfollowedbyheatingthesolutioninseveral23mlpolytetrauoroethylene(PTFE)linedautoclaves(Parraciddigestionbombs)inbatchesof10mlataconstanttemperatureof180C.Theautoclaveswerecooledbypassingcoldwateraroundthemaftertheheating.TheQDspreparedinthistechniqueweretakenoutandthencharacterizedafterwashing.FinallytheseQDswerewashedbycentrifugingthemat2600rpmfor4-5minutesinthe`AmiconUltra-15CentrifugalFilterUnit',whichwasusedwithamembranesuitablefor30kiloDaltonproteinltration. 37

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3.2.2CharacterizationExceptthemagneticmeasurementusingSQUID(superconductingquantuminterferencedevice)allothercharacterizationtechniqueswereperformedbyDr.A.K.SahafromProf.B.M.Moudgillab.SpectraMaxM5wasusedforultraviolet-visibleabsorptionemissionspectraatroomtemperature.ThePLquantumyields(QYs)oftheQDsweredeterminedatroomtemperaturebycomparingwithRhodamine-6ginethanolwhichwastakenas95%[ 59 ].TheopticalabsorbanceofRhodamine-6gandtheQDswereadjustedtolessthan0.1forQYdetermination.JEOL2010Foperatingat200kVwasusedforHRTEMoftheQDs.TheTEMsamplepreparationsweredonebydroppingthenanoparticlessuspendedinwateroncarboncoatedCugrids(01813-FTedPellaInc.,USA)anddriedovernightatroomtemperature.ThesameTEMmicroscopeandsampleswereusedforEDXanalysisoftheQDs.Inductivelycoupledplasmaopticalemissionspectrometer(ICP-AESPerkinElmerOptima3200RL)wasusedtodeterminethechemicalcompositionoftheQDsandcomparedwiththedataobtainedfromEDXanalysis.Thedesiredconcentrationoftheelementsfortheanalysiswasobtainedbydrying500loftheQDsovernightatroomtemperatureandthenbydissolvingthemin2-3mlaquaregiaanddilutingtheresultingsolutiontoavolumeof10mlusingdistilledwater.ThepowderdiffractionpatternsfortheQDswereachievedusingaPhilipsX-raydiffractometerAPD3720usingCuKradiation.TheX-raypatternswereobtainedbyvaryingthe2valuesfrom20to130.ForXPSstudiesPerkingElmer5100XPSsystemhasbeenusedandsampleswerepreparedbydroppingQDsuspensionson1mm1mmsiliconwafersatroomtemperatureandallowingthesamplestodryinopenairfor24hours. 38

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Allmagneticmeasurementsweretakeninourlabusingaquantumdesign(MPMS-5S)SQUID.Magnetichysteresiscurvesweremeasuredatdifferenttemperaturesrangingfrom10Kto300Kandtemperaturedependenceofmagnetizationwasalsoperformed.Non-magneticlterpaperwassoakedwith15Lliquidsampleandplacedinsidenon-magneticemptygelatincapsules.ThesegelatincapsuleswerefurthermountedonthemeasuringstrawinsideSQUID.Theexternalmagneticeldwasvariedwithintherange5Tatconstanttemperature. 3.3ResultsAndDiscussion 3.3.1OpticalMeasurementsReactiontemperature,pH,reactantconcentration,reactiontime,andCd2+concentrationhavegreateffectonthequalityofthepreparedQDs.FirstwestudiedtheeffectofpHconcentrationonquantumyield(QY)oftheseQDs,whichindicatesthepHrangingbetween8.1-8.4ismostoptimalforthebestquantumyield.TheCd:Femolarratiowaskeptconstantat8.5:1.AdditionofexcessFeledtotheuorescentquenchingoftheQDs.Thesolutionswereheatedfortimeintervalsrangingbetween30-100minutesat180C.HeatingfordifferenttimeintervalsproducedQDswithPLemissionwavelengthsvaryingwithin560-740nm(Fig. 3-2 ).HeatingtheQDsformorethan100minutesproducedagglomerationandsubsequentquenchingoftheQDuorescence.Thisphenomenonmaybecausedbyhydrolysisandsubsequentdecompositionofthethiols.ThisdecompositioneventuallyleadstothedepletionofligandsrequiredtostabilizetheQDsatthelaterstageofthereaction. 3.3.2TEM,XRDAndEDSStudyTheQDswerecharacterizedusingXRD,TEM,EDXandXenogenIVISSpectrumBiophotonicImager.ThequantumyieldfortheFedopedCdTeSdotsemittinginthe560-740nmregionvariedwithin40-60%.Fig. 3-2 showstheemissiontunabilityofthedots.TEMimages(Fig. 3-3 )wereusedtocalculatethesizeoftheQDswhichrangeswithin3-6nm.TEMimagesalsoconrmsomekindofcrystalstructureintheQDs, 39

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Figure3-2. AbsorbanceandPLemissionpeaksforFedopedCdTeSQDswhenexcitedat300nm whichisclearfromthepresenceoflatticefringes.XRDonbothundopedandFedopedQDswasperformedandshowninFig. 3-4 .Asitisevidentfromtheimage(Fig. 3-4 ),sharpnessofthepeakshasbeendeterioratedinFe-dopedQDs,whichisanindicationofcrystalstructurechange.Thisisconrmedbychangeofd111valuefrom3.59AinundopedQDsto4.71AforFedopedQDs.ThechangeofthelatticeparameterwithFedopingindicatesthestructuralmodicationoftheQDswhichistheprobablecausethatledtotheshapechangeintheXRDpeakofthedopedQDs.Afterthesemeasurements 40

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Figure3-3. TEMimageofFedopedCdTeSQDsemittingat730nm Figure3-4. XRDofFedopedandundopedCdTeSQDs 41

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Figure3-5. EDSspectrafortheFe-dopedCdTeSemittingat740nm Table3-1. EDSandICPanalysisoftheFe-dopedQDs.Numbersarepresentasatomic% MethodSampleCdTeFeS ICPQD73046.91.510.60.33.10.139.4EDSQD73051.60.89.71.9-38.81.9ICPQD74044.40.311.10.25.60.139.0EDSQD74049.41.110.80.74.50.735.40.8 EDXandICPanalysiswerecarriedouttondoutthechemicalcompositionoftheQDs.BoththeEDSandICPanalysisconrmedthepresenceofFeintheQDswhichisshowninFig. 3-5 andTable 3-1 respectively.ICPmeasurementshows3.1at%and5.6at%FeispresentinQD730andQD740respectively.EDXtechniquecalculates4.5at%FeinQD740,butdidnotshowthepresenceofFeinQD730,mostlikelybecausetheFepresentinQD730isbelowthedetectionlimitofEDS.TheFedopedQDswerealsoanalyzedusingXPSafterthesampleswithAretchingfor0,10and15minutes,whichareillustratedinFig. 3-6 .ThetypicalpeaksoftheelementsCdandTecomesfromthefollowingbindingenergies:Cd3d5=2(404.9eV),Cd3d3=2(411.8eV),Te3d5=2(572.2eV)Te3d3=2(582.6eV).TheS2ppeak161.4eVindicatesthepresenceofmonosulde(S2)]TJ /F1 11.955 Tf 7.08 -4.34 Td[(),whichismostlikelycreatedduetobrokenCdSorFeSbondsduringAretching.TheFe2p3=2peakat708.6eVsigniesthepresenceofFe(II)Sinthematerial[ 60 ]. 3.3.3MagneticMeasurementsMagnetizationloopmeasurementsoftheQDsusingaSQUIDshowtheabsenceofhysteresisatroomtemperaturetherebyindicatingthattheFe-dopedQDsaresuperparamagneticatroomtemperature(Fig. 3-7 ).Themagnetizationsarenormalized 42

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(a) (b) (c) (d) Figure3-6. XPSspectrafor(a)Cd(b)Fe(c)Teand(d)SinFe-dopedQD710 tototalsampleweight.Saturationmagnetizationmeasurements(MS)werecarriedoutforQDsemittingatvariouswavelengthsinthe650-740nmrangeattemperatures10Kand300K.QDsemittingbetween650-740nmexhibitedsignicantchangesinmagnetizationwhensubjectedtoavaryingexternalmagneticeldof-5Tto5Tatconstanttemperature.ThesaturationmagnetizationvaluesoftheFe-dopedQDsandcommercialFeridexNP'saredisplayedinFig. 3-7 andFig. 3-9 (a)respectively.Saturationmagnetizationsaremeasuredintermsofemu/totalweightofthesampleingrams.At10KtheMsvaluesrangefrom3.5emu/gmforQD650,1.6emu/gmforQD730,1.9emu/gmforQD740and12.1emu/gmforcommercialFeridexI.V.,whileat300Kthesevalueschangeto2.8emu/gmforQD650,1.5emu/gmforQD730, 43

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(a) (b) (c) Figure3-7. Hysteresisloopsmeasuredforthequantumdotswithemissionpeakof(a)670nm,(b)730nm&(c)740nm 1.6emu/gmforQD740and7.3emu/gmforcommercialFeridexI.V.NowwhenwerememberthatQD730,QD740andFeridexI.V.containsonly2.2,3.9and10.4weight%ofFe,thentheseMSvaluessignicantlychangewhenwecalculateemu/gmonlyforFepresent.AfterdoingthecalculationsthesaturationmagtetizationcomesoutmuchhigheraspresentedinTable 3-2 44

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Figure3-8. Comparisonofmagnetizationofindicatedquantumdotsmeasuredat10K.Allmagnetizationvaluesareinemu/gmconsideringtheweightofthetotalsample,notonlytheFeweight. Table3-2. SaturationmagnetizationvaluesforindicatednanoparticlesandcommercialFeridexI.V.Allthemagnetizationvaluesareinemu/gmcalculatedconsideringonlyweightofFe. SampleMS@10KMS@300K QD7308076QD7408572FeridexI.V.11972 Thus,weseethattheMSvaluesobtainedfortheFe-dopedQDsarecomparabletothoseofFeridexI.V.Noneoftheparticlestestedexhibitedcoercivityatroomtemperatureindicatingtheirsuperparamagneticbehavioratroomtemperature.Althoughsuperparamangeticatroomtemperature,alltheMNP's(MagneticNanoParticles)showhysteresisloopswithnon-zerocoerciveelds(FIg 3-8 )at10K.The10Kmagnetizationloopsshowhysteresiswithcoerciveeldsrangingwithin240to280Oeforallthesenano-particles,whilethecoerciveeldofcommercialFeridexI.V.cameoutHC90Oeat10K.Althoughnotgrownusinghydrosythesistechniques,therehasbeensomepreviousstudiesonmagneticnanoparticles(MNPs)growninorganicsolvents,whichshowslargehystereisloopsin16nmMNPsofCoFe2O4at 45

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(a) (b) Figure3-9. FeridexNPsmeasuredatSQUID(a)MvsHatxedtemperatures,(b)MvTmeasurementatsmallconstanteld80Oe. both10Kand300K[ 61 ].WhiletheMvsHmeasurements(Fig. 3-7 )weredonebyvaryingmagneticeldataconstanttemperature,MvsTmeasurementswerealsodonebyvaryingtemperaturefrom10to300Katsmallxedmagneticeldof80Oe.WhenMvsHcurvesprovidedinformationonthesaturationmagnetizationandcoercivity,theeld-cooled(FC)andzeroeld-cooled(ZFC)MvsTmeasurementsprovidedinformationontheblockingtemperature(TB),Curietemperature(TC)andBlochparameter(P)oftheNPs[Fig. 3-7 andFig. 3-10 ].ThetemperaturedependentmagnetizationsforbothFCandzero-eld-cooledZFCcaseswereplottedforallthesamplesvizQD670,QDQD730,QD740andFeridexI.V.NPs[Fig. 3-10 andFig. 3-9 (b)].PeakoftheZFCMvsTcurveswereusedtondtheblockingtemperatures(TB)fortheNPs.Asthesampleswereheatedthetransitionfromferromagnetismtosuperparamagnetismoccurredattheblockingtemperature.Blockingtemperatureisthepointbelowwhichthefreemagneticmomentsofthesamplesget'blocked'bytheirmagneticanisotropicenergy,whichleadstoferromagneticbehaviors.Theblockingtemperaturesofallthesesampleswerefoundtoliebetween150to200K(200KforQD670,190KforQD730and150KforQD740),whichmakesthemsuperparamangeticatroomtemperature.TheTBvalueforFeridexI.V.wasfoundtobeevenlower70K. 46

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(a) (b) (c) Figure3-10. TemperaturedependenceofMagnetizationforthequantumdotswithemissionpeaksof(a)670nm,(b)730nm&(c)740nm.ZFCandFCcurvesareindicatedwithineachgraph. 47

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ByttingtheFCcurvewithBloch'sT3=2equation(seethickbluelinesofFig. 3-10 andFig. 3-9 (b))intheregion10Kup-to200K(i.e.intheregion,T<
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highquantumyieldandrobustmagneticpropertyandtheyaresynthesizedusingeasyandefcientaqueoustechnique. 49

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CHAPTER4FERROMAGNETISMINBILAYERSOFPALLADIUM/C60 4.1MagnetismOfPalladiumMagneticmaterialsatnanoscaledimensionshavebeenintensivelystudiedinthelastdecadeinconnectionwiththerecentprogressininformationtechnologyandtheneedforhigh-densitymagneticstoragemedia[ 62 63 ].Whilethemagneticpropertiesofthinlmtransitionmetalsarealteredbystrain/stressviasubstratecoupling,onthenanometerscaleatomsatthesurfacecreatehighdensitydanglingbondswhichcarryunpairedelectronsandchangethemagneticpropertiesofthematerial[ 64 67 ].Recently,nanoparticlesofnon-ferromagnetictransitionmetalshavebeenpushedtotheferromangeticlimitbybondengineeringatthesurface[ 67 70 ].Thusunderstandingoftheoriginoftheconversionofbulknonmagnetictonanoscaleferromagnetictransitionsnotonlyoffersinterestingphysicsbutisalsocrucialforimprovedcontrolofthemagneticproperties[ 71 73 ]ofmaterialsinreduceddimensions.TheelementsGd,Fe,CoandNiareferromagneticwithStonerparameterslargerthanone.AlthoughferromagneticNiandparamagneticPdareinthesamecolumnofthePeriodicTableandhavesimilarelectronicstructure,onlyNihasadensityofstatesattheFermilevelhighenoughtofullltheStonercriterionforferromagnetism[ 74 ]whilenon-ferromagneticPdwithaStonerfactorof0.873liesclosetotheferromagneticinstabilitywheretheStonerfactorisunity.However,Pdhasalargeelectrondensityofstates(DOS)attheFermienergyandasharp4dpeakintheDOSjustbelowtheFermienergy,therebymakingPdmagneticallyverysensitivetoexternalinuences.DuetoitslargeStonerfactor,Pdisthusconsideredtobeonthethresholdofferromagnetism,andadjustmentofitsmagneticpropertiestobringitoverthisthresholdhasattractedmuchattention.Forexample,Sinoharaetal.[ 75 ]andTaniyamaetal.[ 76 ]observedsurfaceferromagnetismwithmagneticmoment0.230.19B/PdatomandCurietemperatureTCnear540KinPdnanoparticleswithanaveragesizeof5to10nm 50

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preparedbyagasevaporationmethod.Ferromagnetismwasproposedtobeassociatedwiththetopfewsurfaceatomiclayerson(100)facets.Hugeretal.[ 77 ]demonstratedferromagnetismwhenPdisbondedtothe(001)facetofNb.FurtherMendozaetal.[ 78 ]reportedblockingtemperaturesofabout450Kforquasi-two-dimensionalPdembeddedinagraphitematrix,therebysuggestingaTCgreaterthan450K.Thereisalsoonestudywherepolymeric-likeparticlesofC60Pdnprecipitatedfromchemicalsolutionshaveshownferromagneticpropertieswithasaturatedmomentofabout0.04emu/gm[ 79 ].InthissectionwearegoingtodiscussmagneticpropertiesofPdnanoparticlesembeddedinC60alongwithdensityfunctionaltheory(DFT)calculationstosupportourexperiment[ 80 ].DFTcalculationsweredonebyourcollaboratorsDr.HasanSahinandProf.F.M.Peeters.ThesequentialgrowthofPd/C60bilayersprovidesanovelroutetoobtainlayerednanosizedPdparticles(clusters)embeddedinalayeredC60host.Firstly,thelargesizemismatchbetweenPdatomsandC60moleculespromotesinterdiffusionatthePd/C60interface.Secondly,incontrasttothealkaliandalkalineearthmetals,whichreadilyformstoichiometriccompoundswithC60,thetransitionmetalshaveahighcohesionenergywhichfavorstheformationofclustersratherthancompoundswhenreactedwithC60[ 81 ].Densityfunctionaltheory(DFT)calculationsareperformedtounderstandthenatureandtheoriginoftheresultingferromagnetism.Wenote,asconrmedbyDFT,thatPdandC60inbothbulkandthinlmformarenon-ferromagneticintheabsenceofinteraction.However,wheninteractionisinducedbycloseproximityofPdatomstoC60molecules,DFTrevealsachargetransferfromPdtoC60ofapproximately0.06e.ThischargetransferisconsistentwiththewellknownhighelectronafnityofC60.Interestingly,thechargetransferisnotthecauseofferromagnetism,ratherthereisanincreaseintheStonerparameterofthePdduetothecloseproximityofC60tothedisorderedPdlayers.Thecalculationsshowthatwhenincludinginteractiontherearethreecongurationsthatleadtosignicantferromagnetism,namely:(1)singlePdatoms 51

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interactingwithaC60moleculeattachedtoaPdslab,(2)thedirectinteractionofC60moleculeswithPdstepedgesand(3)theformationofvariousPdclustersbetweenC60molecules. 4.2ExperimentalAndTheoreticalDetailsPd/C60bilayerscomprisingsequentiallygrown8A-thicksputterdepositedPdlmsfollowedby40A-thickthermallysublimatedC60lmsweregrownontoatomicallyatc-planesapphiresubstrates.ThesputteringofPdwasperformedat12Wattdcpowerinanargonenvironment(10sccmowrate)at110)]TJ /F2 7.97 Tf 6.59 0 Td[(8Torrpressure,andthethermalsublimationoftheC60wasfromaluminacruciblesmaintainedat400Cinapressureof110)]TJ /F2 7.97 Tf 6.58 0 Td[(7Torr.ThelayersofPdandC60weregrownsequentiallywithinthesamegrowthchamber(10)]TJ /F2 7.97 Tf 6.59 0 Td[(9Torrbasepressure)withoutbreakingvacuum.Duringthegrowth,thethicknessoftheindividuallayerswasmeasuredusingacalibratedcrystalmonitor,andtheabove-describedPd/C60bilayerwasrepeated33timestoenhancethesignalofmagneticmeasurements.Across-sectionalschematicofaportion(4bilayers)ofthelayeredstructureisshowninFig. 4-1 .Finally,the33bilayeredstructureofPd/C60wascoveredwitha100A-thickPdcappinglmtoprotectthestructurefromatmosphericexposure.Wefabricatedtwosetsofsamples,oneatroomtemperatureandasecondatlowertemperatures(250K),andfoundthemagneticpropertiestobeindependentofthesesamplegrowthtemperatures.ThemultilayerstructureofPd/C60wasconrmedusingAugerelectronspectroscopy(AES)witha5keVsource.ThesamplewasetchedduringAESmeasurementusingArbombardmentat3keVatbasepressureof10)]TJ /F2 7.97 Tf 6.59 0 Td[(9Torr.Sampleswerefurtheranalyzedusingatomicforcemicroscopy(AFM)toobtainaquantitativemeasureofsurfaceroughness.ThemagneticpropertiesofPd/C60bilayersweremeasuredusingaQuantumDesignmagneticpropertymeasurementsystem(MPMS)attemperaturesintherange5-300Kandmagneticeldsintherange0to50kOe. 52

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Figure4-1. SchematicillustrationofasequentiallygrownstructureconsistingofsputtergrownPdandthermallysublimatedC60layers. OurtheoreticalanalysisoftheinteractionatthePd/C60interfacetakesintoaccountthestructuralandelectronicpropertiesofthePdandC60andutilizesrst-principlesplane-wavecalculations[ 82 83 ]withindensityfunctionaltheory(DFT).Theexchangecorrelationpotentialiscalculatedusingthelocaldensityapproximation(LDA)[ 84 ].Intheself-consistenteldpotentialandtotalenergycalculationsofperiodicallyrepeatingPd/C60structuresasetof(11x11x3)k-pointsamplingisusedforBrillouinZone(BZ)integrationink-space.Herethek-pointmeshisgeneratedbytheMonkhorst-Packscheme[ 85 ].Thekineticenergycutoff~2jk+Gj2=2mfortheplane-wavebasissetistakenas500eV.Theconvergencecriterionofourselfconsistentcalculationswassetto10)]TJ /F2 7.97 Tf 6.59 0 Td[(5eVforthetotalenergyvalues.Pressureonthelatticeunitcellwasdecreasedtovalueslessthan0.5kB.Fermilevelsmearingistakenas0.1eVforgeometryoptimizationand0.01eVforaccurateelectronicstructurecalculations.Byusingtheconjugategradientmethod,allatomicpositionsandunitcellsoftheconsideredmultilayerstructureswereoptimizeduntiltheatomicforceswerelessthan0.05eV/A.ForthecalculationofmoleculesandC60attachedsurfaces,interactionsbetweenneighboringunitcellatomsarehinderedbyusingatleast10Avacuumspacing.For 53

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consistencychecksandthedeterminationofaccuratechargedensityprolesofthePd/C60-Pdsurfacesystem,wealsoperformedaBaderanalysis[ 86 ]. 4.3ResultsAndDiscussionOursamplecharacterizationstartedwiththestudyofsurfacecontaminationusingAugerElectronSpectroscopy(AES)whichclearlyshowsthereisnomagneticsurfacecontaminationupto0.01at%or100ppm.Asseeningure 4-2 (a)&(b),thesurfaceofthePd/C60sampleshowsmostlypalladium(82%elementalconcentration)andsomesulphur(12%elementalconcentration)andnitrogen(7%elementalconcentration)impurities.Furtherstudyshows(gure 4-2 (c)&(d)),afteretching100AmaterialusingArgonion-etchingfromthesurfaceofPd/C60samples,elementalconcentrationsignicantlychangeswhereelementcarbondominates(85%elementalconcentration)alongwithsomepalladium(10%elementalconcentration)andusualimpuritiesofsulphur,nitrogenandoxygen(1%elementalconcentrationeach).Surfacecontaminationsclearlyreducedafteretching100Amaterialfromthesurface,whichisexpected.FollowingthestudyofelementalconcentrationonthesurfaceweusedAESsputterprolingtomeasuretheconcentrateonlyrelativeconcentrationofpalladiumandcarbontoconrmthesupposedlayeredstructureofPd/C60samples.InFig. 4-3 ,wedisplaytheAESsputterproledatatakenonourPd/C60samples.Althoughthe180out-of-phaseconcentrationmodulationsrevealalayeredstructure,wenotethatthePdandCconcentrationsgothroughaminimumratherthantozero.ThiseffectcanbeexplainedbythecloseproximityofPdandCAugerpeaks;themutualoverlapofthePdandCpeaksgivesrisetoaconstantbackgroundcontributiontotheC(Pd)peakwhenPd(C)goesthroughamaximum.WealsoexpectthesharpnessofthePd/C60interfacetobecompromisedbysomediffusionofthePdatomsintotheinterstitialspacesbetweenC60moleculesasshownschematicallyinFig. 4-1 andaswouldbeexpectedbecauseofthelargesize 54

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Figure4-2. (a)and(b)showsAugerElectronSpectroscopyonsurfaceofPd/C60sampleswhichshowsmostlypalladiumasexpected,(c)and(d)showsAugerElectronSpectroscopyafteretching100AmaterialfromthesurfaceofPd/C60samples,whichshowshigherconcentrationofcarbon. mismatchbetweenthemetalatomsandtheC60molecules,whichcanleadtoroughsurfacesinoursamples.FurtherstudyofsurfaceroughnessmeasurementbyatomicforcemicroscopyconrmstheprevioushypothesiswheresurfaceroughnessofPd/C60sampleswerefoundtobe5-8nmrms.Thisroughsurfaceisquiteconsistentwiththeafore-mentionedtransitionmetalclustering[ 81 ]andalsowithpreviousworkonCu/C60systems[ 87 ],wheresurfaceroughnesswasfoundtobe4nmrms.FurtherstudyisunderwaytondoutmoreevidenceofthelayeredstructureofPd/C60samples,usingtransmissionelectronmicroscopy(TEM)techniques.ThemagneticpropertiesoftheC60/Pdbilayersweremeasuredwitheldsappliedalongtheplaneofthelms.Fromthehighelddatathediamagneticcontribution 55

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Figure4-3. Carbon(solidtriangles)andPd(solidsquares)concentrationsversussampleetchingtimemeasuredbysputterAugerElectronSpectroscopyonPd/C60samples.Themaximum(minimum)positionsofthePdpeakscoincidewiththeminimum(maximum)positionsoftheCpeaks,thusconrmingthelayeredstructureofPd/C60. fromthesapphiresubstrateswasdeterminedandsubtractedfromtherawdata.Magnetizationversuseld(M-H)dataatxedtemperatureareplottedinFig. 4-4 (a)aftersubtractingthediamagneticcontribution.WenotethattheM-Hloopshavehysteresisuptoeldsashighas800Oe.Thecoerciveelds,HC50Oe,areessentiallyindependentoftemperatureimplyingthattheCurietemperatureTCismuchhigherthanroomtemperature.WealsonotethattheM-HcurvesinFig. 4-4 (a)scalelinearlyathigheldswithoutanysignofsaturation.Thislinearelddependenceofthemagnetizationisrelatedtotheparamagnetisminthesystem,i.eparamagneticPd,andhencethetotalmagnetizationisasuperpositionoftheferromagneticsignalfromPdclustersinclosevicinitytotheC60moleculestogetherwiththeparamagneticsignalassociatedwiththe100Athickcappinglayer.WesubtractedtheparamagneticcontributionusingthetemperaturedependentPauliparamagneticsusceptibilityofbulkpalladium(Pd)[ 88 ].Aftersubtractingtheparamagneticcontributionassociatedwiththe100A-thickcappinglayer,weobtainedthesaturatedhysteresisloopshowninFig. 4-4 (b).Asthetemperaturedependence 56

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Figure4-4. MagnetichysteresisloopmeasurementonPd/C60atdifferenttemperatures.Hysteresisloopsplottedattheindicatedtemperatures(a)beforeand(b)aftersubtractionofthelinearparamagneticbackground. ofPdisverysmall,aftersubtractionMSvaluesareveryclosetoeachother.Wethenusedtheresultingsaturationmagnetizationvalue,MS=1.810)]TJ /F2 7.97 Tf 6.58 0 Td[(5emushownintheguretondthemagnetization/Pdatom.Dividingthissaturationvaluewiththenumberofnanoclusteredpalladiumatomsyields0.042Bperpalladiumatom.WenotethatonlythenanoclusteredPdatomsareconsideredbecauseclearlythe100Athickcappinglayerisnotthesourceoftheferromagneticsignal.Inpreviousworks,Angappaneet.al.reportedMSvaluesrangingfrom0.006to0.021B/PdatomandObaet.al.reportedvaluesrangingfrom0.009to0.019B/Pd[ 89 90 ].Accordinglyourexperimentalsaturationmagnetizationvalueof0.042B/Pdatomcloselyresemblespreviouslyreportedvalues.InFig. 4-5 weshowthetemperaturedependenceofthemagnetizationfrom300Kdownto10K.Here,thePd/C60systemwasmeasuredby(i)coolingfrom300Kto10Kinanappliedeldof100Oe,andmeasuringthemagnetizationduringwarm-upfrom10Kto300K(eld-cooled(FC)curve)andthen(ii)coolingthesampleinzeromagneticeldandmeasuringthemagnetizationinanappliedeldof100Oeduringwarm-up(zero-eld-cooled(ZFC)curve).FittingtheFCcurvetothedata(openredsquares)withapower-lawdependence[ 91 ],M=M0(1)]TJ /F6 11.955 Tf 12.57 0 Td[((T=TC))(solidblueline), 57

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Figure4-5. TemperaturedependenceofthemagnetizationofPd/C60measuredatH=100Oeforeldcooled( openredsquares )andzeroeldcooled( openblackcircles )conditions yieldsaspontaneousmagnetizationM01.810)]TJ /F2 7.97 Tf 6.59 0 Td[(6emu,aTCnear570Kandapower2.10.4.ACurietemperaturewellaboveroomtemperatureisconsistentwiththetemperature-independentmagnetizationloopsinFig. 4-4 .Here,thevalueofprovidesinformationaboutthenatureoftheferromagneticmaterial;specicallywhenisaround3/2(BlochLaw)theferromagnetismisrelatedtobulkorthinlmferromagnets(3D-2D)whereasfor2themagnetisminthesystemisassociatedwithnanoclusterformation[ 91 ].Ournding(Fig. 4-5 )thathasavaluenear2suggeststhatferromagnetisminoursystemismostlyassociatedwithPdinnanoclusterform.Althoughtheobservedferromagnetismisassociatedwithnanoclusters,theseclustersareconnected;otherwisedisconnectednanoclusterswould,attemperatureshigherthantheblockingtemperature,haveshownsuperparamagnetismmarkedbyanabsenceofhysteresistogetherwithacollapseofthemagnetizationdataonthesamecurvewhenplottedagainstthescalingparameterH=T.AnotherinterestingfeatureofM-TdataisthesuddendipintheFCcurvenearT=60K.ThisbehaviorisunusualforFCmagnetizationswhereMusuallyincreaseswithdecreasingtemperature.Wenotehoweverthatthereisawellknownpeakin 58

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themagneticsusceptibilityofbulkPdnear80K[ 92 ]whichisalsoseeninthesametemperaturerangeinmagnetocapacitancestudiesofPd/AlOx/Pdtrilayers[ 93 ].Thepercentageofmagnetizationreductionisalsoremainswithin11-13%forbothourPd/C60structureandpurepalladium.Theselattermagnetocapacitancestudiesaresensitivetosurfacemagnetismwhichispresumablydominantatthenumerousinterfacesofourmultiplebilayerstructures.Accordingly,weexpectfeaturesfrommagnetismnear60-80KinbothbulkPd(cappinglayer)andfromthemultiplePdsurfaces.Paladiumisaparticularlygoodcandidatefortheobservationofsucheffectsbecauseofthepronouncedtemperature-dependentstructureinthedensityofstatesneartheFermienergy[ 92 93 ]. 4.4ComputationalStudyTounderstandtheoriginoftheferromagnetismmeasuredinourPd/C60bilayers,ourcollaborators(Dr.HasanSahinandProf.F.M.Peeters)adoptdensityfunctionaltheory(DFT)calculationsusingthemethodsmentionedearlier.PriortoanalyzingtheinteractionbetweenPdandC60,werstcalculatethestructuralandmagneticpropertiesofbulkPdandthepristinePd(100)surface(comprisingfourlayersofPd)byusingexchangecorrelationfunctionalswithinthelocaldensityapproximation.ThePd4d95s1andC2s22p2electroniccongurationsaretreatedasvalencestates.ToobtaintheaccurateexcitedstatesandbondingstatesofPd,theelectroniccongurationof4d95s1givesmorereasonableresultsthanthe4d10conguration.SincethesinglePdatomisnonmagneticinitsgroundstate,40meVexcessenergyisneededtoinduce0.15BperPdatom.ForbulkfccPd,thelatticeconstantandPd-Pddistancearecalculatedtobe3.86and2.72Arespectively.However,whenPdatomsareassembledtoformafcclattice,theferromagneticandnonmagneticstatesbecomealmostdegeneratewithaslightpreferenceforthenon-magneticgroundstate.ForathickPdlayeredstructure(Fig. 4-6 (a))thenonmagneticandspinpolarizedstates(with0.15BperPd)areenergeticallywithin2-3meVofeachother. 59

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TheseconsiderationsimplytheincreasedmagneticsensitivityofPdatomstosmallperturbationsviathePd-Pdinteraction.Next,webuilda6x6supercellofPd(100)surfaceforeachC60molecule.WefoundthatfourlayersofPd(100)lmhaveatypical2.72AinterlayerPd-Pddistance.However,uponfullrelaxationoftheslabbytheconjugategradientmethod,thelayer-layerdistancedecreasesto2.67A.Asexpected,thePdlmshowsmetallicbehaviorandhasasshowninFig. 4-6 (b)degenerateferromagnetic(FM)andnonmagnetic(NM)groundstatesassociatedwithitsbulkstructure.TheC60molecule(fullerene)iscomposedentirelyofcarbon,takingtheformofahollowsphere.Eachcarbonatomhasthreesp2hybridizedorbitalsandonehalflledpzorbital.Duetothestrongsp2bonds,theC60moleculeisnotveryreactive.WecalculatethatthemeanballdiameterofaC60moleculeis7.05AandthattheC-Cbondsare1.39and1.44Arespectivelyalongthehexagonandpentagonedges.HalflledpzorbitalsofnearestneighborCatomsform-bondsandhencepairtheirspinsresultinginanon-magneticgroundstate.WealsoexaminedthemagneticstateofseveralcongurationsoftwointeractingC60molecules(dimers)andconrmedthatthereisnonetspinpolarization.FullerenemoleculeshaveanonmagneticgroundstateandtheoriginoftheferromagnetismcannotbeC60itself.WealsocheckedthepossibleeffectsofsurfacePdatomsattachedtoC60moleculesortoPd(100)surfaces.EachsinglePdatomattachestoaC60moleculeonitsbridgesite(ontopoftheC-Cbond)with2.4eVbindingenergy.AsinglePdatomadsorbedontoaC60moleculehaszeronetmagneticmoment.HowevermissingPdatomsdon'tbreakthedegeneracyoftheferromagnetic(FM)andnonmagnetic(NM)states,andthedifferencebetweentheenergyminimaoftheNMandFMstatesiszero.Foroursurfacecalculations,the6x6supercellofPd(100)slabislargeenoughtohindertheC60-C60interactionbetweenadjacentcells.Hexagonsandpentagonsmade 60

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ofcarbonatomsarepossiblepreferentialsitesforadhesionofC60moleculesonthePd(100)surface.WecalculatethatadsorptionofaC60moleculeonahexagonalsiteis1.01eVmorefavorablethanonapentagonalsite.Therefore,uponrelaxationofaC60moleculeonthePd(100)surface,thehexagonalfacet(comprising6carbonatoms)ofthefullerenemoleculestronglybindstothePdsurfaceasshowninFig. 4-6 (b).Thebindingenergyofthefullerenemoleculeinthiscongurationis5.87eV.Moreover,Baderanalysis[ 86 ]showsthattheinteractionbetweenPdandfullerenemoleculesoccursviachargetransferfromPdsurfaceatomstothefullerene.Whilethetransferredchargeis0.06electronperPdatomatthePd/C60interface,chargetransferdecreasesto0.02eawayfromtheintimatecontactregions.InthiscaseeachadsorbedC60moleculeyieldsadegeneracyofthenonmagneticandtheferromagneticstatewith3.85Bnetmagneticmomentfortheferromagneticcase.SimilartoC60moleculesonaPdsurface,thegroundstateofaperiodicstructureofPd/C60/Pdsandwichcongurationisalsodegenerate.Interestingly,thedegeneracyisliftedinfavorofferromagnetismwhensinglePddefectsonthesurfacearecapturedbyC60;thistypeofdefectresultsinasmallferromagneticmomentasshowninFig. 4-6 (c).Thetotalmagneticmomentofthesystemtakesvaluesbetween0.01-0.08BdependingonthepositionofthePdatom.AnothermagneticcongurationoccurswhenC60moleculesinteractwiththestepedgesofthePd(100)slab.RecentstudiesonCu,IrandAusurfaceshaveshownthatC60moleculeshaveahightendencytomigratetowardsstepedges[ 94 95 ].AscanbeseenfromFig. 4-6 (d)periodicstepstructuresonthePdslabcanbeconstructedusingoneexcessPdlayer.Whiletheinitialsystemhaszeromagnetism,a9.22BnetmagneticmomentisinduceduponthedeformationofstepedgebyaC60molecule.TotakepossibleeffectsduetoexistenceofoverlyingupperPdlayersintoaccount,wehavealsostudiedthestructuralandmagneticpropertiesofPd/C60/Pdsandwichcongurations.TheDFTcalculationsshowthateachfullerenebindstwoPdsurfaces 61

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Figure4-6. (a)Pdthicklayersystemisnon-magnetic(NM)withtheenergyminimumoftheferromagnetic(FM)statehigherthanthatoftheNMstatehigherbyanamount>0(b)C60moleculeon6x6supercellof4-layerslabofPd(100)surface-systemisdegeneratewithcoincidingenergyminima(=0).(c)C60moleculeinteractingwithsinglePdatom+Pdthickslab-systemisweaklymagnetic(<0).(d)C60moleculeinteractingwithPdstepedge-systemishighlymagnetic(<0).(e)Pd7clustersadsorbedontheC60moleculesonPdslab(atomsofPdslabarenotshownforclarity)havemagneticgroundstateandresultinanetmagneticmomentinthePd/C60structure. throughitshexagonalsides.AsaresultofthesizedifferencebetweenthefullereneandPd,thetwooutermostsurfacelayersofPdaresignicantlydisturbedwiththedistancebetweenadjacentPdlmscalculatedtobe9.40A.Moreover,sincethesputteringtechniqueresultsinthepenetrationofsomePdatomsamongtheC60molecules,wemustalsoconsiderthepossiblityoftheformation 62

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ofPdculsters[ 96 ].OurcalculationsshowthatPd5,Pd7,Pd8andPd9clustershaveaFMgroundstatewiththemagneticmomentsof2,2,4and2B,respectively.ToillustratetheC60-Pdnclusterinteraction,Fig. 4-6 (e)showsschematicallyaconguration,whichiscalculatedtobemagneticwith0.285BperPd,comprisingasublatticeofPd7clustersembeddedinaC60hostmatrixonPdslab.ConsideringthesensitivedegenerategroundstateofthePd/C60structureandtheexperimentalpowerlawof2.1,theformationofPdclustersisthemostprominentoriginofthebrokendegeneracy.Inadditiontocontributionsofsharpedgesandclusterformations,onecanalsoconsidertheferrromagnetismduetothestrainedPdsurfacebyC60moleculeswhichisexcludedheresinceweapplyfullrelaxation. 4.5ConclusionsWehaveexperimentallyandtheoreticallyshownthatstackedbilayersofPd/C60areferromagnetic.TheobservedferromagnetismissurprisingsincePdandC60arenon-ferromagneticinbulkform.Magnetizationdatarevealtemperature-independenthysteresisloopswithcoerciveeldsaround50Oeandasaturatedmagneticmomentof0.042B/Pdatom.Usingeldcooled(FC)magnetizationvstemperaturedata,weextrapolateapower-lawdependenceofthemagnetizationwithaCurietemperatureTc550K.ThusaTCwellaboveroomtemperaturewhichisconsistentwithtemperature-independentM-Hcurves,andthepower-lawexponent2.1impliesthatthePdisinnanoparticleform.Weconrmourexperimentalndingsusingdensityfunctionaltheory(DFT)calculations.AllpossibleinteractionsbetweentheC60molecules,thePdatomsandthePd-slabswereinvestigatedtheoretically.Inthenon-interactinglimit,thecalculationsshowthatbothPdandC60moleculesarenonmagnetic.ByincludinginteractionsbetweenC60moleculesandthePdslabs,ferromagneticstatesarefoundtobedegeneratewithnon-magneticgroundstates.WhenadditionalsinglePdatomsattachtotheC60thedegeneracyisliftedinfavorofaferromagnetic(FM)groundstate.Therearemanyperturbationsavailablethatcan 63

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breakthedegeneracybetweentheNMandFMstates.TheseperturbationsincludeinteractionofC60moleculeswiththePdstepedges,interactionoftheC60moleculeswithimperfectionsinthePdthin-lmsandtheinclusionofPdclusterswithintheC60hostlattice.ThelargesizedifferencebetweenPdatomsandC60moleculesgivesrisetolmroughnessinourmulti-layeredsampleswhichbyinter-diffusionisfavorableforferromagnetismbypromotingthegrowthofPdnanoclustersandtheformationofC60stepedges. 64

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CHAPTER5INSEARCHOFTWO-PHASESUPERLATTICEMULTIFERROICS 5.1MultiferroicsMultiferroicsarematerialswhichhaveatleasttwo`ferroic'orderings[ 97 ],wheretheclassical`ferroic'orderingsareususallyferromagnetism,ferroelectricityandferroelasticity.Butrecentlythese`ferroic'requirementshavebeenbroadenedtoincludeferroelastic,atiferromagneticandferrotoroidicorderingsalso.Startedin1960sbytheworksofSmolenskiiandVenevtsev[ 98 ],multiferroicsisnowoneofthemostwidelystudiedtopicsincondensedmatterphysics.Magnetoelectricmultiferroicsareaclassofmaterials,wheremagneticeldhassomeeffectonferroelctricpropertyandviceversa.Althoughtherearesomesingle-phasemultiferroics(e.g.BiMnO3,CdCr2S4,EuTiO3,DyScO3etc.)wherebothferromagneticandferroelectricpropertiesarefoundinsamematerial,thesematerialsareveryrare.Toovercomethisproblemofavailabilityinsingle-phasemultiferroics,scientistsrecentlystartedtousearticialsuperlatticeasanalternativetechnique.Thesesuperlatticesaremadeofoneferromagneticlayerfollowedbyaferroelectriclayerandusuallyhaveenhanced`ferroic'propertiescomparedtosinglephasesystems.Usuallythesearticialmultilayersaremadeoutofferroelectricmaterialslike(Pb(Zr,Ti)O3,Ba(Sr,Ti)O3andmagneticmaterialslikeperovskites(e.g.BiFeO3,(La,Sr)MnO3,(La,Ca)MnO3etc.)anddoubleperovskites(e.g.Ba,2FeMoO6,Sr2FeMoO6etc.)[ 99 101 ].PerovskitesareaspecialtypeofcomplexoxidewhichcanbeexpressedusingthegeneralizedformulaABO3,whereAandBaretwocationvalencematerials.ManganitesareagroupofperovskitewheretheBsiteisalwaysmanganese(Mn).Intermsoflatticestructure,ithasalltheoxygenatomsinthecornerofacubicstructure,theAcationisatthecenterofeachfaceandtheBcationisatthebody-centerofthecube(Fig. 5-1 (a)).ThereisanoctahedralcoordinationofoxygenatomsaroundeachB-siteatom.ThechargecombinationofAandBcanvarywithin+1/+5,+2/+4or+3/+3 65

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(a) (b) Figure5-1. Latticestructureof(a)Perovskiteand(b)DoublePerovskite whichallowswidevarietiesinbothstructureandpropertyforperovskites.Thelatticestructureofperovskitescanvaryfromcubic,tetragonal,orthorhombicormonoclinic;andtheyexhibitallkindofpropertieslikeferromagnetism,ferroelectricity,piezoelectricity,pyroelectricity,largeSeebeckcoefcients,superconductivityandnonlinearopticalproperties[ 102 103 ].InthischapterwearegoingtodiscussthemagneticpropertiesoftwodifferentarticialsuperlatticesystemsnamelyBaFeO3-KTa0.47Nb0.53O3systemandBa2FeMoO6BaTiO3system.Bothoftheseperovskitesuperlatticeweregrownusingpulsedlaserdepositiontechnique.ThesynthesisandcharacterizationofthissuperlatticesweredonebyDr.JoeCianfroneandDr.K.W.Kimrespectively,bothfromProf.DavidNorton'slabinMaterialSciencedepartmentatUniversityofFlorida. 5.2MultiferroicPropertiesOfBaFeO3-KTa0.47Nb0.53O3SuperlatticesArticialsuperlatticeofBaFeO3-KTa0.47Nb0.53O3weremadeofferromangeticperovskitesBaFeO3and`supposed'ferroelctricKTa0.47Nb0.53O3(whichisasolidsolutionoftwootherperovskiteKTaO3andKNbO3). 5.2.1SynthesisAndCharacterizationThisarticialsuperlatticeofBaFeO3-KTa0.47Nb0.53O3wasgrownonsinglecrystalLaAlO3andSrTiO3substratesorientedin(100)direction.Beforethedepositionthesubstrateswerecleanedusingultrasonicbathsoftrichloroethylene,acetone,methanolandnallyblowndrywithhighpurity``compressedN2gas.Afterthisrigorouscleaning 66

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allthesubstratesweretestedusingatomicforcemicroscopetondtheirsurfaceroughness.Followingthesubstratepreparationprocess,superlatticesweregrown (a) (b) Figure5-2. X-raydiffractionscanofa24x24BaFeO3-KTa0.47Nb0.53O3superlatticedepositedonaSrTiO3substrate,(a)as-grownsample(b)post-annealedsamples usingapulsedlaserdepositiontechniquewithaKrF(248nm)excimerlaserinProf.Norton'slab.Theincidentlaserenergydensityandpulsefrequencywasmaintainedat1.5J/cm2and1Hzrespectively.TheBaFeO3andKTa0.47Nb0.53O3depositionratewasmaintainedat0.1A/sand0.23A/srespectively.TheseSLsweregrownatasubstratetemperatureof750Cin10mTorrofoxygenandthenannealedex-situat900Cinowingoxygenfor3hours.Betweenthedepositionandannealingstep,thebacksideofthesampleweresandedtocleananyremainingsilverpastewhichwasusedtogluethesubstratewiththeheater.Followingthisallsubstrateswerecleanedagainusingacetone,methanolandcompressednitrogensequentially.Thethicknessesofthesampleswerefoundtobe100nmusingprolometryandcrosssectionalSEM.ThenumberandthicknessofeachBaFeO3andKTa0.47Nb0.53O3variesindifferentsamplestomakesurethattheoverallthicknessremainssame,whichmeansthesameamountofmagneticandferroelectricmaterialsarepresentinallsamples.FollowingthegrowthandannealprocessallthesampleswerecharacterizedusingX-raydiffraction(XRD),transmissionelectronmicroscopy(TEM),X-rayphotoelectron 67

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Figure5-3. X-rayphotoelectronspectroscopydatafor6x6BaFeO3-KTa0.47Nb0.53O3superlatticedepositedonaSrTiO3substrateandannealedinowingoxygenat900Cfor3hours. spectroscopy(XPS)andEnergydispersivespectroscopy(EDS)techniques.AllthesecharacterizationweredoneDr.JoeCianfronefromProf.Norton'slab.AsseenfromFig. 5-2 ,XRDshowsabsenceofanysuperlatticereectionandincreaseoflatticeparametersduetoannealing.Theabsenceofsuperlatticepeakmaybeduetopoorsuperlatticelayeringorhighinterfacialroughness.Duringtheannealingprocessthelatticeparametersassociatedwithpseudocubic(002)peak(eitherfromBaFeO3and/orKTa0.47Nb0.53O3)and(200)peak(fromBaFeO3)increasesfrom4.01Ato4.03Aandfrom4.18Ato4.22Arespectively.ThisindicatesthatatleastsomeoftheBaFeO3takesahexagonalperovskitestructureinthesuperlattice,whichisconsistentwithsomepreviousstudies[ 104 ].CharacterizationbyXPSwasdoneonanannealed6x6BaFeO3-KTa0.47Nb0.53O3sample(depositedonSrTiO3)toinvestigatethepossibilityofprecipitatedFemetaland 68

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Figure5-4. Superlatticelayeringobservedviatransmissionelectronmicroscopyina24x24BaFeO3-KTa0.47Nb0.53O3superlatticedepositedonaSrTiO3substrate FeOxasthesourceoftheferromagnetism.HighresolutionmultiplexscansindicatealargepeaknearthebindingenergyofFe2p3=2(Fig. 5-3 )mostlikelycomingfromFe(III)Oxide(Fe2O3),whichmeansironisinthe+4valencestate.ButasthewidthoftheFe2p3=2isquitelarge,itispossiblethatacombinationofFe(III)andFe(IV)arepresentinthesamples.AGaussianttingofthepeakwouldbetheidealmethodforquantitativeestimationofpercentagesofFe(III)andFe(IV).Butasthereisnostandard 69

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Figure5-5. Energydispersivespectroscopy(EDS)measuredviascanningtransmissionelectronmicroscopy(STEM)fora24x24BaFeO3-KTa0.47Nb0.53O3superlatticedepositedonaSrTiO3substrateannealedinowingoxygenat900Cfor3hours. dataavailableforFe(IV)bindingenergy,thistypeofttingwillnotresolvequantitativepercentagesofthetwopossiblestates.Foracloserlookatthesuperlatticelayeringandlatticestructure,TEMtechniquewasused.FromTEMimagesitisclearlyevidentthatsamplesshownicesuperlatticelayeringbeforeannealing(Fig. 5-4 ),butthelayeringisdistinctlylostinthepostannealedsamples.TEMimagesalsoshowthat(Fig. 5-4 )goodatomiclayeringispresentinsomeareas,whereasinotherareasatomiclayeringisdiscontinuous.TheEDSresults(theresultswereshiftedinFig. 5-5 bytheEDSsoftware)indicatelittleamountofFesignalfromBaFeO3layersinthesuperlattice(Fig. 5-5 ).ButEDStechniqueisonlylimitedto2.4nmbelowthesurface,soitishighlypossiblethatEDSmaymissFesignalcomingfromdeeperthan2.4nmfromsurface.DuetoheterogeneouslayeringofthesuperlatticeEDSwastakenatdifferentpositionsofthesample,whichshowsmoreorlesssimilarFeamountfromdifferentareas.Although 70

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(a) (b) Figure5-6. Hysteresisloopmeasurementatdifferenttemperatures,whichshowspositiveeffectofannealingonmagneticpropertieslike,saturationmagnetizationandcoerciveeldin(a)6By6unitcellBaFeO3-KTa0.47Nb0.53O3superlatticeand(b)24By24unitcellBaFeO3-KTa0.47Nb0.53O3superlattice.Measurementtemperaturesareindicatedineachgraph. magnetizationdatashowssamplesfollowBloch's3/2law,EDSresultsdoesnotshowanyobservableFesignalfromthenanoparticleregions. 5.2.2ResultsAndDiscussionAfterthecharacterizationprocess,QuantumdesignMPMS-4Swasusedtostudythemagneticpropertiesofthesample.Allmagneticmeasurementandanalysisweredoneinourlab.Asseeninpreviousstudies,theannealinghasahugepositiveeffectonmagneticpropertiesofboththin-lmsandthesuperlattice[ 104 105 ].InitiallyasetofBaFeO3thin-lmsweregrownwiththicknessrangingwithin6to24unitcell(UC),whichshowseitherveryweakferromagnetismordiamagnetismat300K.FollowingmagneticmeasurementofBaFeO3thin-lms,anothersetofBaFeO3-KTa0.47Nb0.53O3superlatticeweregrownandthensubsequentlyannealed.Allthesepost-annealedsuperlatticesshowsignicantimprovementinmagneticproperties(e.g.MSandHC)comparedtoun-annealedones.(Fig. 5-6 ).AlsoitisevidentfromFig 5-7 thatallannealedsuperlatticesamplesshowbetterferromagnetismatroomtemperaturecomparedtotopureannealedBaFeO3lms.Whenthevariousmagneticproperties(like 71

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Figure5-7. MagnetichysteresisloopsofBaFeO3-KTa0.47Nb0.53O3superlatticesandBaFeO3thinlmsdepositedonSrTiO3substratesexsituannealedinowingoxygenat900Cfor3hoursandmeasuredat300K theremnantmagnetization,saturationmagnetization,coerciveeldetc.)arecomparedbetweendifferentsuperlattices,wendallthemagneticpropertiesexceptcoerciveeld,increasewithincreasingsuperlatticeperiodicity[Fig. 5-8 ].ToobtainanestimateoftheCurietemperatureforthesamples,thetemperaturedependenceofthemagnetizationwasmeasuredonaseriesofsuperlatticesamples.Allthesamplesweremeasuredatconstanteldasafunctionoftemperaturefrom10Kto300Kinbotheldcooled(FC)andzeroeldcooled(ZFC)conditions[Fig. 5-9 ].Thesedata,showninFigure 5-9 ,werethenttedtoBloch'sT3=2lawtoestimatetheCurietemperature,TC,andBlochexponent,P.TheresultsofthesemeasurementsindicatealargeincreaseintheestimatedCurietemperaturetoover425Kinthesuperlatticesamples,relativetotheestimatedCurietemperatureofapproximately300KinthebareBaFeO3lms.TheBlochexponent,P,wasontheorderof1.5forallsamples,ranging 72

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Figure5-8. MagneticpropertiesofBaFeO3-KTa0.47Nb0.53O3superlatticesandthinlms,measuredat300K,comparedasafunctionofsuperlatticeperiodicity.Note`0unitcell'sampleisaBaFeO3thin-lmsample from1.4-1.75.TheseresultsareisanindicationthattheferromagnetismdoesindeedfollowBloch's3/2law,indicativeofferromagnetismoriginatingfroma3-Dcrystallinelattice,andnotfromnanoparticlecontributions[ 31 106 ].ThisincreasedmagneticstabilitycouldbetheresultofeithersurfacechemicalreductionofFeintheairorapossibleferromagnetic-ferroelectriccouplingstabilizingmagneticdomains.Alsoasdiscussedpreviouslyallmagneticpropertiesincreaseswithsuperlatticeperiodicity(withtheexceptionofcoerciveeld)whichisanindicationofincreasedstabilitywithlargerdomainsize.UntilnowwehaveonlydiscussedthemagneticpropertiesofthesuperlatticewhichiscomingfromtheBaFeO3layer,butthesehetero-structuresarealsocomprisedofferroelectricKTa0.47Nb0.53O3layerswhichdonotshowanyferroelectricityduringremnantpolarizationmeasurements.Althoughthesuperlatticeswerenotelectrically 73

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(a) (b) (c) (d) Figure5-9. FieldcooledandzeroeldcooledmagnetizationmeasuredasafunctionoftemperatureandCurietemperatureestimationforBaFeO3-KTa0.47Nb0.53O3superlatticesdepositedonaSrTiO3substrateandexsituannealedinowingoxygenat900Cfor3hours conductive,therewassignicantleakagecurrentduringferroelectricmeasurement.ThisleakagecurrentmaybecausedfromthevoidsorpoorsuperlatticelayeringseenbyTEMimages.Alsothethicknessoftheferroelectriccanbeanotherfactor,wherepreviousstudieshaveshownthataminimum4nm(10unitcells)thickBaTiO3isrequiredforferroelectricsignal[ 107 ]andsimilarlythereshouldbeaminimumthicknessrequirementforKTa0.47Nb0.53O3.Thisminimumthicknessrequirementmaynotbesatisedduringsuperlattice. 5.2.3ConclusionsArticialsuperlatticeofBaFeO3-KTa0.47Nb0.53O3weregrownusingpulsedlaserdepositiononorientedLaAlO3andSrTiO3substrates.Samplesweregrownat750C 74

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in10mTorrofoxygenandthenannealedat900Cinowingoxygenfor3hours.XRD,XPS,SEM,TEMandEDStechniqueswereusedtocharacterizethesamples.BothXRDandTEMshowsanegativeeffectofannealingonsuperlatticelayering.XPSandEDSsshowsexistenceofofbothFe(III)andFe(IV)statesinthestructure.FollowingthegrowthandcharacterizationprocessesSQUIDmagnetometryisusedtostudythemagnetichysteresisloopsandtemperaturedependenceofmagnetization.HysteresisloopsindicatedalargeincreaseinferromagneticsignalinsuperlatticestructurecomparedtothebareBFOlmsandMvsTcurveswereusedtodeterminetheCurietemperature(TC)425K.ThetemperaturedependenceofmagnetizationalsoshowsagreementwiththeBlochT3=2law.Thisferromagnetismmaybearesultofinterfaceinteractionbetweentheferromagneticandferroelectriclayers. 5.3StudiesOnBa2FeMoO6-BaTiO3SueperlatticesFollowingthestudyofBaFeO3-KTa0.47Nb0.53O3superlattice,anotherarticialstructurehasbeenmadeusing`doubleperovskite(DP)'Ba2FeMoO6andperovskiteBaTiO3.ThistimethegoalwasalsotomakeamultiferroicmaterialwithmagneticBa2FeMoO6andferroelectricBaTiO3.Doubleperovskites(DP)areanotherkindofperovskiterepresentedbyageneralizedformulaA2BB'O6,whereA,B,B'allarecations.Thelatticestructureissimilartotheperovskites,onlyBandB'placethemselvesatthecornersofthecubeinacheckerboardpattern(Fig. 5-1 (B)).Doubleperovskites(DP)areknowntobeferromagneticforB=Cr,Feetc.andB'=Mo,Wetc.Otherthantheirpotentialapplicationinmultiferroicmaterialfabrication,DPsarealsoveryinterestingfromafundamentalphysicspointofview.DPsareoneoffewmaterialswherebothitinerant(comingfromB)andlocalizedferromagnetism(comingfromB')arefoundinthesamematerial.SecondlyDPshavemuchhigherferromagneticTCcomparedtomanganites,becauseneitherJahn-Tellernoranti-ferromagneticsuper-exchangeispresentinDP.TheabsenceofantiferromagneticexchangescanbeattributedtothelargedistancebetweenBandB'[ 108 ]. 75

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5.3.1ExperimentalDetailsSimilertoBaFeO3-KTa0.47Nb0.53O3superlattices,Ba2FeMoO6-BaTiO3superlatticewasalsogrownusingpulsedlaserdepositionwithaKrF(248nm)excimerlaser.AllthesynthesisandcharacterizationweredonebyDr.K.W.KiminProf.Norton'slab.Singlecrystal(100)SrTiO3hasbeenusedassubstrates.Beforegrowingsuperlattices,allsubstrateswerecleanedinconsecutiveultrasonicbathsoftrichloroethylene,acetone,andmethanol,andthenblowndrywithcompressednitrogen.Thesesubstrateswereexaminedviaatomicforcemicroscopyandunitcellheightstepswereconrmedonthesubstratesurface.Depositionwasconductedatasubstratetemperaturerangingwithin600-900Candambientpressureof0.5to5mTO2/ArGas(amixtureof2%O2inArgas).Thelaserenergydensitywasapproximately1.5J/cm2withapulsefrequencyof4Hz.ArticialsuperlatticesofvaryingperiodcityweregrownviadepositionfromalternatingtargetsofBa2FeMoO6andBaTiO3.Ba2FeMoO6targetwassynthesizedusinghighpurity(99.9%pureorhigher)powdersofBaCO3,Fe2O3andMoO3,whereallthepowdersweremixedfor24hoursbydryballmillingandthemixedpowderwascalcinedat900Cunderreducingatmosphereof5%H2bufferedwithArgasfor6hours.Thiscalcinedpowderwasgroundbymortarandpestleandthenhand-pressedintoaone-inchdiameterdiefollowedbymachinepressunder150Mpafor3minutesbycoldisostaticpressure.Itwassinteredat1150Cunderthesamereducingatmospherefor4hours.ThecalcinedandsinteredpowderswereexaminedbyX-raydiffractionandsynchrotrondiffraction.Thecrystalstructureisfoundtobecubicwiththelatticeparameterof8.07AandtheobtainedcompositionisBa2.00Fe1.07Mo0.99O6.33.Forferroelctriccomponent,ahighpuritycommerciallyavailableBaTiO3targetwasused.Thebacksideofeachsamplewassandedtoremoveanyremnantsilverpaste(usedtoadherethesubstratesandprovidethermalcontacttotheheater)andcleanedinacetone,thenmethanol,andblowndryinnitrogen. 76

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Figure5-10. X-raydiffractionscanofaBa2FeMoO6-BaTiO3superlatticedepositedonaSrTiO3substrate.Notethebeautifulsuperlatticereections. X-raydiffractiontechniqueisextensivelyusedtostudythesuperlattice.XRDshowsbeautifulsuperlatticereectionsduring-2scans(Fig. 5-10 ).ThisbehaviorisaclearindicationofhighqualitysuperlatticelayeringwhichwasabsentinthepreviouscaseofBaFeO3-KTa0.47Nb0.53O3superlattices. 5.3.2ResultsAndDiscussionBeforegrowingBa2FeMoO6-BaTiO3superlatticesaseriesofBa2FeMoO6thin-lmsweregrowntostudythemagneticandmagnetotransportpropertiesofthesethin-lms.Ba2FeMoO6thin-lmsweregrownindifferentgrowthtemperaturesrangingwithin600-900Candunderdifferentgasatmosphereandondifferentsubstrates.Thechamberwaspumpeddowntothebasepressureof10)]TJ /F2 7.97 Tf 6.58 0 Td[(9Torrandthepressureduringdepositionwasintherangebetween10)]TJ /F2 7.97 Tf 6.59 0 Td[(7Torr,slightlychangingwiththegrowthtemperature.ThecrystalstructureandphaseofthethinlmswereexaminedbyX-raydiffraction(PhillipsAPD3720).Figure 5-11 (a)showstheXRDpatternsoftheBa2FeMoO6thinlmsgrownat900Cundervacuumand1mTorroxygenambient. 77

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Figure5-11. -2XRDX-raydiffractionscanofaBa2FeMoO6thin-lmgrownonaSrTiO3substrate AnimpurityBaMoO4phaseisobservedinthesamplegrownunderoxygenambientincontrasttothephasepurecubicsamplegrownundervacuum.Figure 5-11 (b)showstheXRDpatternsoftheBa2FeMoO6thinlmsgrowninthetemperaturerange600-900C(100Cincrements)undervacuum.Alllmsarephase-pureandorientedalongthec-directionsinwhichthe(00`)peaksoflmsareobservednexttothe(00m)peaksoftheSrTiO3substrate.AsitisclearlyevidentfromFig. 5-12 (a)samplesgrownonSrTiO3havethehighestmagnetization.NowinFig. 5-12 (b)wendthatinertgasenvironmentandvacuumenvironmentdoesnothavemuchdifferenceintermsofsaturationmagnetization.AndnallyFig. 5-12 (c)and(d)clearlyshowshigherthegrowthtemperaturebetterthesaturationmagnetizationandcoerciveeld.DividingthetotalmagnetizationwithnumberofBa2FeMoO6latticeunits,wegetsaturationmagnetization(MS)withvaluesnear0.6,0.4,0.8,and1.1B/f.u.forthe600,700,800,and900Csamples.Alsomeasuringthecoerciveeld(HC)at10K,wendHCvaluesnear1500,220,300and500Oe.Sootherthantheexceptionofthesamplegrownat600C,allthesampleshavebothhigherMSandHCwithhighergrowthtemperature,presumablybecauseofbettercrystallinequality.ButthelowvaluesofMS(1B/f.u.)comparedtothepredicted4B/f.u.canbeexplainedbythecompositionalvariance, 78

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i.e.,B:B'siteorder-disorderandoxygencontent.Itiswellknownthatthisdoubleperovskitematerial[ 109 ]andthesubstructuralsingleperovskiteBaFeO3[ 110 111 ]andBaMoO3areverysensitivetooxygencontent.IthasbeenalsoreportedpreviouslythatdisorderingofFe/MositesinSr2FeMoO6signicantlyreducesthemagnetoresistanceeffectinSr2FeMoO6[ 112 ].AlsotypicalFC(eldcooled)andZFC(zeroeldcooled)temperaturedependenceofmagnetizationmeasurementsweredoneatasmallxedmagneticeldof100Oe[Fig. 5-13 (a)and(b)].FittingBlochT3=2lawwiththeFCcurve,wendCurietemperature(TC)around300K(whichislowerthan367KreportedforBa2FeMoO6ceramics[ 113 ].)andBlochcoefcientParound1.50.SothesamplesarefollowingBlochLaw,whichmeansoriginofferromagnetismisfrom3Dor2Dsystems.ItisinterestingtonotethatthesaturationmagnetizationdependsongrowthtemperaturewhileboththeCurietemperature(nearwhereMdeviatesfromaconstantvalue)andtheirreversibilitytemperature(markedbythedeviationbetweenFCandZFCcurves)remainsroughlyconstantforthesamplesgrownat800and900C.ThiscorrelatedbehaviorofTCandMScanbeexplainedusingtheantisite(AS)disorder,whereFeandMoexchangetheirsitepositionswithoutchangingcarrierdensityn.Ithasbeenshownboththeoretically[ 108 ]andexperimentally[ 114 ]thatASdisordersystematicallyreducesthesaturationmagnetization(MS)withoutaffectingTCinSr2FeMoO6.Figure 5-14 (c)and(d)showsthemagnetoresistanceofthesamples.Allsamplesshowtypicalnegativemagneto-resistanceatahighmagneticeld.However,thesamplegrownat900Cshowsapositivemagnetoresistancebelow20kOe,whichisunlikepreviousstudies[ 115 ]onSr2FeMoO6thinlms.Thepositivemagnetoresistanceisnotfullyunderstood.Weobservedinthesamplegrownat700Canegativemagneto-resistanceof-3%atatemperatureof10Kandamagneticeldof70KOe.Thesmallvalueofmagneto-resistanceisbelievedtobemainlyduetodisorderinthelms,whichispreviouslyseeninotherDPsystems[ 113 116 ].Thesamplegrownat 79

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(a) (b) (c) (d) Figure5-12. MagneticpropertiesofBa2FeMoO6thin-lms(a)grownonindicatedsubstrates,(b)grownunderindicatedgasenvironment,(c)grownatindicatedtemperatures,(d)similartographshownin(c)butmeasuredatdifferenttemperature.Magneticeldwasappliedparalleltothethin-lm. (a) (b) Figure5-13. TemperaturedependenceofBa2FeMoO6thin-lms(a)grownat800C,(b)grownat900C.BoththeZFCandFCmeasurementsweredoneataeldH=100Oe.Magneticeldwasappliedparalleltothethin-lm. 80

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900Chasasmallernegativemagneto-resistancevaluewhichistosomeextentduetocancellationbythepositiveregionobservedatsmallmagneticelds.TheHallresistivityandconductivityareplottedinFigure 5-14 (b)andFigure 5-14 (a),respectively.Allthesetransportmeasurements(conductivity,Hallandmagnetoresistance)havebeendonebySanalBuvaev.Althoughtheconductivitydecreaseswithdecreasingtemperatureforallthesamples,thereisapronouncedincreaseintheconductivityatalltemperatureswithincreasinggrowthtemperature.Inferromagneticmaterials,thetransverseresistivityisgivenby xy=RHB+0RAMs(5)withthemagnetizationMandtheordinaryandanomalousHallcoefcientsRHandRA,respectively.TheHallresistivityismeasuredatconstanttemperaturesof10,100and300Kupto7Torientedalongthec-axisandshowninFigure 5-14 (b)forthe900Csample.Inlowmagneticelds,theHallresistivityisdominatedbytheanomalousHallcontributionwhichbehaveshole-likeasindicatedbythepositiveslope.Thispositivesignarisesbecausethesingleitinerantelectronassociatedwiththet2gbandoftheMohasaspinantiferromagnetically-coupledtothelocalizedS=5/2corespinsontheFesites[ 117 ].Inhighelds,theordinaryHalleffectisdominantandthedatashowalinearnegativeslopewhichindicatesanelectron-likebehavior.AfterstudyingthemagneticandtransportpropertiesofbareBa2FeMoO6thin-lms,aseriesofsuperlatticeandbi-layershacebeengrownoncleanedSrTiO3substratesusingBaTiO3,SrTiO3orBa0.5Sr0.5TiO3astheferroelectriclayer.Eachsuperlatticeismadeof25bilayerof4nmBa2FeMoO6and4nmofferroelectriclayer(Fig. 5-15 (A)),andeachbilayerismadeof100nmBa2FeMoO6and200nmofferroelectriclayer(Fig. 5-15 (B)).Whenmagnetizationarecompared,itisevidentfromFigure 5-16 thatallthebilayershavelowerMSthanbareBa2FeMoO6thin-lmsandallthesuperlatticeshavehigherMSthanbareBa2FeMoO6thin-lms.Mostlikelythenumberofinterfacelayers(between 81

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(a) (b) (c) (d) Figure5-14. TransportpropertiesofBa2FeMoO6thin-lms:(a)conductivitymeasuredatindicatedtemperatures,(b)Hallmeasurementatindicatedtemperatureofsamplegrownat900C,(c)magnetoresistancemeasurementtakenat10Kforsamplegrownatindicatedtemperature. 82

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(a) (b) Figure5-15. Detailedstructureof(a)Ba2FeMoO6basedsuperlattice(b)Ba2FeMoO6basedbilayer. ferromagneticandferroelectriclayers)hasanimportanteffectonmagneticpropertyofSLandBL.TheFCandZFCtemperaturedependenceofmagnetizationforallthesuperlatticesamplesareshowninFigure 5-17 .FittingofFCtemperaturedependencedatawiththeBlochlawrevealsthatCurietemperaturerangeswithin150to200Kforallthesuperlattices,whichisasignicantreductioncomparedtopureBa2FeMoO6thinlm(whereTCstaysaround300K).Furtherdatacollectionandanalysisarestillunder-wayforsuperlatticeandbi-layersamples.TemperaturedependenceofmagnetizationisshownforBa2FeMoO6-BaTiO3SLandBL,andBa2FeMoO6SrTiO3SLandBLinFigure 5-17 .Withrespecttoferroelectricity,unfortunatelyallofthesearticialsuperlattices/bi-layersshownosignofferroelectricity.Duetoahighdensityofoxygenvacanciesduringgrowth,alltheseferroelectricmaterialswereconductingwithsheetresistancefewk,whichmadeferroelectricmeasurementsimpossible.Ba2FeMoO6waschosen,becauseunlikeBaFeO3theselmsdonotneedanyannealingtoshowmagnetism.Aspertheearlierstudy,annealinghasseverenegativeimpactonsuperlatticelayeringwhichmighthavecausedtheabsenceofferroelectricsignal.But 83

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(a) (b) Figure5-16. MagnetizationcurvesofBa2FeMoO6basedsuperlatticesandbi-layersmeasured(a)at10Kand(b)at300K herewehadadifferentproblemofoptimizationofoxygenpressure.AsitisevidentfromFig. 5-12 (B)toomuchoxygenpressuredestroysmagnetismofBa2FeMoO6,andtoolittleoxygenpressurecreatesoxygenvacancieswhichmaketheferroelectricmaterialconducting. 5.3.3ConclusionsPurethinlmsofBa2FeMoO6andarticialsuperlattices(SL)andbilayers(BL)ofBa2FeMoO6-BaTiO3,Ba2FeMoO6-SrTiO3andBa2FeMoO6-Ba0.5Sr0.5TiO3were 84

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(a) (b) (c) Figure5-17. Temperaturedependenceofmagnetizationof(a)Ba2FeMoO6-BaTiO3SL,(b)Ba2FeMoO6-SrTiO3SLand(c)Ba2FeMoO6-BaSrTiO3SL grownusingpulsedlaserdepositiononorientedSrTiO3substrates.ThinlmsofBa2FeMoO6weregrownunderdifferentconditionsvaryingthechamberpressure,growthtemperature,surroundinggasatmosphereandsubstratetooptimizethemagneticproperty.Thisoptimizationstudyconcludesthatsamplesgrownundervacuumorinertgas,at900ConSrTiO3substratesarebestintermsofmagneticproperties.SuperlatticeandbilayerSamplesweregrownat700Cin0.5mTorrofO2/Argasmixture(2%O2inAr)andthenanalyzedusingXRDtechnique.WellresolvedsuperlatticepeakswereseenfromXRD-2scanswhichindicategoodsuperlatticelayering.Afterthestructuralcharacterization,SQUIDmagnetometrywasusedtostudythemagneticpropertiesofthesuperlattices.Comparingmagneticpropertiesweseeall 85

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superlatticesampleshavehighersaturationmagnetizationandallbi-layersampleshavelowersaturationmagnetizationcomparedtopureBa2FeMoO6thin-lm.Unfortunately,justlikethepreviousworkonBaFeO3-KTa0.47Nb0.53O3superlattices,thesesuperlatticeandbilayersdonotshowanyferroelectricproperties.Although,unlikeBaFeO3(magneticmaterialchoseninpreviousstudy)Ba2FeMoO6doesnotneedanyannealingstepforthemagneticproperty,thesuperlatticeshowsabsenceofanyferroelectricsignal.Thiscanbeattributedtolowoxygenpressureduringgrowthwhichmaycreateoxygenvacanciesintheferroelectriclayers.Oxygenvacanciesmadeferroelectricmaterialstooconductiveforanyferroelectricmeasurement.Wearemovinginthedirectionofoxygenpressureoptimization,whereBa2FeMoO6layerswillbegrowninlowoxygenpressureandferroelectriclayerswillbegrowninhigheroxygentoreducetheiroxygenvacancy.Thiscanbeoneapproachtoachievemultiferroicpropertyinasinglesuperlatticestructure.Anotherapproachcanbecombiningothermagneticdouble-perovskites(likeSr2FeMoO6,Sr2CrMoO6,Ba2CrMoO6etc.)withferroelectricsBaTiO3,SrTiO3orBa0.5Sr0.5TiO3. 86

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CHAPTER6QUANTUMCORRECTIONSINDISORDEREDMETALInthischapterwearelayingthetheoreticalbackgroundofquantumcorrectionsinmagneticthin-lmswhichwillbeextensivelyusedinthefollowingtwochapters.StudyonelectricalconductivityofmetalstartedwiththepioneeringworkofBlochin1928[ 2 ].TheBlochtheoremassumeselectronsasextendedquantummechanicalwavesmovingfreelythroughoutaperfectlatticestructure.Althoughthistheoremwasagreatpieceoftheoreticalwork,realworldexperimentaldatademandedtheorieswhichincorporatedisorderordeviationsfromperiodicity.Thisdisordercanbeweak,wheretheelectronwavefunctionremainsextendedthroughoutthesamplebutitlosesitsphasecoherenceabovelengthscale`(meanfreepath),ordisordercanbestrong,wheretheelectronwavefunctiondecaysexponentiallyoverlength.Intheweakdisorderlimitquantumcorrectionstotransportpropertiescomesfromeitherelectronsinterferencewithitsownwave-function(weaklocalization)orwithotherelectronswave-function(electron-electroninteractions),whereasinthestrongdisorderlimitcorrectioncomefromaphenomenoncalledAndersonlocalizationwhichleadstometal-insulatortransitionfordimensiond>2.Thesequantumcorrectionscanbeseenexperimentallyinthetemperaturedependenceofconductivity,magnetoresistanceandHalleffectmeasurements.Althoughmanyexperimentshavebeenperformedonnon-magneticmetals,theeffectofdisorderonmagneticmetalsstillneedsmoreexperimentalandtheoreticalunderstanding. 6.1WeakLocalization(WL)Themotionofelectroninmetaliscontrolledbytwotypeofscattering,inelasticelectron-phononscatteringandelasticelectron-impurityscattering.Whenaelectronismovingfromonepointtoanotherthetotalquantummechanicalprobabilityfortheelectrontoreachthenextpointcanbeexpressedas[ 118 ]: W=jXi ij2=Xij ij2+Xi6=j i j(6) 87

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Herethersttermcomesfromsummingtheprobabilitiesofeachpaththeelectronistravelingandsecondthetermrepresentsinterferenceofvariouspaths.Usuallytheinterferencetermiszerobecauseofthewidevariationofindividualphases(denedby=~)]TJ /F2 7.97 Tf 6.58 0 Td[(1RPoint1Point2~k~dl)associatedwitheachdifferenttrajectory.Butincaseofself-intersectingtrajectoriesthesecondtermisnotnegligibleanymore,astherearetwodifferentamplitudes 1and 2traversinginthesameloopbutintheoppositedirection.Asthephaseisindependentofthedirectionofmovement,phaseissameforboth 1and 2whichmeansthetotalquantummechanicalprobabilitytondtheelectronatagivenpointcanbewrittenas: W=j 1+ 2j2=j 1j2+j 2j2+ 1 2+ 1 2=4j 1j2(6)ComparingEqn. 6 andEqn. 6 wegetthatquantummechanicalprobabilityistwiceaslargeifinterferenceisneglected(classicalsituation).Soduetoquantuminterference,probabilityofanelectronleavingonepointandreachinganotherpointdecreases,whichleadstoanincreaseinresistivity.Thisphenomenoniscalledweaklocalization. 6.1.1ConductivityCorrectionByWLTodeterminethequantumcorrectionininconductivity(=)causedbyweaklocalization,wehavetorstcalculatetheprobabilityofobtainingaself-intersectingelectrontrajectory.Forthiscalculationweneedtointegrate(overtime)theratioofthevolumewhichleadstheelectrontowardstheorigin(vFdt2)andthevolumeaccessibletotheelectronatanymomentt((p x2)3=(Dt)3 2).Sothemathematicalexpressionforthecorrectioncanbeexpressedas[ 119 ] ')]TJ /F14 11.955 Tf 23.91 16.27 Td[(Z'vF2dt (Dt)d 2b3)]TJ /F5 7.97 Tf 6.59 0 Td[(d'8>>>>>><>>>>>>:)]TJ /F7 11.955 Tf 10.49 8.09 Td[(vF2 D3 2(1 1 2)]TJ /F6 11.955 Tf 16.33 8.09 Td[(1 1 2')d=3,)]TJ /F7 11.955 Tf 10.49 8.09 Td[(vF2 Dbln('=)d=2,)]TJ /F6 11.955 Tf 10.49 8.09 Td[(2vF2 Db2(L')]TJ /F7 11.955 Tf 11.96 0 Td[(l)d=1.9>>>>>>=>>>>>>;(6) 88

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whereL'('p D''`p '=>>`)iscalledthephase-breakinglength,bisthethicknessofalmordiameterofawire,isthedeBrogliewavelengthoftheelectron,vFisFermivelocityofelectronsandDisthediffusionconstant.Notethattheintegrationisdonefromelasticscatteringtime(inwhichtheelectronpreservesitsenergysothatdiffusionconceptcanbeapplicable)toinelasticscatteringtime'(afterwhichelectronforgetsitsphaseandamplitudecoherenceisnotpreserved).Althoughistemperatureindependent,'hasastrongtemperaturedependencewhichcanbeexpressedas: d=3:1 '=AT2+BT3LowT)166(!AT2(6) d=2:1 '=AT+BT3LowT)166(!AT(6)Herethersttermcomesfromofelectron-electronscatteringandthesecondtermfromelectron-phononscattering.NowputtingthelowtemperaturelimitofEqn 6 andEqn 6 intoEqn 6 weget: '8><>:Td=3,lnTd=2.9>=>;(6).Anti-localization:Inpresenceofspin-orbitinteractionlocalizationcorrectionstotheconductivitychangessignicantlyastheelectronscanipthespininthecourseofelasticscattering[ 120 ].Usuallyatsufcientlylowtemperaturethespin-orbitscatteringtimesosatisesthefollowingrelation, so'(6)Tounderstandmixtureofwavefunctionsofelectronswithdifferentspins,wehavetoconsideracompoundparticlemadeupoftwoelectrons.Thetotalspinofthisparticlecanbeinoneofthefourpossiblestates(1spinzerostate[singlet]and3spinonestate[triplet]).Asaresult,thewavefunctionofthecompositeparticlecanbeexpressedas 89

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[ 121 ]: =0BBBBBBB@01,)]TJ /F2 7.97 Tf 6.58 0 Td[(11,01,11CCCCCCCA=0BBBBBBBB@1 p 2('(1)+'(2))]TJ /F9 11.955 Tf 14.49 2.61 Td[()]TJ /F4 11.955 Tf 11.95 0 Td[('(1))]TJ /F4 11.955 Tf 11.83 2.61 Td[('(2)+)'(1))]TJ /F4 11.955 Tf 11.83 2.61 Td[('(2))]TJ /F6 11.955 Tf -61.99 -13.21 Td[(1 p 2('(1)+'(2))]TJ /F6 11.955 Tf 14.49 2.61 Td[(+'(1))]TJ /F4 11.955 Tf 11.83 2.61 Td[('(2)+)'(1)+'(2)+1CCCCCCCCA(6)where'(1)and'(2)denotethewavefunctionsoftherstandthesecondelectrons,respectively,andthesubscripts+and-denotethespinpartofthewavefunctionandindicatedifferentspinprojections.Aftertraversingtheself-intersectingloop,thecompositeparticleinterfereswithitselfandtheinterferencetermisthesumofthefourterms.Thestates1,mcarryinformationabouttheelectronspin(sotheyaredampedwithtimeso)andthestate0isdampedwithtime'.Nowomittingthecumbersomecalculations,herewepresentquantumcorrectionsinthepresenceofspin-orbitcoupling[ 119 ]: ')]TJ /F14 11.955 Tf 23.91 16.28 Td[(Z'vF2dt b(3)]TJ /F5 7.97 Tf 6.59 0 Td[(d)(Dt)d 2(3 2e)]TJ /F5 7.97 Tf 6.59 0 Td[(t=so)]TJ /F6 11.955 Tf 10.49 8.09 Td[(1 2)'2vF8>>>><>>>>:D3=2(3 2)]TJ /F2 7.97 Tf 6.59 0 Td[(1=2so)]TJ /F2 7.97 Tf 13.15 4.71 Td[(1 2)]TJ /F2 7.97 Tf 6.59 0 Td[(1=2')]TJ /F4 11.955 Tf 11.96 0 Td[(1=2d=3,(Db))]TJ /F2 7.97 Tf 6.58 0 Td[(1)]TJ /F2 7.97 Tf 10.49 4.71 Td[(3 2ln)]TJ /F15 7.97 Tf 6.68 -4.98 Td[(so +1 2ln)]TJ /F15 7.97 Tf 6.68 -3.82 Td[(' d=2,D)]TJ /F2 7.97 Tf 6.59 0 Td[(1=2b)]TJ /F2 7.97 Tf 6.58 0 Td[(2)]TJ /F2 7.97 Tf 10.49 4.71 Td[(3 21=2so+1 21=2'd=1.9>>>>=>>>>;(6)WhentheconditioninEqn. 6 issatised,thequantumcorrectionofconductivityispositive.Sincethequantumcorrectionofconductivityduetoweaklocalizationisnegative,thecorrectionduetospin-orbitinteractionisgenerallycalledantilocalization. 6.1.2MagnetoresistanceCorrectionByWLInthepresenceofanexternalmagneticeldtheweaklocalizationeffectchangesasthephasesoftwointerferingloopsarenotsameanymore.Introductionofmagneticeldchangesmomentumvector~pto~p)]TJ /F6 11.955 Tf 12.62 0 Td[((e=c)~A,wherethe~Aisthemagneticvectorpotential.Nowthephasedifferencebetweentwointersectingloopsisgivenby: 'H=1 ~Z )]TJ /F4 11.955 Tf 8.74 .5 Td[(~p)]TJ /F7 11.955 Tf 13.15 8.09 Td[(e~A c!()]TJ 9.3 8.3 Td[()777(!dl))]TJ /F6 11.955 Tf 13.24 8.09 Td[(1 ~Z ~p)]TJ /F7 11.955 Tf 13.15 8.09 Td[(e~A c!)777(!dl=2e c~I~A.~dl=2 0(6) 90

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whereisthemagneticuxacrosstheloopand0=hc=2eistheuxquantum.Theappearanceofaphasedifferenceresultsindestructionoftheinterference,leadingtoadecreaseintheresistivity,whichmeansweaklocalizationhasanegativeeffectonmagneto-resistance.Tocalculatethemathematicalexpressionofthisnegativemagneto-resistance,weneedtointroduceanewtimescalecalledmagneticscatteringtime(H)denedas'H2andis H0 HD(6)WecalculatetheminimumeldbyusingthecriterionH',whichgives H0 D'.(6)Nowtocalculatetheweaklocalizationcorrectioninmagnetoressitance,wehavetojustreplacethe'byHinEqn. 6 soweget[ 119 ]: ')]TJ /F14 11.955 Tf 23.91 16.27 Td[(ZHvF2dt (Dt)3 2b3)]TJ /F5 7.97 Tf 6.58 0 Td[(d'8>><>>:e2 ~eH ~c1 2d=3,e2 ~lneHD' ~cd=2.9>>=>>;(6) 6.1.3HallEffectCorrectionByWLThequantumcorrectionsofnormalHallconductivityduetoWLin2DsystemsshowthatthenormalHallcoefcientRn=Ey=Bjxisconstantoveravariedtemperaturerange[ 122 ].SotheHallresistanceRnxy=RnBcanbewrittenas: Rnxy Rnxy=0.(6)Usingthefollowingapproximations, xx1 Rxx;xyRxy R2xx.(6) 91

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whichareareappropriateinmostexperimentswhereRXX>>RXY,thebehaviorofthenormalHallconductivitycanbededucedas: nxy nxy=Rnxy Rnxy)]TJ /F6 11.955 Tf 11.96 0 Td[(2Rxx Rxx.(6)UsingEqn. 6 ,wehave nxy nxy=)]TJ /F6 11.955 Tf 9.3 0 Td[(2Rxx Rxx=2xx xx(6)ThisexpressionclearlyshowsthatthereisquantumcorrectiontothenormalHallconductivityfromweaklocalizationandthetemperaturedependencehasaslopetwicethatofthelongitudinalconductivity. 6.2Electron-ElectronInteraction(EEI)Intheprevioussectionwediscussedtheinterferenceofanelectronwavewithitself,andinthissectionwewilltalkabouttheinteractionsbetweentheelectronwavesofdifferentconductionelectrons.Thiseffectiscalledelectron-electroninteractionandalsocreatesquantumcorrectionstothetransportpropertiesofametal[ 119 ].Inaperfectmetalwhenelectronofstate~k1=)]TJ /F2 7.97 Tf 6.59 0 Td[(1=2ei~k1.~rscattered(byanotherelectron)toanotherstate~k2=)]TJ /F2 7.97 Tf 6.58 0 Td[(1=2ei~k2.~rmomentumisconservedintheformofmomentumtransferq=~k2)]TJ /F4 11.955 Tf 13.63 3.15 Td[(~k1.Butinadisorderedmetalthismomentumconservationwillbreakdownifq`<1.Thismeansthatthestrengthofelectron-electronscatteringwillbeenhancedinthisregime(whereq`<1)asthenumberofsucheventsisnotrestrictedbymomentumconservation.Fromtheenergypointofview,theenergyEofanelectroninastateEchangestoanewenergyEduetoelectron-electroninteraction.ThisnewenergyEcanbeexpressedas: E=E+E,(6)whereEiscalledtheself-energy.Nowtheinteractionthroughtheself-energyleadstotwoimportantconsequence, 92

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itchangesthedensityofstatesbyanamountN(E), N(E) N(E)=@
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(b)Exchangeenergyterm: )]TJ /F14 11.955 Tf 11.95 16.27 Td[(ZZ E0(~r) E(~r0)V(~r)]TJ /F4 11.955 Tf 12.26 2.74 Td[(~r0,t) E0(~r) E(~r0)d3~rd3~r0(6)whichispurelyquantum-mechanicalinnatureandcomeswhenthetotalelectronwavefunctionismadeantisymmetric.Thecontributionofanexchangetermtotheselfenergyisgivenby: E=)]TJ /F14 11.955 Tf 11.29 11.36 Td[(XE0ZZ E0(~r) E(~r0)V(~r)]TJ /F4 11.955 Tf 12.26 2.73 Td[(~r0,t) E0(~r) E(~r0)d3~rd3~r0(6)Foragivendimensionalityd,thiscanbewrittenas: E=)]TJ /F6 11.955 Tf 21.72 8.09 Td[(1 (2)dZdE0N(E0)Zql<1dd~qVb(~q) (~q,E)]TJ /F7 11.955 Tf 11.95 0 Td[(E0)jh Ejexp(i~q.~r)j E0ij2(6)whereVb(~q)istheFouriertransformofthebareCoulombpotentiale2=r,(~q,E)]TJ /F7 11.955 Tf 12.2 0 Td[(E0)isthedynamicscreeningfunctionofanelectrongas,jh Ejexp(i~q.~r)j E0ij2istheFouriertransformofj (~r,t)j2and (~r,t)isthetimedependentwavefunctionofanelectroninarandomsystem.Foranelectronundergoingmanyelasticcollisions,thej (~r,t)j2canbeexpressedas j (~r,t)j2=1 (4Dt)d=2exp()]TJ /F7 11.955 Tf 9.3 0 Td[(r2=4Dt),(6)whichisessentiallythesolutionofthediffusionequation.PerformingtheFouriertransformoftherighthandsideoftheEqn. 6 weget[ 124 ] jh Ejexp(i~q.~r)j E0ij2=1 ~N(E)Dq2 (Dq2)2+(E)]TJ /F7 11.955 Tf 11.95 0 Td[(E0)2=~2.(6)PluggingEqn. 6 intoEqn. 6 ,wegettheself-energyas: E=)]TJ /F6 11.955 Tf 45.11 8.09 Td[(1 ~N(EF)(2)dZdE0N(E0)Zql<1dd~qVb(~q) (~q,E)]TJ /F7 11.955 Tf 11.96 0 Td[(E0)Dq2 (Dq2)2+(E)]TJ /F7 11.955 Tf 11.95 0 Td[(E0)2=~2.(6)NowusingtheEqn. 6 wecancalculatethedensityofstates,whichisgivenby N(E) N(E)=)]TJ /F6 11.955 Tf 45.12 8.08 Td[(1 ~N(EF)(2)dZql<1dd~qDq2 (Dq2)2+(E)]TJ /F7 11.955 Tf 11.95 0 Td[(EF)2=~2(6) 94

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NotethattheenergyderivativeoftheselfenergyEisessentiallytheintegrandofEqn. 6 ,leadingtoEqn. 6 6.2.1ConductivityCorrectionByEEIUsingtheEinsteinrelationwegetthatthechangeinconductivity(duetotheelectron-electroninteraction)isapproximatelyrelatedtothechangeinthedensityofstatesbytherelation: =N N(6)Forsmall=E)]TJ /F7 11.955 Tf 13.21 0 Td[(EFandusingEqn. 6 ,Eqn. 6 yieldsthefollowing[ 124 ]temperaturedependenceofconductivity: /8>>>><>>>>:T1=2d=3,lnTd=2,T)]TJ /F2 7.97 Tf 6.59 0 Td[(1=2d=1.9>>>>=>>>>;(6)NotethatthetemperaturedependenceofEEIcorrectionin2DisexactlysimilartotheWLcorrection(Eqn. 6 ).OnlywaytodifferentiatebetweenEEI&WLeffectsin2Disbyapplyingexternalmagneticeld,asmagneticelddestroysWLcorrectionmuchfasterthanEEIcorrection. 6.2.2MagnetoresistanceCorrectionByEEITheeffectofexternalmagneticeldislessdramaticinEEIcomparedtoWL.Frommany-bodypointofviewweaklocalizationeffectsarisefromtheparticle-particlechannelandelectron-electroninteractioneffectsarisefromtheparticle-holediffusionchannel.Theparticle-particlechannelishighlysensitivetomagneticeldcomparedtoparticle-holechannel.ThemaineffectofmagneticeldinEEIisthesplittingofthespinupandspindownbands[ 125 ].TheintroductionofmagneticeldsplitseachelectronenergystateintoatripletofSZ=0,+1&-1.Thissplittingchangesthetotalself-energy,asweuseelectronenergystatesduringtotalselfenergycalculation.ThespinsplittingproducesagapgBHbetweenthelowestunoccupiedspin-upandthehighestoccupied 95

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spin-downelectron.ThemathematicalexpressionfortheEEIcorrectioninmagnetoresistancecanbeexpressedas: 'e2 22~1)]TJ /F7 11.955 Tf 13.15 8.09 Td[(ln(1+F0) F08><>:lnhh>>1,h2h<<1.9>=>;(6)whereh=gBH=kBTandF0isthenon-universalFermi-liquidconstant.F0cananddoeschangesfromsystemtosystemasitdependsonthedetailsofthepotentialdescribingelectron-electroninteraction. 6.2.3HallEffectCorrectionByEEIPreviousstudiesshowthatnormalHallconductivitydoesnothaveanyquantumcorrectionfromelectron-electroninteractionin2Ddisorderedmetals[ 126 ].AlthoughtheHallconstantincreaseslogarithmicallyatlowtemperature,therateequaltotwicethatofresistivity.NowusingEqn. 6 wegetthatthenormalHallconductivityisindependentoftemperatureandgivenbythefollowingrelation: nxy nxy=Rnxy Rnxy)]TJ /F6 11.955 Tf 11.96 0 Td[(2Rxx Rxx=0.(6) 6.3AnomalousHallCorrectionInMagneticMetalThehallresistivityinmagneticmetalscanbeexpressedbythefollowingequation: xy=RnB+0RsMs(6)whereRnisthenormalHallcoefcient,Bistheappliedmagneticeld,0isthepermeabilityoffreespace,RsisthespontaneousHallcoefcientandMSisspontaneousmagnetization.TherstpartisthenormalhalleffectcomesfromLorentzforceactingontheelectrons.ClearlythesecondpartarisesonlyinthemagneticmetalsasMsiszerofornon-magneticmetals.Thisiscalledanomaloushalleffectwhichcomesfromeitherskewscattering(whenelectronscatteringprobabilityWfromktokisnotequaltotheinverseprocessi.e.W(k,k)6=W(k,k),thenitiscalledskewscattering[ 127 ]) 96

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orsidejump(Whenmagneticallypolarizedfreeelectronsundergoasmallsidejumpduetospin-orbitinteractionduringeachscattering,thenitiscalledside-jump[ 128 ])mechanism.HerewearegoingtodiscussthequantumcorrectionstotheanomalousHallconductivitycomingfromelectron-electroninteractionsandweaklocalization. 6.3.1QuantumCorrectionsFromElectron-ElectronInteractionsJustlikenormalhalleffectanomaloushalleffectalsodoesnotreceiveanycorrectionfromelectron-electroninteractioninskewscatteringregime[ 129 ],whichisexplainedinthefollowingequation: AH(SS)xy AH(SS)xy=RAH(SS)xy RAH(SS)xy)]TJ /F6 11.955 Tf 11.95 0 Td[(2Rxx Rxx=0.(6)ThistheoreticalpredictionwasexperimentallyconrmedbyBergmannandYe[ 130 ],wheretheyfoundtemperatureindependentAHconductivityinamorphousthinlmsofiron. 6.3.2QuantumCorrectionsFromWeakLocalizationSideJumpRegime:Thelocalizationcorrectionto2DAHconductivitywithinsidejumpmechanismcanbeexpressedas[ 131 ]: AH(SJM)xy AH(SJM)xy1 ("F)3,(6)whereas xx xx1 "F.(6)Butthelocalizationeffectisonlyseenintheregimewhere"F>>1,whichmeansthatfollowingrelationisvalidbetweenconductivitycorrection&AHconductivitycorrection AH(SJM)xy AH(SJM)xy<
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Skewscatteringregime:Inthecaseofskewscattering,localizationeffectdoeshaveanon-zerocontributiontoAHconductivitywhichisgivenby[ 131 ]: AH(SS)xy=)]TJ /F7 11.955 Tf 17.89 8.09 Td[(e2 36~20k2F""3 2ln"1 so"+1 '")]TJ /F7 11.955 Tf 11.96 0 Td[(k2F##3 2ln#1 so#+1 '#.(6)Where01=m0c,m0isfreeelectronmass,2and3areparameters,characterizingthestrengthofthedisorderpotentialandalsothestatisticalpropertiesoftherandomeld,kF"(#)ismomentaofspin-up(down)electronsatFermisurface,"(#)arethedensitiesofstatesforspin-up(down)electronsattheFermilevelanddifferent'saredifferentelectronscatteringratesdiscussedearlier.TheexpressionshowninEqn. 6 isonlyfortwodimensionalsystems.NowtheAHconductivityandlongitudinalconductivitycanbeexpressedas: AH(SS)xy=e2 18203 2(k2F"2"2F"")]TJ /F7 11.955 Tf 11.95 0 Td[(k2F#2#2F##)(6) AH(SS)xx=n"e2" m+n#e2# m(6)NowusingtheEqn. 6 &Eqn. 6 andassumingaparabolicbandwecansimplifytheEqn. 6 intothefollowingexpression: AH(SS)xy AH(SS)xy=1 2e2 22~1 xx"(#)ln"(#)1 '"(#)+1 so"(#)(6)anditshowsthattheanomalousHallconductivityreceivesaquantumcorrectionwithlogarithmictemperaturedependence. 98

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CHAPTER7EXPERIMENTALSTUDIESONCHROMIUMTHINFILMSChromium(Cr)belongstothefamilyoftransitionmetalsingroupVIoftheperiodictable.ThegroundstateelectroniccongurationofChromiumis[Ar]3d54s1Chromiumexhibitsawiderangeofpossibleoxidationstates.Themostcommonoxidationstatesofchromiumare+2,+3,and+6,with+3beingthemoststable.The+1,+4and+5statesarerare.CrisantiferromagneticmaterialwithaNeeltemperatureof311K.Itbecomesparamagneticabovethattemperature.Ithasabodycenteredcubicstructurewiththeatomicradiusof1.85Aandcovalentradius1.18A.Bulkchromiumisanitinerantantiferromagnetwithanincommensuratespin-densitywave(ISDW)andhasbeenwidelystudiedasanarchetypalbandantiferromagnet[ 132 ].TheSDWinbulkCrisverysensitivetoperturbationbydopantatoms,pressure,etc[ 133 ].Antiferromagnetism,islikeferromagnetismandferrimagnetism,amanifestationoforderedmagnetism.Butunlikeferroorferri-magnetismherethemagneticmomentsofatomsormolecules,aligninaregularpatternwithneighboringspins(ondifferentsublattices)pointinginoppositedirections.Generally,antiferromagneticordermayexistatsufcientlylowtemperatures,vanishingatandaboveacertaintemperature,theNeeltemperature(namedafterLouisNeel,whohadrstidentiedthistypeofmagneticordering)[ 134 ]abovewhichthematerialistypicallyparamagnetic.Motivatedbythepreviousexperimentsdoneinourgroupontheitinerantferromagnetironandmorelocalmomentferromagnetgadoliniumlms,wehavestartedstudyingantiferromagnetchromiumoverawiderangeofdisorder.AsinourpreviousexperimentstheR0sheetresistanceat5KisthemeasurementofdisorderandR0inthisstudyvariesfrom360to2.51M. 7.1ExperimentalDetailTheultrathinlmsofpurematerial(inthiscase-Chromium)areextremelyairsensitiveandespeciallyinthecaseofmetaltheytendtoformmetal-oxides.This 99

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requiresaninstrumentwhereinsitudepositionandcharacterizationcanbedonewithoutbreakingvacuum.Makingelectricalcontactstosuchultrathinlmsisabigproblembecausetheremaybeahighcontactresistance.Tominimizethecontactresistance,ngeredcontactpads(asshowninFig 7-1 )havebeenused.Thecontact Figure7-1. Pre-depositedcontactpadstructurewithserpentineedgesforbettercontact padswithserpentineedgesincreasetheprobabilityofcontactandreducescontactresistance.Therearesomesequentialstepstoprepareeachcontactpad.Sapphiresubstratesarecleanedinasonicatorwithdeionizedwater,acetoneandmethanolatleast10minuteseach.Thesubstratesarethendriedwithanitrogenblowandinspectedwithanopticalmicroscopeforcleanliness.Afterwearesatisedwithcleanlinessthesesapphiresubstratesweretakenforphoto-lithographywithShipley1813photoresistthinnedwithaP-Thinnerintheratioof3:1.Thephotoresistisreleasedataspinspeedof700rpmfollowedbyspinspeedof3500rpmfor30seconds.Thenitisplacedonahotplatefor120secondsattemperature110C.Thisiscalledprebakingofphotoresist.Thisprocedureresultsinaphotoresist(PR)thicknessaround0.5mm.Afterprebakingthephotoresistlm,itisexposedtoultravioletlightthroughatransparencymaskfor20seconds.MIF319developeristhenusedtodevelopthelmfor45seconds,followedby 100

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cleaningwithdeionizedwaterfor10-15seconds.Wenowhavethepatterntransferredontothesubstrate.Ontothispatternwhichdenesthecontactpads,wedeposit50Aofchromiumfollowedby200Aofpalladiumusingthermalevaporation.Theliftoffisthenperformedbysonicatingthesampleinacetoneforseveralminutesfollowedbycleaningofacetoneresiduewithmethanolfor10minutes. 7.1.1ThinFilmDepositionUsingtheabove-describedsapphiresubstrateswiththepredepositedcontactpads,chromiumthinlmshavebeengrownatroomtemperatureusingR.F.magnetronsputteringwithgrowthparameterslistedinTable 7-1 Theselmsweredepositedusing Table7-1. Growthparametersforchromiumlms ParametersValues Rfpower45WDCbias-35VArowrate10sccm ashadowmaskintheHallcrossgeometry,whichisshowninFig 7-2 alongwithitsaspectratios.AllthenumbersspeciedintheFig 7-2 areininches.Thesevalues Figure7-2. Shadowmaskgeometryalongwithitsaspectratios.Allthenumbersareininches yieldmeasurementswhichhaveverysmalldeviationsfromtheideal[ 135 ].Duringthegrowthofthinlmsthecurrentandvoltageleadsofthedepositedsampleoverlapped 101

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withthepre-depositedpalladiumcontacts,sowecangetreliableelectricalconnection.Immediatelyafterdeposition,samplesweretransferredwithoutexposuretoairfromthehighvacuumdepositionchambertothecryostatformagnetotransportandheldatatemperatureof80Korbelow.Atthesetemperaturesthesamplesarestableanddonotundergoanytime-dependentchangesinresistance.Duringdeposition,sampleresistanceandthicknessarecontinuouslymonitoredinsitu.Toparameterizethedisorderinagivenlm,weusethesheetresistanceR0=RXX(T=5K)whereRXXisthelongitudinalresistance.Inthisstudy,R0spanstherangefrom300to2510Kforlmswiththicknessoftheorderof20A. 7.1.2MeasurementTechniqueTheinsitucharacterizationofthethinlmshasbeendoneinthecryostatofSHIVA.Four-terminald.c.measurementsaremadeusingaKeithley236SMU,Keithleyswitchingcard7012SandKeithley182nanovoltmeter(Fig. 7-3 ).TheyallhaveGPIBcapability,sousingthatallthemeasurementscanbedoneautomatically.ThelongitudinalandtheHallresistanceareextractedusingthereversemagneticeldreciprocity(RFMR)theorem[ 136 ].UseoftheRFMRtheoremmakesthemeasurementeasierandsavestimebyallowingeldsweepsinonlyonedirectionwhilestillobtainingbothRXXandRXYaccurately. 7.2PreviousStudyOf3DMetal-InsulatorTransitionInGadoliniumInthepreviousmeasurementdonebyDr.RajivMisrafromourgroup,wepresentedtheexperimentaldataandatheoreticalinterpretationofthetemperature-dependenceconductancenearthemetal-insulator(M-I)transitioninthinferromagneticGdlmsthatareeffectivelyinthethree-dimensionalregime.[ 137 ].AlllmsaregrownintheSHIVAapparatusatT=130KandthenimmediatelytransferredtotheadjoiningcryostatandheldatT=77Korbelowwherethesamplesarestableanddonotundergoanytime-dependentchangesinresistance.Thetemperaturedependenceoftheconductivityisstudiedinatemperaturerangeof5Kto50K,whereweobtainreproducibledata. 102

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Figure7-3. SchematicrepresentationoftypicalDCmeasurementcircuitusedduringchromiumthinlmmeasurements. ShowninFig 7-4 (a).aretheplotsofconductivityasafunctionoftemperatureforallthesamplesstudied.Wehaveincludedthegraphsforallthesamplesstudiedintheseriestoshowthequalityofthedataandthets.Theconductivityofallthedatasetsiswelldescribed(solidredlinesinFig. 7-4 (a))bytheequation, (T,R0)=L0=A+BTP(7)HereA,B,parettingparametersandL0isthefundamentalquantumofconductancegivenbye2/~=25813)]TJ /F2 7.97 Tf 6.59 0 Td[(1.TherearethreeimportantttingparametersA,Bandp.WewillthestudythevariationofthesettingparameterswithdisorderasmeasuredbyR0.ThebehavioroftheparameterAasafunctionofR0isshowninFig. 7-4 (b).WecanseethattheparameterAhasadependenceondisorder.AstartswithapositivevalueatlowvaluesofR0inthebeginning,goesthroughzeroandthenbecomesnegativewithhigherdisorder(greaterR0).ThegradualandsystematicchangeofR0wasachievedby 103

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(a) (b) (c) (d) Figure7-4. PreviousStudyofGadolinium:(a)Typicalpower-lawtemperaturedependenceofnormalizedconductivityindisorderedGadolinium,(b)VariationofpowerAwithsheetresistance,(c)FigureBindetail,(d)VariationofpowerB&pwithsheetresistance, annealingasinglegadoliniumthin-lmabovethegrowthtemperatureof150K.ThechangeoftheparameterAfromapositivetonegativesigniesametal-insulatortransition[ 137 ].Thecleverexperimentaldesignallowsonetochangedisordersystematicallytodrivethesystemthroughthetransition,whereAgoesthroughzeroandtheconductivityispurepower-law.TheexponentpandprefactorBareweaklydependentuponthedisorder.Thepowerpisalmostconstantaroundthevalueof0.4andthecoefcientBslowlyincreasesasdisorderincreases[Fig. 7-4 (c)].AcloserlookintheregionnearthecriticalresistancesuggestsabetterunderstandingofparameterAwithvariationofdisorder[Fig. 7-4 (d)].IthasbeenseenthatAnotonlydecreaseswith 104

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increasingdisorderitvarieslinearlynearthecriticalresistancedescribedbyEqn. 7 A/j(R0)]TJ /F7 11.955 Tf 11.95 0 Td[(RC)L0js(7)wheres(==1.38)istheconductivityexponentforthemetallicsideandR0isthemeasureofdisorder(characterizedbythesheetresistanceRxxatT=5K)andRCisthevalueofcriticaldisorder.ThevalueofcriticaldisorderRC=22741(50).ThiscorrespondstothedisorderwherethevalueoftheparameterA=0.ThebehavioroftheparameterAandthecollapseofallthedataontoasinglecurveoneachsideofthetransitionshowsthatwearecharacterizinga3DAndersonlocalizationtransitioninthethinferromagneticgadoliniumlms.Theeffectivedimensionalityofthesystemisd=3ifthephasebreakinglengthL(duetoinelasticscatteringofelectronoffspinwaves)islessthansamplethicknessb(i.e.L<1K. 7.3StudiesOnChromiumThinFilmMotivatedbythepreviousresearchofmetal-insulatortransitioninferromagneticultra-thingadoliniumlms,wehaveinitiatedthestudyonanti-ferromagneticchromium.HerewearechangingsheetresistancehencedisorderofchromiumlmsandtryingtondwhetherwecanseeanAndersontypedisorderdrivenmetal-insulatortransitionalsoinantiferromagnets.Duringthisresearchwehavestudiedthreedistinctregionsofdisorderdependenceofconductivity:1.Belowasheetresistance6Kwehaveseenthetemperaturedependenceofconductivityisapowerlawplusaconstant.2.SheetresistancerangingwithinR0=6K&250Kshowsapurelylogarithmictemperaturedependenceofconductivity.3.Intheregionwheresheetresistanceisabove500K,temperaturedependenceofconductivityisexponentialinnature. 105

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7.3.1Temperature-DependentConductivityOfWeaklyDisorderedCrWehavemeasuredthechromiumthinlmstemperaturedependentconductivity.ThechromiumthinlmshavebeengrownintheSHIVAatroomtemperatureandthenrightaftergrowingtheyhavebeentransferredtocryostatkeptat80Korbelow.Alltheconductivitydependencefollowsequation 7 ,whereA,B&pareparametersofttingandL0isdenedabove.AsdepictedinFig. 7-5 ,Adecreasesassheetresistanceincreasesbutdoesnotgoesthroughzero.Buttheexponentpofthepowerlawremainsalmostxedaround0.2spanningarangeofdisorderfrom350to6K.Asthepowerpinthispower-lawttingisverysmall,wehavecomparedthepowerlawttingwithlogarithmicttinginFigure 7-6 forsomechromiumthin-lms.Figure 7-6 clearlyshowspower-lawttingisabetterttingcomparedtologarithmic.Furtheranalysisshowthatrelativechangeinconductivityisaround10%orsmaller.Thatmightimplythatthispowerlawnatureofconductivityisduetoapowerlawquantumcorrectiontoconductivity.Whenwestudythedisorder-dependentbehavioroftheparametersA,BandpweseethatparameterAisdecreasingveryfastasweincreasedisorder[Fig. 7-7 (a)].PlottingparameterAwithdisorderinlogarithmicscalewendalinearrelationship[Fig. 7-7 (b)]betweenparameterAandR0withaslopeof-1.ThepowerlawprefactorBstaysaround1.6forsheetresistanceuptoR0=1500andthendrasticallydecreases[Fig. 7-7 (c)].Thepowerpstaysaround0.2overtheentirerangeofdisorderfrom370to6K,whichismorethanafactorof15[Fig. 7-7 (d)].Althoughthisbehaviorisinteresting,thereisnoavailabletheorytoexplainthisresult.Incomparisonwiththesedataifwediscusstheweakdisordergadoliniumdataweseeasignicantdifference.Insteadofapurepowerlaw[ 138 ],apowerlawinseriescombinationwithalogarithmiccorrectionwasseen.Thelongitudinalconductivityfor 106

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Figure7-5. Temperaturedependenceofnormalizedconductivityinweaklydisorderedchromiumshowspower-lawbehavior. 107

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Figure7-6. ComparisonofpowerlawandlogarithmicttingforchromiumthinlmswithR0366and5.99K typicalthinGdlmscanbeexpressedas: xx=L00=P1+P2lnT T0+P3lnT T0p(7)whereP1,P2,P3&pareparametersofttingandL00=e2/handT0=5Kisareferencetemperature,hasbeenusedtoteachofthecurves.Thehighqualityofthetsshowsthatbothlogarithmicandlineartemperaturedependencesarenecessary[ 138 ].Nowwearegoingtodiscussthevariationoftheseparameterswithdisorder.AgaindisorderisparameterizedbyR0(Rxx@5K).ThesheetresistanceR0isvariedbyalmostafactorofeightinthegraphsshowninFig 7-8 (b).Thereareseveralimportantpointsinthistting.First,thepowerpremainsnearunityovertheindicatedrange.(Athigherdisorder,R0>4K,thepowerpdecreasessignicantlywhichisa 108

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Figure7-7. (a)variationofttingparameterAwithdisorderinchromium,(b)Graph(a)plottedinlog-logscaleshowslinearrelationshipbetweenparameterAandR0,(c)variationofttingparameterBwithdisorderinchromium&(d)variationofttingparameterpwithdisorderinchromium (a) (b) Figure7-8. WeaklydisorderedGadolinium:(a)Temperaturedependenceofnormalizedconductivity,(b)VariationofttingparameterP1,P2,P3&pwithdisorder 109

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differentdisorderregime).TheparameterP1changesbyalmostafactorofeightwhichisoftheorderofthechangeinR0.Next,thecoefcientP3decreaseswithincreasingdisorderbyalmostafactoroftwoandthensaturates.Finally,theprefactorP2ofthelogarithmicterm,whichisacombinationoflocalizationandinteractioncorrections,isconstantnearunityovertherangewediscussed.Astheauthorsstate[ 138 ]Theunusualtemperaturedependencerevealedbythesedataisconsistentwithasumofcontributionsfromwell-knownquantumcorrectionsintwo-dimensionsandanovelspin-wavemediatedcorrectionanalogoustotheAltshuler-Aronovelectron-electroncontributionindisorderedsystems.WhiletheAltshuler-Aronovcontributiongivesrisetologarithmictemperaturedependenceintwodimensions,thespin-wavemediatedcontributioncanbelinearintemperaturewithincertainrangesoftheparameters,consistentwiththeexperiments.Thistheorydoesnotworkforlargedisorder(R0>4K). 7.3.2Temperature-DependentConductivityOfHigherDisorderedCrIntheregionofhigherdisorder(6K
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Figure7-9. Logarithmictemperaturedependenceofnormalizedconductivityinstronglydisorderedchromium 111

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Figure7-10. PlotofnumericalprefactorARforlogarithmictemperaturedependenceoflongitudinalconductance(equation 7 )fordifferenthighlydisorderedchromiumlms,asafunctionofsheetresistanceR0 Fig. 7-10 wasalsoseeninthepreviousstudyonultra-thinironlms[ 139 ]andattributedtotheemergenceofgranularitywithincreasingdisorder.Finallycomparingthetemperaturedependentdataofnormalizedconductivityinhighlydisorderedchromium(Fig 7-9 )withexistingtheoriesofonquantumcorrectionstoconductivityin2Dmetals,weconcludethatlogarithmictemperaturedependenceisduetoquantumcorrectionsweaklocalizationandelectron-electroninteraction. 7.3.3Temperature-DependentConductivityOfUltra-HighDisorderedCrIntheregimewhereR0isabove500Kweseethattemperaturedependenceofnormalizedconductivitydoesnotfolloweitherpowerlaworlogarithmictemperaturedependence.Butthelongitudinalconductanceratherfollowstheexponentialhopping 112

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Figure7-11. Temperaturedependenceofnormalizedconductivityinultra-highlydisorderedchromium 113

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behaviorexpressedbythefollowingequation[ 140 ]: Lxx(T)=L0xx=exp T0 T)]TJ /F15 7.97 Tf 6.58 0 Td[(!(7)whereL0xxandT0arethecharacteristicconductanceandenergyscaleinatwodimensionalsystemwithlocalizedelectronicstates.Theexponentialbehaviorclearlyshowstheonsetofgranularitywhereconductivityiszeroatzerotemperature((T=0)=0),whichisanindicationofinsulatingbehavior.Theexponentis1fornearest-neighborhopping,1/2forEfros-Shklovskiivariablerangehoppingand1/4forMottvariablerangehopping.Tocomparewhichtypeofhoppingisprominentinoursampleswehaveplottedthenormalizedconductancewithdifferentpowersoftemperature.AsshownintheFig. 7-11 ,normalizedconductivitydoesnotshowanygoodlineartwhenplottedagainstT)]TJ /F2 7.97 Tf 6.59 0 Td[(1,butconductivityshowssatisfactorylineartwhenplottedagainsteitherT)]TJ /F2 7.97 Tf 6.58 0 Td[(1=2orT)]TJ /F2 7.97 Tf 6.59 0 Td[(1=4[ 118 ].Sonallywecanconcludethatvariable-rangehoppingisthemainactivationphenomena.ItisnotveryclearwhetherMotttypeorEfros-Shklovskiitypehoppingisdominanthere. 7.3.4W-PlotForChromiumShowninFig. 7-12 (a)isthedependenceofthelongitudinalresistanceontemperatureforaseriesofchromiumthinlms.Wecanseefromthisgurethatwehaveawiderangeofsheetresistances.Toanalyzethesedata,wedotheT-dependentreducedactivationenergyplotsof(T)[Wplots]forlmsspanningalargerangeofdisorderstrengthswhenR0varieswithin366and5.99K(Fig. 7-12 (b)).TheparameterWisdenedby: W=Tdln(xx) dT(7)Nowitcanbeeasilyshownthatincaseofpowerlawwheretemperaturedependenceofconductivityisfollowing: (T,R0)=L0=A+BTP(7) 114

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Figure7-12. (a)Rxxasafunctionoftemperatureforaseriesofchromiumthinlms,(b)PlotofparameterW,asdenedinEqn. 7 asafunctionoftemperatureforthinlmofchromium. 115

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wecangetW=ponlywhenA=0,whichiscalledpurelypowerlawregime.HerewehaveshownW-plotontheanti-ferromagneticchromiumlm.OnlythelowerdisorderlimitofchromiumdatawereusedtomaketheW-plotwherewehaveseenpowerlawbehaviorintemperaturedependenceofnormalizedconductivity.Itisevidentfromtheg 7-12 (b)thatwehaventgotanyconstantWregionasthevalueofparameterAneverwentfrompositivetonegativethroughzero.ThevalueofparameterAalwaysremainedpositive,whichisconsistentwithpositiveslopeofeverycurveintheW-plot(Fig 7-12 (b)). 7.4ConclusionInthischapterwehavereportedasystematicstudyofthein-situtransportpropertiesofthin-lmsofchromium.Asetofsamplesweregrownwithsheetresistancefrom370to2510k.Thetemperaturedependenceoflongitudinalelectricalconductanceinthischromiumlmsexhibitsthreedifferentbehaviorsasthesheetresistanceisincreased.FromR0370to6kwehaveseenthetemperaturedependenceofconductivityisapowerlawplusaconstant.Secondwhenthesheetresistancerangesbetween6kand250k,temperaturedependenceoflongitudinalelectricalconductanceshowsapurelylogarithmicbehavior.FinallyintheregionwhereR0isabove500k,thetemperaturedependenceofconductivityisexponentiallyactivated. 116

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CHAPTER8EXPERIMENTALSTUDIESONDISORDEREDMANGANESETHINFILMSManganeseisasilvery-graymetalresemblingiron.Ithasaatomicnumberof25withgroundstateelectroncongurationof[Ar]4s23d5.Ithasabody-centeredcubic(BCC)structure.Themostcommonoxidationstatesofmanganeseare+2,+3,+4,+6and+7,thoughoxidationstatesfrom-3to+7areobserved.Manganesecompoundswheremanganeseisinoxidationstate+7,whicharerestrictedtotheunstableoxideMn2O7andcompoundsoftheintenselypurplepermanganateanionMnO)]TJ /F2 7.97 Tf 0 -7.97 Td[(4,arepowerfuloxidizingagents.Oneoffourallotropicmodicationsofmetallicmanganese,-Mn,hasacomplicatedcrystalstructurewhichiscomposedoffourcrystallographicallynonequivalentsites.-Mntransformsintoananti-ferromagneticstatebelowtheNeeltemperatureTN=95K.Thehighlycomplexmagneticstructureofmanganeseemphasizesthatinter-atomicspacingandthegeometricalstructureofatomicarrangementhasahugeeffectonthemodeofspinalignment.AsaresultitwasfoundthatforverysmallseparationsofMnatoms(2.37A)thereisnotendencyforspincoupling,thatforintermediaterangesofdistances(2.49to2.82A)thecouplingisanti-parallelandforthelongdistances(>2.96A)parallelspincouplingoccurs[ 141 ].Inspiredbythecomplexnatureofmagnetisminmanganesewehavestartedtostudyspinandelectrontransportofultra-thinlmsofmanganese.Herewereportthedependenceofconductivityofultra-thinlmsof-Mnwithsheetresistance(RXXat5K)rangingfromaround6kupto20MK. 8.1ExperimentalDetailAllexperimentalprocedures,substratepreparationandmeasurementtechniquesareidenticaltothoseusedforthechromiumthinlmsdescribedinsection7.2.Theonlydifferenceisinthinlmgrowthmechanism¶meters.Unlikechromium,manganesethinlmsweregrownusingDCsputteringinsteadofRFsputtering.Soaseriesofmanganesethinlmsweredepositedonhighlypolishedsapphiresubstrateat 117

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atemperatureof250KusingDCmagnetronsputteringwithaDCpower12WattandArowrateof10sccm. 8.2Power-LawTemperatureDependenceInIntermediate-DisorderMnInspiredbythepreviousstudyongadoliniumdiscussedinthepreviouschapter,manganesethinlmsaregrownusingsputteringtechniquesandstudiedintheSHIVAcryostatwithoutbreakingvacuum.OnemanganesesampleofR06Kwasgrownat250Kandthenannealedtogetsubsequenthighersheetresistancesamples.Everytimethesampleisheatedtoatemperaturenearoraboveitsgrowthtemperature,thesheetresistanceofthelmincreases.Theincreaseofsheetresistancecanbeattributedtoclusterformationathighertemperatures.Afterannealingthesamplearound300Kthesampleiscooleddownto5Kandthesheetresistanceofthesampleincreases.Nowthis`new'sampleismeasuredfrom5to50Ktostudythetemperaturedependenceofconductivity.Justlikethegadoliniumthin-lms,themanganesethinlmsfollowpower-lawbehaviordescribedinequation 8 (T,R0)=L0=A+BTP(8)TemperaturedependenceofnormalizedconductivityforasetofsamplesareshownintheFig 8-1 .Thesolidbluelineineachgraphisshowingthepowerlawtting.TherearethreettingparametersA,Bandpwhichvarywithdisorder.ThisdisorderinthiscaseisthesheetresistanceR0measuredatT=5K.WeareshowingthedependenceofA,BandpwithR0intheFig. 8-3 .AsshowninthegureparameterAdecreasesfrom1.0to0.2withincreasingsheetresistanceupto40KandthenAparametersaturatesatavalueof0.2.ThisAvaluestaysatthisvalueforaR0valuerangingfrom38kto185k.TheparameterB&parealsodependentonR0shownintheFig 8-3 (b).Asshown,parameterBinitiallyslowlyincreaseswithintheR0rangeof6Kto20Kfrom0.20to0.25.ThenwhenR0isgraterthan20KtheparameterBstaysatforR0from20Kto40K.After40KtheBparameter 118

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Figure8-1. TemperaturedependenceofnormalizedconductivityinweaklydisorderedMn 119

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Figure8-2. Temperaturedependenceofnormalizedconductivityinweaklydisorderedmanganese(continued) 120

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Figure8-3. (a)VariationofparameterAwithsheetresistanceforT0=5K,(b)Graphshownin(a)showninlog-logplotforT0=5K,(c)VariationofpowerBwithsheetresistanceT0=5K,(d)VariationofpowerpwithsheetresistanceT0=5K. suddenlystartstodecreaseassheetresistanceincreases.Parameterpshowsidenticalbutcomplementarybehavior.Initiallyparameterpdecreasesfrom0.30to0.18whenR0changesfrom4Kto20K,thenstaysconstantat0.18forR0from20Kto40KandnallypstartsincreasingwithsheetresistancewhenR0ismorethan40K.Tochecktherobustnessofourpower-lawtting,wehavestudiedthepower-lawttingforT0=8K.T0istheminimumtemperaturefromwhichthettingisdone.FittingwiththenewT0,wendthatthepower-lawproperlytsasshowninFig. 8-4 .AfterttingthetemperaturedependenceofnormalizedconductanceforseveraldifferentR0 121

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Figure8-4. TemperaturedependenceofnormalizedconductivityinweaklydisorderedmanganeseforT0=8K 122

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Figure8-5. (a)VariationofparameterAwithsheetresistanceforT0=8K,(b)Graphshownin(a)showninlog-logplotforT0=8K,(c)VariationofpowerBwithsheetresistanceT0=8K,(d)VariationofpowerpwithsheetresistanceT0=8K. samples,wefoundanothersetofparametersA,B&pforthisnewT0=8K.TheplotsofFig 8-5 showthattheparametersA,B&phavesimilarmagnitudeandvariationasdisorderR0increasesindependentofT05Kor8K.AcomparisonofthedependenceoftheparameterAwithdisorder(R0)showsaprofounddifferencefortheferromagneticGdlms(bluetriangles)andtheantiferromagneticMnlms(redcirclesandgreentriangles)[Fig. 8-6 (a)].ForGdtheparameterAcrossesfrompositive(metal)tonegative(insulator)valuesatcriticaldisorder(A=0)withacriticaldisorderstrengthR0=Rc=22.67kattheM-Itransition[ 137 ].ForMnhowevertheparameterAasymptoticallyapproacheszerobutalwaysremainspositiveonthemetallicsideofapossibleM-I 123

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(a) (b) Figure8-6. (a)ComparisonofbehaviorofparameterAforMn&Gd,(b)Amountofquantumcorrectioninmanganesethinlms. transitionforthismaterial.ThisbehaviorextendsouttodisorderstrengthsashighasR0=185k.Interestingly,attemptstofurtherannealthethin-lmwerenotsuccessfulasnofurtherchangeinR0hastakenplace,whichmostlikelyindicatesthatallthermallyinducedstructuralrelaxationsforthisparticularlmhavebeenalreadytakenplace.Othermanganesethin-lmsweresubsequentlygrownandstudiedseparately(greentriangles).Thesedataoverlapwellwiththedatafortheannealedlm(redcircles)andindicatesanexcellentrun-to-runreproducibility.ThesedataforantiferromagneticMndisplaypower-lawbehavioroveraconsiderablerangeofdisorderstrengths(factorof26increaseinR0)andyetdonotexhibitinsulatingbehaviorLxx(T=0)=0untilgranularityasexpressedbyEq 8 hasemerged.ThisbehaviorisstrikinglydifferentwhencomparedwithGd,wheretheM-Itransitionoccursbeforegranularityemerges(denedbyLxx(T=0)=0).ThesedataeventuallyleadustoamajorquestionconcerningthedifferencebetweenferromagneticGdandantiferromagneticMnwhichbothobeypower-lawbehavior(Eq. 8 )butapproachcriticaldisorderincompletelydifferentways.AlthoughGdandMnthin-lmshavesomesimilarityintermsoftheirdisorderstrengthastheygoestohoppingregimefollowingapower-lawbehavior(unlikeFe,Ni&Co),GdandMnaresubstantiallydifferentastheyareferromagnetandanti-ferromagnet 124

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respectively.Theorderparameterforferromagnetisfundamentallydifferentthananti-ferromagnet,whichhavethestaggeredmagnetization(i.e.,differencebetweenthemagnetizationoneachsublattice)astheorderparameter[ 142 ].Inotherwordsferromagnetshavesoftmodesatzerowavenumberunlikeantiferromagnetswhichhavesoftmodesatnitewavenumber[ 143 ].Thesedifferencesarehighlyimportantwhenstudyingquantumcorrections(QCs)toconductuctivitynearquantumcriticalpointsforferromagnets[ 144 ]andantiferromagnets(AFMs)[ 145 ].JustliketheGd,inMnthin-lmswehaveshowntheamountofquantumcorrectionwhichshowscorrectiontermdominatesintherangewhereR0>30k[Fig. 8-6 (b)].FurtherstudiesonquantumcorrectionsinAFMsshowthatnearcriticallityQCsaredominatedbythemomentaofthelowest-energyspinuctuationsthatareclosetothereciprocalvectorsQ(i.e.,softmodes)deningthespinsuperlatticeintheAFMphase,whileinthehighestfrequenciestheconductivityistemperature-independent[ 145 ].Alsothereisatheoreticalpossibilitythatnon-Fermi-liquidbehavioroccursinitinerantantiferromagnetsontheorderedsideofaquantumcriticalpointwhenQ6=0[ 146 ].Althoughitisnoteasytondoutwhethertheseandsimilartheoriesapplytoourresults,onethingwecansurelysaythattheinelasticphasebreakingscatteringrate()]TJ /F2 7.97 Tf 6.59 0 Td[(1)isnotsufcientlyhighinantiferromagnetmanganesetoreachthe3Dlimitwhereinelasticphasebreakinglength(L)islessthanthelmthickness.Thepresenceofpower-lawbehavioratintermediatedisorderstrengthsforbothGdandMnimpliesphysicalprocessesthatarescaleinvariantandcanbeexplainedusingniteTscalingtheories. 8.3ExponentialHoppingBehaviorInHighlyDisorderedMnIntheregionabove185KweseeasuddenjumpinR0isdenedatT=T0=5K(Fig 8-8 (a)),whichischaracteristicofchangefromweakdisordertostrongdisorder.Inthisdisorderregimethetemperaturedependenceofnormalizedconductivityshows 125

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(a) (b) Figure8-7. Hoppingbehaviorinultra-highdisordermanganesethin-lms exponentialhoppingbehaviordenedbyequation 8 Lxx(T)/exp )]TJ /F14 11.955 Tf 11.29 16.86 Td[(T T1=2!(8)whereTisthecharacteristicenergyscaleinatwodimensionalsystemwithlocalizedelectronicstates.Thisexponentialbehaviorintemperaturedependenceofconductivity,whichisfoundforallMnthin-lmswithR0(measuredatT0=20K)>500k,impliesthatatabsolutezerotemperaturethelmsareinaninsulatingstatedenedbytheconditionLxx(T=0)=0.Figure 8-7 showstemperaturedependenceofnormalizedconductivityinthin-lmsofmanganesewithsheetresistancesof640kand18M,whereln(Lxx/L00)goeslinearlywithT)]TJ /F2 7.97 Tf 6.59 0 Td[(1=2(L00isthequantumconductancedenedas1/81000)]TJ /F2 7.97 Tf 6.59 0 Td[(1).Thisexponentialsquarerootdependenceinnormalizedconductivityisoftenobservedingranularlmsandcanbeattributedtoanelectron-electroninteractionmediatedhoppingconductivitymechanism[ 140 ]. 8.4W-PlotStudyForManganeseJustlikepreviousstudiesonchromium,W-plotcalculationisdoneformanganesethin-lmswhichisshowninthegure 8-8 .AsdescribedinthepreviouschapterWisdenedasT(dlnxx/dT),andincaseofpowerlawtemperaturedependenceofconductivityWequalstopBTp/(A+BTp).Itisevidentfromthepreviousdiscussion 126

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(a) (b) Figure8-8. W-plotfortheanti-ferromagnetmanganese 127

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W=p,onlywhenA=0,whichisapurelawbehavior.WehavedonetheW-plotcalculationsforallthelmswheretemperaturedependenceofconductivityfollowspowerlaw,i.e.R0rangingwithin6Kand185K.WeseethatalltheW-plotsshowapositiveslopeexpectedformetallicsideofmetal-insulatortransition,butwhensheetresistancereachesabove100KweseetheplotsnearlybecomeparalleltoX-axisasparameterAapproacheszero.Thisbehaviorisdifferentthanseeninpreviousworkonmetal-insulatortransitioningadoliniumthin-lms[ 137 ],wheretheslopeofW-plotschangesfrompositive(inmetallicside)tonegative(ininsulatorside)throughzeroslopewhichmeansW-plotlineparalleltoX-axiswhenparameterA=0. 8.5ConclusionsOnManganeseWehavesystematicallystudiedin-situtransportpropertiesofultra-thinmanganese(Mn)lmswithsheetresistancerangingfrom6kto20M.Wehaveseenapower-lawtemperaturedependenceofnormalizedconductivityforallthethin-lmswhenconductivityrangeswithin6kand180k.Above200k,weseeasuddentransitionfrompower-lawscatteringbehavioratintermediatebehavior(beyondquantumcorrection)toexponentialhoppingbehavioratstrongdisorderregime.WehavestudiedfewmanganesethinlmswithinR0650kand20Mwheretemperaturedependenceofnormalizedconductivityfollowssquareroothoppingbehavior,whichisanevidenceofemergenceofgranularity.Comparingwithpreviousstudiesdoneongadolinium,weseethatinthecaseofmanganesetheparameterAapproachestowardszerofrompositivevaluebutstaysonthepositivesideatavalue0.25.ThisresultisunlikegadoliniumwheretheparameterAchangesfrompositivetonegativenumberthroughzero.SoferromagneticGdwentthroughaM-ItransitionbeforegoingtohoppingregimewhileAFMMndirectlygoesfrommetallicpower-lawregimetoinsulatingexponentialhoppingregime.ThisdifferenceofbehaviorinGdandMncanbeattributedtosmallerinelasticphasebreakingscatteringrate()]TJ /F2 7.97 Tf 6.58 0 Td[(1)inAFMmanganesewhichpresumablyisnotsufcientlyhightoreachthe3Dlimitwhereinelasticphase 128

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breakinglength(L)islessthanthelmthickness.Theexperimentalresultsonquantumcorrectionsinferromagnetsandantiferromagnetsprovokesimportanttheoreticaldiscussions,suchashow3DM-Itransitiondependsupontherelativevaluesofelasticmeanfreepath(e),inelasticphasebreakinglength(L)andthelmthickness(b).FurtherexperimentalandtheoreticalstudiesarenecessarytounderstandquantumcorrectionsandM-Itransitionindisorderedmagneticmetals. 129

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CHAPTER9SUMMARYInthisdissertationwestudieddifferentmagneticnano-structuresinreduceddimensionsandreachedvariousconclusions.Intherstpartofthethesiswehavemainlyreportedtheexistenceofferromagnetisminvariousnano-structureslikeFedopedsemiconductorquantumdotsystemofCdTeFeS,stackedbi-layersofPd/C60andsuperlatticesystemsofperovskiteslikeBaFeO3-KTa0.47Nb0.53O3,Ba2FeMoO6-BaTiO3,Ba2FeMoO6-BaSrTiO3etc.Tothebestofourknowledgethisisthersttimeferromagnetismisreportedinalloftheseabovementionedsystems.Interestingly,inmostofthesesystemstheCurietemperature(TC)isaboveroomtemperature(e.g.TCofCdTeFeSQDwithin600-800K,TCofPd/C60system550K&TCofBaFeO3-KTa0.47Nb0.53O3super-latticerangesbetween400-600K)excepttheBa2FeMoO6-BaTiO3super-latticesystemwhereTCwas250K.Inthesecondpartofthesiswearereportingquantumcorrectionstothetemperaturedependenceofnormalizedconductivityofanti-ferromagneticchromium&manganese.Ourstudyconcludesthatthenatureofquantumcorrectionchangeswithincreasingdisorder,wheredisorderisdenedbysheetresistanceat5K(R0=RXXat5K).Inchromiumwehaveseenthattherearethreedisorderregimes;weak(370250k).Intheweakdisorderregimeofchromiumwefoundthatthetemperaturedependenceofnormalizedconductivityfollowspower-lawequation,andintheintermediatedisorderthetemperaturedependenceofnormalizedconductivityshowslogarithmicbehaviorandnallyinthestrongdisorderlimittemperaturedependenceofnormalizedconductivityfollowssquarerootexponentialbehavior.Similarlywestudiedmanganeseandfoundtwodistinctdisorderregimes;intermediate(6k650k).Whilethetemperaturedependenceofnormalizedconductivityinthestrongdisorderregimeshowssomeexponentialhoppingbehaviorwhetheritis 130

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manganeseorchromium,intheintermediatedisorderregionofmanganesewenddifferenceofbehaviorinmanganeseandchromium.Intheintermediatedisorderregimeofmanganesewendtemperaturedependenceofnormalizedconductivityfollowspower-lawequationintheform(T,R0)=L0=A+BTP,wheretheparameterAdecreaseswithincreasingR0butneverbecomeszeroornegative.Asaconcludingremark;myresearchinterestbroadlyliesintheeldoffabrication,characterizationandstudyofmagneticnano-structures.TofurthercontinueourunderstandinginthiseldIwouldliketostudymagnetizationdynamicsandprocessesinnano-structuresandhowmagnetizationparameterslikeCurietemperature(TC),coerciveeld(HC),saturationmagnetization(MS)varywithdisorder,temperature,pressure,dimensionalityandmagneticeld(parallelandperpendiculartotheplaneofthesampleincaseofthinlms).OneparticularlyinterestingeldofresearchcanbethestudyofvariationofTCwithdisorder,sinceTCisthetemperatureabovewhichallmagneticsystemslosetheirferromagneticpropertiesandmostlybecomeparamagnetic.Butincaseoftransitionmetalferromagnetism(e.g.Fe,Ni,Co)theTCistoohighforsuchastudy(rangeswithin600-1400K),soweneedtolookatmetalalloysystemswheretransitionmetalferromagnetsaremixedwithquasi-magneticmetals(e.g.FexPd1)]TJ /F5 7.97 Tf 6.59 0 Td[(x,NixPd1)]TJ /F5 7.97 Tf 6.59 0 Td[(x,CoxPt1)]TJ /F5 7.97 Tf 6.58 0 Td[(xetc.)whereTCrangesfrom10Ktoroomtemperature[ 147 149 ].AlthoughtherehavebeenpreviousstudiesonhowTCvarieswithcomposition[ 150 152 ],itwillbereallyfascinatingtostudyhowTCvarieswiththevariationofeitherthecompositionofmetals,orbydisorderorbyboth. 131

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BIOGRAPHICALSKETCH SiddharthaGhoshwasborninKolkata,WestBengalinIndiainApril,1982.HegrewinsuburbanareaBallyastheonlychildofDr.DipakGhose,aprofessorofphysicsandMrs.DipaliGhose,ahousewife.Siddharthawasrstintroducedtoscienceandscienticthinkingbyhisfather,whoiscontinuouslyinspiringforhimthroughouthisacademiclife.SiddharthanishedhishighschoolstudiesatBallySikshaNiketan.SiddharthadidhisundergraduatestudiesatRamakrishnaMissionVidyamandira(underUniversityofCalcutta),wherehewasmotivatedtowardsphysicsresearchbytheprofessorslikeDr.M.K.Mukherjee,Dr.A.ChatterjeealongwithhisfatherDr.D.Ghoseandbecameparticularlyinterestedinexperimentalphysics.ThenattheendofthreeyearsstudyhereceivedtheBachelorofScienceinphysicsonJuly,2003.AftercompletingtheundergraduatestudiesSiddharthawenttoIndianInstituteofTechnology,Kanpur;wherehewasexposedtomodernexperimentaltechniquesandfurthermotivatedtocarryonresearchintheeldofcondensedmatterphysicsbythehighlyqualiedprofessorslikeProf.A.K.Majumdar,Prof.Z.Hossain,Prof.K.P.Rajeev,Prof.V.Subrahmanyam,Prof.A.Duttatonameafew.HereceivedtheMasterofPhysicsdegreeonAugust,2005fromthissameinstitute.SiddharthathenjoinedthegraduateprogramattheUniversityofFloridaintheFallof2006andlearnedmoreaboutadvancedphysicsresearchtopicsbythecoursestakenbyProf.R.Woodard,Prof.D.Maslov,Prof.P.Ramond,Prof.S.Peartonandmanymore.Theninthefallof2007hebeganworkingforProfessorArthurHebard'slaboratory,aperfectplacetostarthisresearchlife.Duringthesummerof2007Siddharthametwonderfulandfriendlylady,Moumitaandthengotmarriedwithherinthewinterofnextyear. 140