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Size Effects in Phase Separated Manganite Nanostructures

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Title:
Size Effects in Phase Separated Manganite Nanostructures
Creator:
Singh, Guneeta
Place of Publication:
[Gainesville, Fla.]
Publisher:
University of Florida
Publication Date:
Language:
english
Physical Description:
1 online resource (150 p.)

Thesis/Dissertation Information

Degree:
Doctorate ( Ph.D.)
Degree Grantor:
University of Florida
Degree Disciplines:
Physics
Committee Chair:
Hebard, Arthur F.
Committee Members:
Biswas, Amlan
Hirschfeld, Peter J.
Tanner, David B.
Nino, Juan C.
Graduation Date:
5/2/2009

Subjects

Subjects / Keywords:
Capacitance ( jstor )
Electric current ( jstor )
Electric fields ( jstor )
Electrical phases ( jstor )
Magnetic fields ( jstor )
Magnetism ( jstor )
Magnets ( jstor )
Orbitals ( jstor )
Thin films ( jstor )
Transition temperature ( jstor )
Physics -- Dissertations, Academic -- UF
bias, blockade, colossal, coulomb, domain, electroresistance, exchange, film, insulating, intrinsic, laprcamno, magnetiresistance, magnetoresistance, manganite, nano, nanofabrication, nanostructures, perovskite, phase, polarization, separation, simmons, spin, stripe, thin, tunneling, wall
Genre:
Electronic Thesis or Dissertation
born-digital ( sobekcm )
Physics thesis, Ph.D.

Notes

Abstract:
Size Effects in Phase Separated Manganite Nanostructures This work describes a detailed nanometer scale experimental study of a phenomenon known as phase separation, in a class of ceramic materials know as the manganites. The manganite (La,Pr,Ca)MnO3 was chosen for the studies due to the micrometer scale phase separation in this particular material. In (La,Pr,Ca)MnO3 phase separation is electronic, magnetic and structural in nature, and occurs within a small window of temperatures. Within this temperature range the sample becomes electronically `texturized' in that the sample is no longer homogeneously insulating or conducting, even though the physical chemistry and properties of the sample remain constant. It contains a mix of both insulating and conducting properties within well defined spatial regions. The regions are on the order of a micrometer. The conducting regions are ferromagnetic and have a psuedo cubic (orthorhombic but very nearly cubic) atomic structure while the insulating regions are anitiferromagnetic with an orthorhombic, distorted structure. To understand the physics of the individual phase separated regions a technique was developed for fabricating narrow (La,Pr,Ca)MnO3 wires (in the shape of bridges) of nanometer width such that during the phase separated temperature range, one or a few phase separated regions form along the length of the wire. This has allowed transport measurements across a discrete number of phase separated regions giving physical insights into the nature of the individual regions and the boundaries between them. In this way, it is possible to identify several distinct physical mechanisms that act simultaneously on the nanometer scale giving rise to the unusual properties observed in bulk or unpatterned thin film samples. Transport measurements across the narrow bridges as a function of temperature and magnetic field revealed evidence of alternating insulating and metallic regions spanning the bridge width, aligned along the length of the bridge. First, evidence of direct electron tunneling between two or more ferromagnetic metallic (FM) regions separated by antiferromagnetic insulating (AFI) regions was observed. Magnetoresistance measurements reveal that often, the ferromagnetic metallic regions have different coercive fields (possibly due to varying sizes) which affect the tunnel probabilities (i.e. the probability decreases when the spins are anti-aligned). This gives rise to large and sharp low field peaks when resistance is measured as a function of magnetic field---the classical signature of tunneling magnetoresistance (TMR). Further, signatures of an exchange bias which gives rise to asymmetric TMR peaks were also identified in the measurements. These two phenomenon can help explain anomalous low field magnetoresistance observed in bulk and unpatterned thin film samples. The data also reveal that at temperatures below the phase separated temperature range, when the unpatterned thin film samples are nearly fully ferromagnetic metallic, the narrow bridges in contrast have a high resistance. The resistance is temperature independent and thus is not a signature of an insulating state within the bridge (since it is possible that lower dimensions could eliminate the insulator to metal transition). Current-voltage measurements point to a direct tunneling phenomenon thus suggesting that the metallic regions are separated by very thin AFI tunnel barriers. Magnetic field measurements reveal that the barriers are metastable with respect to very small fields (on the order of the manganite coercive field). The data in this low temperature range hint at the presence of novel, insulating, stripe domain walls where tunneling occurs across the domain boundary. The results were compared to theoretical calculations of insulating stripe domain walls predicted to form in phase separated materials. In addition to the magnetic field effects, the current-voltage measurements reveal a hysteresis and a breakdown to a low resistance state with a high enough applied current. The breakdown occurs in sharp steps while a much smoother transition to a lower resistance state is observed in bulk. Further, unusual bifurcations show evidence of coulomb blockade across a few metallic islands. Lastly, the effects of film thickness in the nanometer range on phase separation in thin films were investigated. Capacitance measurements were used to probe the properties of (La,Pr,Ca)MnO3 as a function of thickness. An unusual geometry was developed and employed for fabricating a capacitor structure such that the material under study, the (La,Pr,Ca)MnO3, forms one of the electrodes. Next, detailed circuit analysis was used to understand the complex dielectric response in this unconventional geometry as a function of changing frequency and magnetic fields. It was found that the dielectric response deviates from the universal dielectric response expression by an exponent that is different from unity, and the value of which depends on the exact phase composition of the (La,Pr,Ca)MnO3. This method allows for a novel probe of phase boundaries in thin films, where the boundaries may not be straightforward to detect with DC transport measurements. Additionally, it was found that capacitance as a function of time shows a different phase transition temperature than the temperature dependent resistance measurements. The two different transition temperatures begin to converge as the film thickness increases, showing the effect of film thickness on two different transitions: one in the plane of the film and one perpendicular to the plane of the film. ( en )
General Note:
In the series University of Florida Digital Collections.
General Note:
Includes vita.
Bibliography:
Includes bibliographical references.
Source of Description:
Description based on online resource; title from PDF title page.
Source of Description:
This bibliographic record is available under the Creative Commons CC0 public domain dedication. The University of Florida Libraries, as creator of this bibliographic record, has waived all rights to it worldwide under copyright law, including all related and neighboring rights, to the extent allowed by law.
Thesis:
Thesis (Ph.D.)--University of Florida, 2009.
Local:
Adviser: Hebard, Arthur F.
Electronic Access:
RESTRICTED TO UF STUDENTS, STAFF, FACULTY, AND ON-CAMPUS USE UNTIL 2011-05-31
Statement of Responsibility:
by Guneeta Singh.

Record Information

Source Institution:
University of Florida
Holding Location:
University of Florida
Rights Management:
Copyright Singh, Guneeta. Permission granted to the University of Florida to digitize, archive and distribute this item for non-profit research and educational purposes. Any reuse of this item in excess of fair use or other copyright exemptions requires permission of the copyright holder.
Embargo Date:
5/31/2011
Resource Identifier:
665097853 ( OCLC )
Classification:
LD1780 2009 ( lcc )

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Thedoctoralprocessforme,asforthosebeforeme,hasbeenalongtermchallengerequiringstrongsupportfrommanypeopleinmylife,bothprofessionallyandpersonally.BelowIwillbeliberalwiththespaceIusetoacknowledgesomeofthemanypeoplewhohaveliftedmeupandhelpedmeclimbthismountain.Firstandforemost,IamgratefultoDr.ArthurF.Hebardforsupportingmethroughouttheyearsandprovidingthehavenofhislaboratoryformetoexperimentinfreely.IhavelearnedatremendousamountintheyearsIhavespentinhislaboratory:IhavegonefromzerotoeverythingInowknowaboutexperimentalphysics.NextIwouldliketothankaclosecollaborator,Dr.AmlanBiswasforteachingmehowtousethepulsedlaserdeposition(PLD)systemandsomuchmoreonthetopicofmanganites(andpolitics)andcomplexoxidesingeneral.IwouldalsoliketothankmycollaboratorsinJapan,Dr.HaroldY.HwangandDr.ChristopherBellforbeingexcellenthostsduringmystayandfortheirinspirationaldiscussionsonthetopicofcomplexoxides.Iwouldliketothankmytheoreticalcollaborators,Dr.DenisI.GolosovinIsraelandDr.SelmanHersheldandhisstudentSaraJoyfortheirpatienceandinsightfultheoreticalperspectives.IwouldalsoliketothankseveralothermembersoftheUFPhysicsandMaterialScienceDepartmentfortakingthetimetohavediscussionswithmefromwhichIhavelearnedalot:ThankyouDr.PeterJ.Hirshfeld,Dr.DimitriiMaslov,Dr.DavidTanner,Dr.PradeepKumar,Dr.JuanNino,Dr.AndrewRinzlerandDr.GeraldBourne.IamalsogratefultoDr.KatiaMatchevaandDr.PetkovaforprovidingthesupportandpracticaladvisethatisanessentialingredientforPhDstudents,butironicallyalmostcompletelynonexistent.Ifeelluckytohavehadit,sothankyou!IthankXuDu,SinanSelcuk,SefTongay,BoLiu,TaraDhakalandPatrickMickelforalltheirsupport,collaborationanddiscussions.IthankotherpresentandpreviousmembersofmylaboratoryandtheUFphysicsdepartmentfortheirinsights,friendshipandsupport:Thanks,NikoletaTheodopolous,SanalBuveav,JayHorton,Sandraand 4

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page ACKNOWLEDGMENTS ................................. 4 LISTOFTABLES ..................................... 9 LISTOFFIGURES .................................... 10 ABSTRACT ........................................ 13 CHAPTER 1AnIntroductionto(La,Pr,Ca),MnO3andMicro-ScalePhaseSeparation .... 16 1.1AGeneralIntroductiontoManganites .................... 16 1.2TheStructureandBasicPropertiesofManganites .............. 17 1.2.1InherentDistortionsintheManganiteUnitCell ........... 18 1.2.2InducedDistortionsintheManganiteUnitCell ........... 22 1.2.3TheEectsofDopingonElectronicandMagneticProperties .... 25 1.2.4TransportMechanismsatHighandLowTemperaturesinDopedManganites ............................... 27 1.2.5TheGeneralHamiltonianfortheStronglyCorrelatedManganites 29 1.3BasicCharacteristicsof(La,Pr,Ca)Mn)O3 30 1.3.1PropertiesandCharacteristicsof(La,Ca)MnO3 31 1.3.2PropertiesandCharacteristicsof(Pr,Ca)MnO3 32 1.3.3PropertiesandCharacteristicsof(La,Pr,Ca)MnO3 34 1.3.4SubstrateInducedStrainin(La,Pr,Ca)MnO3ThinFIlms ...... 37 1.4NanoscaleConnementof(La,Pr,Ca)MnO3ThinFilms ........... 38 1.5ChapterSummary ............................... 40 2SampleFabricationandMeasurementTechniques ................. 41 2.1(La,Pr,Ca)MnO3ThinFilmDeposition .................... 42 2.2(La,Pr,Ca)MnO3NanobridgeFabrication ................... 44 2.2.1ChallengesinManganiteNanofabrication ............... 45 2.2.2NanopatterningofSubstrates ..................... 46 2.2.3NanobridgeFormationUsingPhotolithographyandWetEtching .. 49 2.2.4BackandTopGatingof(La,Pr,Ca)MnO3bridges .......... 53 2.3(La,Pr,Ca)MnO3|AlOx|MetalCapacitorFabrication ........... 53 2.3.1RFMagnetronSputteringofHighQualityAlOxDielectricThinFilms ................................... 55 2.3.2ThermalEvaporationofMetalThinFilms .............. 57 2.4SummaryofSamples .............................. 58 2.5TransportMeasurements ............................ 59 2.5.1BasicResistanceMeasurementCircuit ................. 60 2.5.2ElectricFieldGating .......................... 62 6

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.............. 63 2.6TemperatureandMagneticFieldDependenceforTransportMeasurements 64 2.7MagnetizationMeasurements ......................... 64 2.8DataAcquisition ................................ 67 2.9ListofCollaboratorsandSummaryofContributions ............ 69 3IntrinsicTunnelingMagnetoresistancein(La,Pr,Ca)MnO3 71 3.1Introduction ................................... 71 3.2Motivation .................................... 71 3.3ReviewofTransportAcrossUnpatternedLPCMOThinFilms ....... 72 3.4SampleFabricationandMeasurementTechniques .............. 74 3.5TemperatureDependentResistivityofLPCMOBridges ........... 76 3.6MagnetoresistanceAcrossthe0.6mWideLPCMOBridge ........ 76 3.6.1MagnetoresistanceforTIMO>T>TIM 76 3.6.2MagnetoresistanceforTIM>T>TG 79 3.6.3MagnetoresistanceforTG>T 80 3.7ChapterSummary ............................... 83 4EvidenceofUnusualInsulatingDomainWallsin(La,Pr,Ca),MnO3 85 4.1Introduction ................................... 85 4.2Motivation .................................... 85 4.2.1TheoreticalWorkonInsulating(Stripe)DomainWallFormation .. 86 4.2.2InsulatingStripeDomainWallFormationin(La,Pr,Ca)MnO3 86 4.3SampleFabricationandMeasurementTechniques .............. 87 4.4TemperatureDependentResistanceofNanobridge .............. 87 4.4.1TemperatureIndependentResistanceBelowTG 89 4.4.2ColossalResistanceDropUponFieldWarming ............ 89 4.5IntrinsicTunnelinginNanobridge ....................... 90 4.5.1DirectTunnelingofElectronsacrossIntrinsicTunnelBarriers .... 90 4.5.2JouleHeatingandNon-linearI-VCurves ............... 90 4.6AnisotropicMagnetoresistance ......................... 93 4.7UnderstandingInsulatingStripeDomainWalls ................ 96 4.7.1Competingphasesandstrainsensitivityin(La,Pr,Ca)MnO3 96 4.7.2StripeDomainWallsandtheChargeDisorderedPhase ....... 97 4.7.3StripeDomainWallsinRelationtotheVariousInsulatingPhases 99 4.8EvidenceofAnomalousDomainWallsinWider,ThinnerBridges ..... 100 4.9ChapterSummary ............................... 101 5ColossalElectroresistanceAcross(La,Pr,Ca)MnO3Nanobridges ......... 103 5.1Introduction ................................... 103 5.2Motivation .................................... 103 5.3FabricationandMeasurementTechniques ................... 104 5.4ColossalElectroresistanceinManganiteThinFilms ............. 104 5.4.1ColossalElectroresistancein(Pr,Ca)MnO3andRelatedCompounds 105 7

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.... 106 5.5ColossalElectroresistanceinPatternedandUnpatterned(La,Pr,Ca)MnO3ThinFilms ................................... 107 5.5.1DiscreteCurrent-VoltageStepsin(La,Pr,Ca)MnO3Bridges ..... 108 5.5.2AnalyzingChangesinBarrierPropertiesUsingSimmons'Model .. 112 5.5.3ComparingChangesinBarrierPropertiesforAppliedElectricvs.MagneticFields ............................. 113 5.5.4ShortcomingsoftheRectangularBarrierSimmons'Model ...... 114 5.6ChapterSummary ............................... 115 6ColossalMagnetocapacitanceandAnisotropicTransportin(La,Pr,Ca)MnO3ThinFilms ...................................... 116 6.1Introduction ................................... 116 6.2Motivation .................................... 117 6.3Methods ..................................... 118 6.4ComparisonofLongitudinalandPerpendicularVoltageDrops ....... 120 6.5Maxwell-WagnerAnalysis ........................... 125 6.6DependenceofAnisotropyonFilmThickness ................ 127 6.7ScaleInvariantDielectricResponse ...................... 130 6.8DeterminingPhaseBoundariesusingCole-ColePlots ............ 132 6.9ChapterSummary ............................... 138 7FinalRemarksandFutureDirection ........................ 139 7.1GeneralSummary ................................ 139 7.2FutureDirection ................................ 141 REFERENCES ....................................... 144 BIOGRAPHICALSKETCH ................................ 149 8

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Table page 2-1SampleSummaryTable ............................... 59 2-2ListofCollaboratorsandSummaryofContributions ............... 70 9

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Figure page 1-1Manganiteunitcellstructure ............................ 18 1-2CrystaleldsplittingintheMnO6octahedron ................... 20 1-3Jahn-TellersplittingintheMnO6octahedron. ................... 21 1-4Charge,OrbitalandSpinOrderinginManganites ................. 24 1-5TheDoubleExchangeMechanisminManganites. ................. 26 1-6The(La,Pr,Ca)MnO3PhaseDiagram. ....................... 35 1-7SubstrateInducedStrainIllustrated. ........................ 38 2-1Pulsedlaserdepositionsystem ............................ 42 2-2Imageoflaserablationplume ............................ 43 2-3NdGaO3substratecoatedwithacarbonnanotubethinlm ........... 47 2-4NdGaO3substratepatterning ............................ 48 2-5DualBeam-FocusedIonBeamStrataDB235apparatus ............ 49 2-6LPCMOdepositedonetchedsubstrate ....................... 50 2-7UVphotolithographyisusedtodeneLPCMObridge .............. 50 2-8Photolithographymaskschematicfornanobridge ................. 50 2-9OpticalimageofLPCMObridgealignedwithlithographymask. ......... 52 2-10PPMStransportmeasurementpuck ......................... 52 2-11Schematicoftopgatestructure ........................... 54 2-12LPCMOcapacitorstructure ............................. 55 2-13SchematicoftheAlOxdepositionsystem,Hamedon ................ 56 2-14Opticalimageofacapacitor ............................. 57 2-15Tungstenthermalevaporationboat ......................... 58 2-16Fourcontactresistancemeasurementdiagram ................... 60 2-17Twoterminalresistancemeasurementdiagram ................... 61 2-18Diagramforelectriceldgatingmeasurement ................... 62 10

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.......................... 63 2-20SchematicofPhysicalPropertiesMeasurementSystem(PPMS) ......... 65 2-21MagnetizationmeasurementofunpatternedLPCMOthinlmonNGO. .... 66 2-22MagnetizationmeasurementofunpatternedLPCMOthinlm. .......... 67 2-23Opticalimageofmultiple1mwideLPCMOstripes ............... 68 2-24Magnetizationdataformultiple1mwideLPCMOstripes ........... 68 3-1R(T)curveforunpatterned(La0:5Pr0:5)0:67Ca0:33MnO3 73 3-2PronouncedstepsinR(T)for2.5mand0.6mwidebridges .......... 75 3-3R(H)forT>TIM 77 3-4UnpatternedthinlmR(H)datainrangeT=120K>TIMO 78 3-5R(H)at57Kinthe0.6mwidebridgeshowstunnelingmagnetoresistance .. 81 3-6R(H)foranunpatternedthinlmat50Kshowslow-eld`notches' ....... 82 3-7Waterfallplotshowsevolutionoftunnelingmagnetoresistance .......... 83 4-1Rvs.Tunpatternedthinlmvs.0.6mwidebridge .............. 88 4-2IVcharacteristicsforthe0.6umwidebridge .................. 91 4-3FittotheSimmons'model .............................. 92 4-4R(T)curvesobtainedatdierentappliedcurrents ................. 93 4-5Zeroeld-cooledandeldcooledRT 94 4-6MagneticelddependentIV 95 4-7MagneticelddependentIVcurvesnormalizedtoVmax. ............ 96 4-8Mechanismsforinsulatingstripedomainwallformation .............. 98 4-9Mechanismsfortunnelingmagnetoresistance(TMR)junctionformation ..... 100 4-10R(T)curvesfora2.5mwidebridge,10nmthicklm .............. 101 5-1R(T)curvesforthe0.6mwidebridgeatseveralappliedcurrents. ....... 108 5-2IVcurvesforthe0.6mwidebridgedepictingcolossalelectroresistance. .. 109 5-3IVcurvesforthe0.34mwidebridgedepictingcolossalelectroresistance. .. 110 5-4Simmons'modeltstoIVcurvesforthe0.34mwidebridge. ........ 111 11

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........ 112 5-6Barrierheightsandwidthsobtainedforthe0.6mwidebridge. ......... 114 6-1Crosssectionalschematicviewofthetrilayercapacitorstructure ......... 119 6-2Circuitdiagramsshowsourcesoflongitudinalandperpendicularvoltagedrops. 122 6-3Impedanceplotscomparinglongitudinalvs.perpendicularvoltagedrops .... 124 6-4IMtransitionsasafunctionofLPCMOthickness. ................. 128 6-5WithincreasingLPCMOthicknesstheanisotropyasmeasuredbyT#"IM=T#"IM;jjT#"IM;?decreasestowardszeroandbulklikebehavior ................ 129 6-6Cole-Coleplotsshowingdatacollapseandpower-lawscalingofthedielectricresponse ........................................ 133 6-7DeterminationoftheboundariesofthePLSCregion ............... 134 6-8PhasediagramofupperandlowercriticalregionofPLSCregion ......... 136 12

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Tounderstandthephysicsoftheindividualphaseseparatedregionsatechniquewasdevelopedforfabricatingnarrow(La,Pr,Ca)MnO3wires(intheshapeofbridges)ofnanometerwidthsuchthatduringthephaseseparatedtemperaturerange,oneorafewphaseseparatedregionsformalongthelengthofthewire.Thishasallowedtransportmeasurementsacrossadiscretenumberofphaseseparatedregionsgivingphysicalinsightsintothenatureoftheindividualregionsandtheboundariesbetweenthem.Inthisway,itispossibletoidentifyseveraldistinctphysicalmechanismsthatactsimultaneouslyonthe 13

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Transportmeasurementsacrossthenarrowbridgesasafunctionoftemperatureandmagneticeldrevealedevidenceofalternatinginsulatingandmetallicregionsspanningthebridgewidth,alignedalongthelengthofthebridge.First,evidenceofdirectelectrontunnelingbetweentwoormoreferromagneticmetallic(FM)regionsseparatedbyantiferromagneticinsulating(AFI)regionswasobserved.Magnetoresistancemeasurementsrevealthatoften,theferromagneticmetallicregionshavedierentcoerciveelds(possiblyduetovaryingsizes)whichaectthetunnelprobabilities(i.e.theprobabilitydecreaseswhenthespinsareanti-aligned).Thisgivesrisetolargeandsharploweldpeakswhenresistanceismeasuredasafunctionofmagneticeld|theclassicalsignatureoftunnelingmagnetoresistance(TMR).Further,signaturesofanexchangebiaswhichgivesrisetoasymmetricTMRpeakswerealsoidentiedinthemeasurements.Thesetwophenomenoncanhelpexplainanomalousloweldmagnetoresistanceobservedinbulkandunpatternedthinlmsamples. Thedataalsorevealthatattemperaturesbelowthephaseseparatedtemperaturerange,whentheunpatternedthinlmsamplesarenearlyfullyferromagneticmetallic,thenarrowbridgesincontrasthaveahighresistance.Theresistanceistemperatureindependentandthusisnotasignatureofaninsulatingstatewithinthebridge(sinceitispossiblethatlowerdimensionscouldeliminatetheinsulatortometaltransition).Current-voltagemeasurementspointtoadirecttunnelingphenomenonthussuggestingthatthemetallicregionsareseparatedbyverythinAFItunnelbarriers.Magneticeldmeasurementsrevealthatthebarriersaremetastablewithrespecttoverysmallelds(ontheorderofthemanganitecoerciveeld).Thedatainthislowtemperaturerangehintatthepresenceofnovel,insulating,stripedomainwallswheretunnelingoccursacrossthedomainboundary.Theresultswerecomparedtotheoreticalcalculationsofinsulatingstripedomainwallspredictedtoforminphaseseparatedmaterials. 14

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Lastly,theeectsoflmthicknessinthenanometerrangeonphaseseparationinthinlmswereinvestigated.Capacitancemeasurementswereusedtoprobethepropertiesof(La,Pr,Ca)MnO3asafunctionofthickness.Anunusualgeometrywasdevelopedandemployedforfabricatingacapacitorstructuresuchthatthematerialunderstudy,the(La,Pr,Ca)MnO3,formsoneoftheelectrodes.Next,detailedcircuitanalysiswasusedtounderstandthecomplexdielectricresponseinthisunconventionalgeometryasafunctionofchangingfrequencyandmagneticelds.Itwasfoundthatthedielectricresponsedeviatesfromtheuniversaldielectricresponseexpressionbyanexponentthatisdierentfromunity,andthevalueofwhichdependsontheexactphasecompositionofthe(La,Pr,Ca)MnO3.Thismethodallowsforanovelprobeofphaseboundariesinthinlms,wheretheboundariesmaynotbestraightforwardtodetectwithDCtransportmeasurements.Additionally,itwasfoundthatcapacitanceasafunctionoftimeshowsadierentphasetransitiontemperaturethanthetemperaturedependentresistancemeasurements.Thetwodierenttransitiontemperaturesbegintoconvergeasthelmthicknessincreases,showingtheeectoflmthicknessontwodierenttransitions:oneintheplaneofthelmandoneperpendiculartotheplaneofthelm. ThesamplefabricationandotherexperimentaldetailsarediscussedinChapter2,whiletheTMRphenomenonisdiscussedinChapter3.ThenovelstripedomainwallswhichallowdirectelectrontunnelingarediscussedinChapter4andtheanomalouscurrent-voltageandotherelectriceldeectsarepresentedinChapter5.AllresultsandconclusionsderivedfromcapacitancemeasurementsarediscussedinChapter6andnallyinChapter7thegeneralconclusionsandfuturedirectionsarepresented. 15

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1 ],colossalmagnetoresistive(CMR)materialsonceagainresurfacedandquicklyestablishedranksintheforefrontofresearchinthelasttwodecades.Initially,theresurrectionwaslargelyfueledbytheracetoenhancemodernmagneticmemorydeviceswhicharebasedonagiantmagnetoresistanceorGMReect.CMRwouldbeanobviousenhancement.However,researchhasnowclearlyrevealedthatthemagneticeldsrequiredfortheCMReect,whichareontheorderof1Tesla(or10kOe),areordersofmagnitudelargerthantheeldsrequiredincurrentdevicesutilizingtheGMRprinciple,whichareontheorderof10to100Oe.Thusinthewakeofanunrealizeddream|thatofloweldCMRdevices|awholenewclassofmaterialswasestablishedandfoundtoexhibitaninterestingrangeofpropertiespreviouslyunknowninothermaterials.Todaytheinterestinmanganitesisprimarilyonafundamentallevelbutisfurtherinspiredbytheexoticpropertiesofawiderclassofcorrelatedelectroncomplexoxidematerialstowhichmanganitesbelong. Thewiderclassofcorrelatedelectroncomplexoxide(CECO)materialsexhibitsomeofthemostunusualelectronicandmagneticpropertiescurrentlyknownincondensedmatterphysics.Theseincludehightemperaturesuperconductivity[ 2 3 ],ferroelectricity[ 4 ],electronicdopingofinterfaces[ 5 ],multiferrocity[ 6 7 ],andseveraltypesofordered[ 8 9 ]anduid[ 10 ]phaseseparation.Becauseoftheelectroncorrelationeect,simplybendingaCECOmaterialcanchangeitselectronicpropertiesfromaninsulatortoametal[ 11 ]anantiferromagnettoaferromagnet[ 11 ]andfromaninsulatortoaferroelectric[ 12 ].Additionally,temperature,pressure,light,electricandmagneticeldscanalsodrasticallyalterthephasesofCECOmaterials[ 13 14 ].Thistunabilityimpliesalargepotentialforpreviouslyunrealizeddeviceapplications. 16

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15 ].Inthislight,themanganitesalongwithmanyotherCOCEmaterialscurrentlyconnedtoacademicinterests,mayonceagainbepoisedtoentertherealmofpracticalelectronicsandbandengineering.Thediscoveryandunderstandingofcomplexoxidematerialsandtheirnovelphasesisongoingandholdsexcitingpromisesforthefutureofelectronics.Thus,themanganitesmaystillholdhiddenpotentialforintegrationintomodernelectronics. 1 8 9 14 16 ]. 17

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9 ].Figure 1-1 showsthebasiccubicstructureofthemanganiteoctahedronwiththeAsiteatomatthefourcornersandtheMnatomatthecenterofsixOatoms.TheMnsiteinthisstructureissaidtooccupytheBsite(ABO3). Figure1-1. BasiccubicstructureofthemanganiteunitcellshowingtheMnatomencagedinanOoctahetron.TheMnO2planesareseparatedbyAOplanes,i.e.theAatomslieinthesameplaneastheapexOatomsofeachoctahedron.TheAatomsareeitherdivalentrareearthortrivalentalkalineearthelements. Theoutermost3dorbitalsontheMnsitearesubjecttoaliftingofthedegeneracyinorderforthesystemtoreducetherepulsiveCoulombinteractionswiththeelectrons 18

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1-2 .ThustheCoulombrepulsionandhencetheenergyislowerfortheo-axis3dorbitals(yellow),specically,thosenotalignedalongx,yorz(i.e.thexy,yzandxzlevels,butnotthex2y2and3z2r2).Thisliftingofthedegeneracyisknowascrystal-eldsplitting[ 14 ]. LoweringofCoulombrepulsiondrivesasecondsplittingofthedegeneracywithinthealreadysplitt2gandeglevels.ThissecondsplittingismainlydrivenbythesinglyoccupiedeglevelinthecaseofMn3+.Inthiscasethesingleegelectroncanoccupyeitherthex2y2orthe3z2r2orbitals,bothofwhicharealignedalongtheO2porbitals.Theenergyofthiselectroncanbeloweredifthelevelthatitoccupiescanbe`distanced'fromtheO2porbitals.Thesystemaccomplishesthisbybecomingslightlyelongated(distorted),whileretainingtheunitcellvolume,aspicturedinFigure 1-3 .Thesingleegelectrontheninhabitsthe3z2r2(orthex2y2)orbitalcausingtheoctahedrontoelongatealongthezdirection(orthex-ydirection).Thislowerstheenergyofthe3z2r2(x2y2)levelwithrespecttothex2y2(3z2r2)level.ThedistortionalongzalsohastheeectofslightlyloweringtheenergyoftheyzandxzlevelswithrespecttothexylevelwhichisnowclosertotheO2porbitalsinthexyplane.ThisisknownastherstorderJahn-Teller(J-T)distortion,orJahn-Tellereect.Alternatively,CoulombrepulsioncanbeavoidedbyahybridizationoftheegelectronwiththeO2porbitalsifthecoret2gspinsarealignedferromagnetically,andthiseectcompeteswiththeJ-Tdistortion[ 8 14 ]. TheJ-Ttheoremdoesnotspecifywhichorbital,3z2r2orx2y2,willbeoccupied,butratheronlystatesthatthesystemwillundergoasymmetrybreakingdistortiontolowerenergyfornon-linearmolecules[ 14 ].Hereitisintuitivetoseethatloweringofthe3z2r2maybeenergeticallymorefavorablesinceitalsofavorsloweringofboththeyzandxzasopposedtojustthexylevel,thusloweringtheoverallsystemenergy.FollowingsimilarCoulombrepulsionarguments,itisstraightforwardtoqualitativelyimaginethesecondorderJahn-Tellerdistortionthatarisesfromanocenterdisplacementofthe 19

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Anillustrateddemonstrationofcrystal-eldsplittingintheMnO6octahedron.Redandyellowdottedlinesinthexyplane(labeled)oftheillustratedMnO6octahedronontheleftarevisualaidsdemonstratingthedirectionsoftheegandt2gorbitalsrespectively.ExamplesofapproximateorbitallobesareshownforMneg(red)x2y2,Mnt2g(yellow)xyandtheO2porbital.TheredegorbitalswhichpointinthedirectionoftheO2porbitalsandtheyellowt2gwhichpointat45toeachaxisareclearlyshownwithrespectthethexyzaxesontherightportionofthegure.ElectronsoccupyingtheegorbitalsinthiscasewillundergoCoulombrepulsionfromtheadjoiningO2porbitals.Thus,withthreevalenceelectrons,asinthecaseofMn4+,theenergyofthesystemisloweriftheelectronsoccupythet2gorbitalsinordertominimizeCoulombrepulsionfromtheO2porbitals.AswillbeshowninFigure 1-3 ,anadditionalvalenceelectron(Mn3+)givesrisetoanadditionalsplittingoftheegorbitalsinordertoonceagainminimizeCoulombrepulsion. 20

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InadditiontothecrystaleldsplittingillustratedanddescribedinFigure 1-2 ,anMn3+ionwiththeegelectronundergoesasecondenergy(Coulombrepulsion)loweringsplitting,theJahn-Tellersplitting,withintheegenergylevelsasshown.Theillustrationontheleftshowsacubic,undistortedandunsplitoctahedronthathasnotundergonesplittingoftheegorbitals.Thesingleegelectronwilloccupyeitherthex2y2orthe3z2r2levelandthesystemwillelongateinthedirectionofthatparticularorbitalinordertolowerCoulombrepulsion,asillustratedontheright. Mnion,furthersplittingthet2genergylevels.ThesecondorderdistortionispresentinferroelectricandmultiferroicCOCEsystems.Ingeneral,inacrystaltheJ-Tdistortioniscollective,withthecrystalelongatingasawholeinonedirectionorwithchainsofJ-Tdistortionsofastaggeredoccupationofthe3z2r2andx2y2orbitals[ 9 ]. Itisimportanttonotethatthet2gspins(3/2)arehighlylocalizedandforallpracticalpurposesareconsideredasclassical,corespinsintimatelytiedtothelatticeandnotaectedbytheegspins.TheJ-Tdistortionsonlyoccurforanoddnumberoccupationoftheegorbitals(oneinthecaseofthemanganites,suchasLaMnO3).The 21

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13 17 ](orchargetransfer[ 18 ])insulatingstateintheMn3+manganitessincetheconventionalbandpicturedictatesthatLaMnO3withit'ssinglyoccupiedegstateshouldbeaconductor.CaMnO3ontheotherhand,anMn4+manganitewithnoegelectrons,isabandinsulatorwithantiferromagneticallyorderedspins[ 9 ]. ThevalencyoftheMnionsinthemanganitecrystal(Mn3+vs.Mn4+)isdictatedbytheA-sitevalence[ 9 14 ].A-siteatomsbondionicallytotheOatomsintheMnO6octahedra,i.e.,theygiveupanelectrontotheOatoms.ThisextraelectronisthensharedbetweentheMn-OsiteswithintheMnO6octahedra,givingrisetotheMn3+vs.Mn4+valencyoftheMnsites.ThevalenceoftheA-sitecanbevariedandevenmixedwithinagivencrystalsuchthatMn3+andMn4+canco-existwithin,givingrisetoelectricalconductivity.TheMottinsulatingstateinthiscaseis`broken'bytheegelectronbeingsharedbetweentheMnionsviaanintermediateOatom.ThustheextraelectroncannowhopbetweenMnsitesoreectively,dierentoctahedra.ThesystemisnolongeruniformlyJ-Tdistorted,butisdisorderedandnowalsocontainscubicMn4+octrahedra.ElectronscannowconductviapolaronichoppingconductionordoubleexchangeferromagnetismatlowertemperaturesasdiscussedinSection 1.2.3 furtherbelow.Asdiscussedinthenextsection,thesize,orionicradiusoftheA-siteioncanalsodrasticallyaecttheelectricalconductivityandmagneticproperties. Anadditionalelectron-latticecouplingthatcanaectthepropertiesofmanganitesisalatticebreathingmodedistortionwhichchangesallsixMnO6bondlengthsbythesameamount.Thishastheeectofloweringtheenergyoftheunoccupiedegorbitalswhileraisingtheenergyoftheoccupiedorbitals. 22

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13 17 ],f, Hereri(i=O;Mn;A)representstheionicradiusofeachelement.Iffiscloseto1,thenthecubicperovskitestructureconsistingpurelyoftheinherentMnO6distortionsisrealized.Asfdecreasessothat0.96
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Anillustrationofthedierentlatticedistortionsinducedwithachangingtolerancefactor.Clockwisefromtopright,theundistortedcubicstructureisshown,followedbyanoveremphasizedcooperativeJahn-Tellerdistortion,arhombohedraldistortionandnallyanorthorohmbicdistortion.ThelattertwoarebothJahn-Tellerdistorted,thoughitmaynotbeapparentfromtheillustration. Thevarioustypesofspinandorbitalorderingsymmetriescanbemodiedbydopingandcationsize[ 1 9 16 ].Thespinorderingwhichhasalowertemperaturethanorbitalordering(andisthusinuencedbyorbitalordering)ismediatedbyasuperexchangemechanismwherehalflledt2gorbitalsinneighboringMnsitesexchangeavirtualelectronwhichmediatesantiferromagneticspinordering(dependingonthelatticedistortion)viatheHund'srulecouplinginneighboringMnsites.Theoccupationof3z2r2vs.x2y2orbitalscangiverisetoantiferromagneticorderingalongthezaxisandpossiblyferromagneticordering(dependingonegelectrondopinglevel)withintheplane. 24

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9 14 ]. ThedoubleexchangemechanismwasrstproposedbyZener[ 21 ]in1951andrevisitedbyAndersonandHasegawa[ 22 ]in1955.Inthisscenario,electrontransferoccurssimultaneouslybetweenanMn3+andanO2andfromtheO2toanMn4+asschematicallyshowninFigure 1-5 .ThechargetransferoftheegelectroniscoupledferromagneticallytothelatticeasaresultoftheHund'srulecouplingwhichisontheorderof2to3eVinmanganites[ 17 23 ]andfarexceedstheintersitehoppingenergy.Inotherwords,becauseoftheHund'srulecouplingandthefactthattheMndorbitalsarelessthanhalflled,anyelectronshoppingintotheemptyegstatemusthavethesamespinasthet2gelectronswhichareeectivelylocalizedduetothecrystaleldsplitting.Thusforpracticalpurposes,thetransferofegelectronsfromoneMnsitetothenextdependsonit'salignmentwiththecoret2gspins.ThiscanbeexpressedintermsoftheAnderson-Hasegawarelationship[ 18 ]: wheretheberryphasecanbeneglectedtogivethesimplerform, 25

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Anillustrationofthedoubleexchangemechanisminmanganites.HeretwoMnatomsareshownconnectedwithanOatom(bottom)andtheMnegorbitalsarehybridizedwiththeO2porbitals.Thedegreeofdeviationfrom180oftheangleintheMn-O-Mnbonddeterminesthedegreeofchargelocalizationvs.hybridizationpresentinthecompound.Theredarrowsrepresentegelectronspins.TheschematicdiagramoftheMnenergylevelswiththecorespinsandtheegspinsinteractingwiththeO2pstatesisalsoshown(top).Note:SchematicreproducedfromapublicdomainimageavailablefreelyonWikipedia,thefreeweb-basedencyclopedia,andisagood[ 14 17 ]schematicdescriptionofthemechanism. 1{2 and 1{3 26

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17 20 ]. Itispossibleincertainmanganitestoichiometriestohaveferromagnetismbutnoconductingstate,orlocalized,ferromagneticallyalignedt2gelectrons(i.e.aferromagneticinsulator),thoughthisisnotcompletelyunderstood.Intheferromagneticmetallicstatehowever,themanganitesareexpectedtobehalfmetallic(fullyspin-polarized)giventhedoubleexchangemechanismandstrongHund'srulecoupling.Recentmeasurementshaveconrmedthisspeculationin(La,Sr)MnO3whichwasfoundtobeover90%spinpolarized[ 24 ].Magnetizationmeasurementsrevealthatsaturationmagnetization(3.8B/Mn)isachievedintheferromagneticmetallicstate[ 25 ]. 1 9 26 ]beforetheonsetofferromagnetismarewelldescribedwithinthesmall(Holstein)polaronhoppingmodel.Thisisparticularlytruenearroomtemperaturefortheparentcompoundsofthemanganitediscussedinthiswork,namelyPr0:7Ca0:3MnO3andLa0:7Ca0:3MnO3.AsmallpolaronistheJ-Tlatticedistortionaccompanyingachargecarrierwithinthecrystal.Thelatticedistortionsurroundingthecarrierisessentiallyaquantumwellwhich`self-traps'thecarrier.Alargepolaronontheotherhand,embodiesaweakcouplingbetweenthesurroundinglatticeandcarrier.Asdiscussedearlier,theoctahedracontainingtheegelectronscanlowertheirenergyviaaJ-Tdistortion.Thus,inamixedvalencesystemwhereboththecubicoctahetraandJ-Tdistortedoctahedraco-exist,thecarrierhopstothenextsiteeachtimethelatticeoftheneighboringsite 27

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Asthetemperatureiscooled,theundopedmanganites(singlyoccupiedA-site)orderintotheexoticstructural,chargeandorbitallyorderedphasesasbrieyintroducedinSection 1.2.2 .Thesamplesthusremaininsulatorsdowntolowtemperatures.Dopedmanganiteswithdopinglevelsbelowthoserequiredforelectricalconductionexhibitsimilarordering,thoughoften,asinthecaseofPr0:7Ca0:3MnO3thereiscoexistenceinthesampleoforderedphasesandparamagneticdisorderedinsulatingphasesandtheconductivityisactivated,beinggovernedbyEquation 1{4 .Theonsetofaninsulatortometaltransitionuponcoolingcanbecontrollednotonlybythedopantconcentration,butalsothedopantionicradius.Itwasfoundthatifthenominaldopantconcentrationandaveragevalencewerekeptconstant,reducingtheA-siteionicradiusalsoreducesthetransitiontemperature,sinceJ-Ttypedistortionsbecomeenergeticallyfavorable[ 13 27 ]. Inthedopedmanganites,atoptimaldopinglevels,themanganitesbecomeferromageticandmetallicuponloweringtemperature.Transportinthistemperaturerangeisgovernedbythedoubleexchangemechanism.However,thediscrepancybetweentheconductivityvaluescalculatedfromdoubleexchangeandthemeasuredvaluessuggeststhatlatticedistortionsplayaroleevenintheferromagneticmetallicstate.Theeectofsuchelectron-phononcouplingwouldbeapronouncedtemperaturedependanceofthemeasuredresistivity,andthoughobservedexperimentally,ithasnotbeenresolvedintheliteraturesatisfactorily[ 13 27 ].InSection 1.3 below,theimportanceoftheseeectsintermsofthe(La,Pr,Ca)MnO6phasediagramwillbeintroduced. 28

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18 ]: Herethersttwotermsdescribetheessentialphysicsofthedouble-exchangemechanism,withthersttermdescribingtheabilityoftheelectrontohopfromsitetositeintheBravaislattice, where+p;isatwocomponentspinorwhichaccountsforcreationandannihilationofelectronsofspininmomentumspace(p).ThesecondtermembodiesspindependentelectronhoppingbetweenadjacentMnsitesandthedoubleexchangemechanism.Inthiscase,theegelectrononsiteiisconstrainedbythestrongHund'scoupling,whichisestimatedtobeabout3eV,tohavespinparalleltothecoret2gspin: HereJHistheferromagnetic(orHund's)couplingconstant.IfJHScislargeenough,thenanelectronhoppingfromsiteitojgoesfromhavingspinparallelto~Sciandto~Scj.HHundscanessentiallybeexpressedintermsofthehoppingamplitudegivenbyEquations 1{2 and 1{3 (seeforexample[ 14 18 ]). ThenexttermofEquation 1{5 describesthecorespininteractions,i.e.theantiferromagneticsuperexchangeinteraction: Thecorespinsinthiscasearerepresentedby~Scjwithiandjrepresentingdierentlatticesites. 29

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1{5 describetheelectron-latticeinteractions,withHBbeingthebreathingmodegivenby: whereQ0isthebreathingmodeamplitude,whiled+iaanddiaarethecreationandanhilationoperatorsforelectronsofspinonorbitalaonsitei,ascombinedinthetwo-componentmomentumspacespinorofEquation 1{6 .Thesecondelectron-latticeinteraction,theJahn-TellerdistortionHJTcanbeexpressedas: whereaandbaretwodierentlatticesites,whilegj~QJTjgivestheamplitudeofthesplittingbetweentwodegenerateeglevelsandthedirectionof~QJTspeciestheparticularlinearcombinationsofegstateswhichvaryinenergyduetothedistortion. Finally,thelastterm,HUdescribestheCoulombrepulsionbetweentheegelectrons: whereUisdenedastheenergydierencebetweenacongurationinwhichsiteihaszerowhilejhas2egelectronsandacongurationinwhicheachsitehasoneegelectron. TheHamiltoniangiveninEquation 1{5 canbesolvednumericallyandanalyticallydependingontheamountofsimplicationandtypesofassumptionsusedforeachofthecomponentsshownabove. 30

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1.2.2 ,aretheMn3+manganiteLaMnO3andtheMn4+manganiteCaMnO3.SincebothCaandLahavesimilarionicradiussize,mixingthetwospecies(orinterchangingsomeoftheLainLaMnO3withCaions)resultsinmobilechargecarriers(holedoping)andmixedvalencyratherthaninduceddistortions.ItshouldbenotedthataslightdistortionwillexistbecauseofthedierentionicsizesofanMn3+vs.Mn4+,andtheveryslightmismatchbetweentheCaandLaradii.Suchdistortionsgiverisetoaverydiverserangeofcharge,orbitalandspinorderingasafunctionofLa:Caratioandtemperature. WhentheLaMnO3parentendcompoundisdopedwithCasubstitutions,thevariousstructural,chargeandorbitalorderedphasesundergoaphasetransitionatcriticaldopantconcentrations.(Quitecuriously,thetransitiontemperaturesforthephasesaremaximizedatdopantconcentrationsthataremultiplesof1/8[ 13 ]).Forinstance,forsmalldopantconcentrations(Ca<5%),LCMOisaparamagneticinsulatorathighertemperaturesandundergoesatransitiontoacantedantiferromagneticstate.ForCasubstitutionsbetween5%and20%,LCMOexhibitsaninsulatingferromagneticstateandachargeorderedstateatlowtemperatures.AtCaconcentrationsof20%to50%,LCMOtransitionstoaferromagneticmetallicstateatlowtemperatures.Higherconcentrationsresultinchargeordered,antiferromagneticandcantedantiferromagneticstatesatlowtemperatures[ 13 ].ThestoichiometryofinterestforthisworkisLa1yCayMnO3withy=0.33(i.e.33%Caconcentration),wherethecompoundisaparamagneticinsulatoratroomtemperatureandundergoesaninsulatortometaltransitiontoaferromagneticmetallicstateatabout240K. LCMOretainsapseudocubic(slightlyorthorhombic,verynearlycubic)orderingbetweentheMnO6octaheraforalldoping(y)andtemperatureranges.Thusthe 31

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13 14 ].Hence,inadditiontoachangeinvalencewithincreasingCasubstituionofPrinPrMnO3,therearestructuraldistortionswithincreasingMn-O-Mnbondanglesandareducedtolerancefactor,f(seeEquation 1{1 ).WithincreasingPrconcentration,thestructurebecomesincreasinglyorthorhombic,resultinginareducedoneelectronbandwidth,i.e.reduceddoubleexchangechargetransfer. Becauseofthehighlevelofstructuraldistortions,PCMOisinsulatingthroughouttheentiredopingrange(ally)andatalltemperatures.However,withchangingy,thereisachangeinphasecharacterizedbydierentorbital,spinandchargeordering.ThedopedchargesinPCMO(i.e.Mn3+siteswithanegelectron)andtheMn4+sitesorderinasublattice(chargeordering)withtheegoccupationbeingstaggeredorarrangedonadierent(sometimesthesame)sublattice(orbitalordering).Thischargeandorbitallyorderedstateismoststablewithareductionofthetolerancefactorandwhenthecarrierconcentrationcoincideswitharationalnumberofperiodicityofthecrystallattice[ 27 ]. TheendcompoundPrMnO3isaparamagneticinsulatoratroomtemperaturewithatransitiontoanantiferromagneticspin-cantedinsulatingstatenear100K.Atanominalconcentrationof15%Ca,thesysteminsteadtransitionstoaferromagneticinsulatingstatenear100Kto150K,dependingontheholeconcentration.Caconcentrationsof30%to40%resultinthreetransitiontemperatures.Firstthereisatransitionfromaparamagneticinsulatingstatetoachargeorderedinsulatingstate,followedbyantiferromagneticorderingandnallyatransitiontoacantedantiferromagneticinsulatoratlowtemperatures.TheincreaseinholedopingviaCaconcentrationenhancesthetendencytowardsferromagnetism,thusresultinginthecantedantiferromagneticinsulatingbehavioratlowtemperaturesfortheseconcentrations.However,thetendency 32

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27 ]. AlthoughPCMOremainsinsulatingatalldopinglevelsandtemperatures,aninsulatortometaltransitioncanbeinducedwithanappliedmagneticeld.Thisisoftenreferredtoa`melting'ofthechargeorderedphase:Theferromagneticalignmentofcore-spinswithanappliedmagneticeldalsoalignstheegspinsviatheHund'srulecoupling,andthusaidscarriermobilityviathedoubleexchangeinteraction(seeEquations 1{2 and 1{3 ).Thermodynamically,theappliedmagneticeldreducesthepotentialbarrierforthesystemtobecomeconductingbyaligningthecorespinsandenablingdoubleexchange.Thus,thehigherthetemperature,thelowertheeldrequiredforthetransitionsincethermalenergycanassistinovercomingthepotentialbarrier(thermallyinducedlatticeuctuations)formeltingthechargeorderedphase.ItshouldbenotedthatunlikethetemperatureinducedinsulatortometaltransitioninLCMO,theeldinducedtransitioninPCMOisarstordertransitionaccompaniedbyachangeinlatticeparametersoriginatingfromtheeldinduceddestructionoftheorbitallyorderedstate[ 8 14 ]. ThestoichiometryofinterestforthisworkisPr1yCayMnO3withy=0.33,wherethecompoundisaparamagneticinsulatoratroomtemperatureandundergoesachargeorderingtransitionnear240Kwiththespinsorderingantiferromagneticallybelow150K.Belowabout80K,theantiferromagneticstatebecomescantedandweaklycoupledsuchthatitisverynearlyferromagnetic.Infact,thecantedstateismetastablesinceapplicationofamagneticeldirreversiblydrivesthesystemintoaferromagneticstate[ 13 14 ]. 33

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1.3.1 and 1.3.2 above.AnapproximatephasediagramadaptedfromtheLCMOandPCMOdiagrams[ 13 27 ]forLPCMOisshowninFigure 1-6 .(La1xPrx)1yCayMnO3withx=0.5andy=0.33exhibitspropertiesinherenttobothLCMOandPCMOwithdecreasingtemperature.ThereisacompetitionbetweentheferromagnetictendenciesofLCMOandthechargeandorbitallyorderedtendencyofPCMOresultinginaninterplayofbothstates[ 14 27 28 ].Forsometemperatures,boththeferromagneticmetallicstateandthechargeorderedinsulatingstateareenergeticallyfavorableandthustheycoexistonthemicrometerscale.Thisphenomenonisknownasphaseseparation.Contrarytointuition,thephaseseparatedregionsdonotappeartobepinnedwithinthelattice,sincetheincommensuratemixturemaybeexpectedtocontainLCMOorPCMOrichsites.Instead,eachcoolingrunexhibitsadierentspatialoccupationofeachphase[ 10 ] OnewaytounderstandthepropertiesofLPCMOisbyconsideringstudiesofchemicalpressureintheparentcompoundLCMO[ 13 ].AsdiscussedinSection 1.3.1 ,sinceLaandCahavesimilarionicradii,theeectsofamixedconcentrationissimplyachangeintheaveragevalenceofthecompound,i.e.amixtureofvacantandoccupiedsingleegorbitalsontheMnsites.TheMn-O-Mnbondangleinthiscompoundremainscloseto180andthecompoundisferromagneticmetallicfortemperaturesbelowabout240Kforthey=0.33dopingconcentration.TheMn-O-Mnbondanglecanbereducedbelowtheoptimalvalueof180byapplyingchemicalpressuretoLCMO.Inthiscase,dopingtheLasitewithPrwillchangetheeectivetolerancefactorofthesystemwithoutchangingtheaveragevalenceoregcarrierconcentration.AstheLCMObecomesincreasinglydistortedwithPrions(increasingxin(La1xPrx)0:67Ca0:33MnO3),theinsulatormetaltransitiontemperaturedecreasesandthetransitionbecomesincreasinglyhystereticandrstorder.Thereisanincreasingtendencytowardschargelocalizationandcharge 34

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Theapproximate(La,Pr,Ca)MnO3phasediagramshowingtheendcompounds(La,Ca)MnO3and(Pr,Ca)MnO3phasediagrams.Theredlinedenotesthex=0.33Cadopingconcentration.Althoughsamplesfory=0.4to0.6werestudied,themainresultsdescribedinthisworkarefory=0.5ashighlightedbythegreybox.IllustrationprovidedcourtesyofAmlanBiswas. 29 ].Thepseudocubicstateishypothesizedtobeparamagnetic,andsometimesreferredtoasthecharge-disorderedinsulatingstate(noclearchargeororbitalorderingsublattice)[ 29 { 31 ].Neutrondiractionmeasurementssuggestthepresenceofchargeorderednano-clustersintheparamagneticbackgroundcoexistingwithlatticepolarons[ 14 ].Itisthechargedisorderedinsulatingstatethatundergoesarstorderinsulatortoferromagneticmetallictransitionatlow 35

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14 ]. ThePrdopedLCMOorLPCMOremainsferromagneticatlowtemperaturesforx<0.7,abovewhich,thecantedantiferromagneticinsulatingstateofPCMOisprevalent.Forx<0.7thelowtemperatureferromagneticstateinLPCMOcanbeunderstoodbynotingthatbelowabout80K,thecantedinsulatingstateinPCMOismetastableandverynearlyferromagnetic.Thus,whenanalyzedfromtheperspectiveofLadopedPCMO,increasingLacontentincreasesthecompetitionbetweenantiferromagnetismandferromagnetismeventuallytippingthescaleinfavorofferromagnetismwhenahighenoughLaconcentrationisintroduced(orintheLCMOpicture,ferromagnetismincreasesforsmallPrconcentrationsinLCMO)[ 8 ].ThisfactdemonstratesthatbothmagneticeldorareductioninchemicalpressurecaninduceferromagnetisminPCMObychangingtheeectivedoubleexchangehoppingintegralandreducingthesuperexchangeantiferromagneticinteractions. Essentially,fortheLPCMOconcentrationdiscussedinthiswork,specically(La0:5Pr0:5)0:67Ca0:33MnO3,inbulkformthecompoundisaparamagneticinsulatoratroomtemperature[ 13 ].Withdecreasingtemperature,around240K,thereisatransitionofportionsofthesampletoachargeorderedstatewhiletheotherportionsremaininsulating,butintheabsenceofachargeororbitallyorderedsublattice.Belowabout100K,thechargedisorderedportionsofthesampletransitiontoaferromagneticmetallicstateandthereiscoexistenceoftheinsulatingandmetallicregionsinthesample.Atlowtemperatures,thesampleisphaseseparatedintochargeorderedregionsandmajorityferromagneticregions.Amagneticeldaslowas2Tcantransformthesampleintoafullymetallicferromagneticstate. 36

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32 ].Acompressiveortensilestraininthiscaseactstoreduceorenlarge,respectively,thelatticeconstantsintheplaneofthelmwhiletheoutofplanelatticeconstantsareincreasedordecreasedrespectively.Figure 1-7 schematicallydepictstheeectsofsubstrateinducedstrain.TheeectonLPCMOthinlmsgrownonorthorhombicNdGaO3substrateswitha(011)orientationisaveryslightcompressivemismatchwithintheplaneofthelmwithanelongationperpendiculartotheplaneofthelm.NdGaO3(011)isessentiallyorthorhombicwithcalculatedin-planelatticeparametersof0.3855nmand0.3860nmatroomtemperature(usingunitcelllatticeconstantsofa=0.5430nm,b=0.5500nm,c=0.7710nm[ 33 ]).ThelatticeconstantforLPCMOonaverage(sinceitismultiplydoped)intheparamagneticpseudocubicstateatroomtemperatureis0.384nm[ 34 ].Thusatroomtemperature,thelatticemismatchbetweenLPCMOandtheNdGaO3substratesiswith0.4%inonedirectionand0.6%intheotherin-planedirection.TheNdGaO3substrateshenceinduceaveryslighttensilestrainontheLPCMOthinlms,slightlyincreasingtheaverageMn-O-Mnbondangleanddecreasingdistortionsthusenhancingtheoneelectronbandwidth(tendencytowardsMn-Oorbitalhybridizationanddoubleexchange). ThelatticeconstantsaredierentforthedierentphasespresentinLPCMO(ferromagneticmetallicvs.chargeorderedinsulating).Thus,asthetemperatureisloweredandtheLPCMOundergoesphasetransitions,thelatticemismatchincreases,aectingthephasechangesforverythin(<100nm)LPCMOlmsstudiedinthiswork,whichareconstrainedtothelatticeparametersofthesubstrate.ThetwomainaectsofNdGaO3(011)substratesontheLPCMOphasetransitionsare:a)ThelackofahystereticfeatureintheR(T)datanearthechargeorderingtransitiontemperature,suggestingthatthechargeorderedphaseissuppressedduetosubstrateinducedtensilestrainwhicheectivelyincreasestheMn-O-Mnbondangleinthiscase.Notethatthechargeordered 37

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Anillustrationdemonstratingsubstrateinducedstrain.Thesubstrateisshowninbluewiththewhitecirclesrepresentingatomicsites.Thestrained,distorteddepositedlmisshowningreywithblackcircles.Inthisparticularillustration,thestrainisrelaxedonthetoplayer.InLPCMO,thestrainisnotfullyrelaxedforthethicknessesconsideredinthiswork. phaseisassociatedwithincreasedlatticedistortions,decreasingMn-O-Mnbondanglesandhencelocalizedcarriers.b)Thesecondeectofthesubstrateinducedstrainappearstobeatlowtemperatures,wheremagnetizationmeasurementsshowthatthecompoundisfullyferromagnetic.Thelattereectisexpectedifthe(former)chargeorderingissuppressedduetosubstrateinducedstrain. 38

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2 .Inthismanner,asdescribedindetailinthefollowingchapters,afewinsulatingandmetallicphasesappearacrossthelengthofthebridgeduringthephaseseparationtemperaturerange. ThereareseveralpotentialwaysinwhichthepropertiesofLPCMOstructuresconnedtothenanometerscalemaybeaected.Forinstance,surfacestatesdierfromthebulkduetothestrongdependenceofcharge,spinandorbitalorderingonthelatticestructure.Danglingandincompletebondsonthesurfacecanresultindrasticallydierentpropertiesonthesurfacesuchasthesuppressionofdoubleexchangeevenifthebulkportionsareferromagneticmetallic[ 24 ].Chargeandorbitalorderingmayalsobesuppressedresultinginadisorderedstate.Innanostructures,thesurfacetovolumeratioisenhancedandthussurfacesplayanimportantroleindeterminingthepropertiesofthesystem.Secondly,longrangeCoulombinteractionsaresuppressedinnanostructures.Inthecaseofbridges,theinteractionsaresuppressedalongoneaxis,possiblymodifyingthephaseseparationtendenciesinthesample.ThepotentialconsequencesofsuppressedlongrangeCoulombinteractionsinreduceddimensionsinmanganitesisaddressedinChapter 4 TheadvantageofstudyingtheeectsofmagneticandelectriceldsontransportinnanoscaledLPCMOstructuresisclearfromtheexperimentsdescribedinChapters 3 4 and 5 .Measurementsonnanostructuresmakeitpossibletoseparatelyidentifyeachofthedierenteectssimultaneouslyatplayinthemanganites,givingtheexoticelectronictransportpropertiesobservedinbulkmaterials.Forinstance,itispossibletoseparateelectrontunnelingeectsacrossdierentinsulatingregionsfrommetallictransportandcomparetheeectsoftheelectronicvs.magneticeldsontheinsulatingregions.Thedatahintatthepresenceofanintrinsicexchangebiasbetweentheinsulatingandmetallicregionswithinthephaseseparatedtemperaturerangeandadditionally,thepossibilityofCoulombblockadedmetallicdropletswithintheinsulatingbackgroundathighertemperatures(seeChapters 3 and 5 ). 39

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Theparentcompoundsofthemanganite(La,Pr,Ca)MnO3discussedinthisworkhavegroundstatesatlowtemperaturesthatareferromagneticmetallicfor(La,Ca)MnO3andacombinationofcharge/orbitalorderedandcantedantiferromagneticinsulatingfor(Pr,Ca)MnO3.Theincommensuratemixture(La,Pr,Ca)MnO3isthusanintermediatecompoundwithmetastablestatesandanintimateinterplaybetweeninsulatingandmetallicbehavior,givingrisetothemicrometerscalephaseseparationobservedatcertaindopinglevels. Inthiswork,astudyofthenanoscaleelectronicpropertiesofphaseseparationarepresented.Thin(La,Pr,Ca)MnO3lmsarepatternedintonarrowbridgestructuressuchthatoneorafewregionsofeachphasearepresentallowingadirectelectronicmeasurementofthepropertiesofeachofthetwophases. 40

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Inordertoprobetheelectronicpropertiesofphaseseparatedmanganitesonthenanometerscale,anovelnanofabricationtechniquewasdeveloped.Thenanofabricationtechnique,asdescribedinthischapter,hasallowedthemeasurementofnotonlythestabilityofphaseseparationonthenanometerlengthscalebutalsotransportacrossindividualphaseseparatedregions.Suchameasurementwaspossiblebyfabricatingthinwires(orbridgestructures)withwidthslessthenthephaseseparationlengthscalesothatafewdiscretephaseseparatedregionsweretrappedalongthelength.Additionally,anoveltechniqueforfabricatingmanganitecapacitorswithauniquegeometrywasemployedtoprobeanisotropictransportthatresultsfromconninglmthicknessestothenanometerlengthscales.Asdiscussedindetailinthesubsequentchaptersofthisthesis,usingtheformerunconventionalfabricationtechniquesseveraleectsuniquetothislenghscalewereobserved,including(1)tunnelingacrossintrinsicinsulatingregionsseparatingadjacentferromagneticmetallicregions,(2)evidenceofanewtypeofhighlyresistivemagneticdomainwall,(3)discretecolossalelectriceldinducedresistancestepsand(4)inherenttransportanisotropieslinkedtoanisotropiesincrystalstructureresultingfromsubstratestrain.Theinvestigationishoweverongoingandmanynewphenomenonbeyondthosedescribedinthisthesisremaintobeuncovered.Thefabricationtechniquespresentedbelowcanalsobeutilizedonotherphaseseparatedorcorrelatedelectronoxidesystemstobetterunderstandphysicsonthenanometerlengthscales. InthisChapter,thetechniquesusedtofabricatethemanganitenanobridgesaswellasthemanganitethinlmcapacitorsarediscussedindetail.Themeasurementset-upforboththeacanddcfourterminalresistivityandthethreeterminalcapacitancewillbediscussedfollowedbyadescriptionoftheQuantumDesignPPMSapparatususedforbothtemperatureandmagneticelddependence.Lastly,magnetizationmeasurements 41

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B A.Showsaschematicofthepulsedlaserdeposition(PLD)systemwhile,B.showsaphotographofthePLDmainchamber(circular,metallic,withmultiple`feedthruarms')withthelaserunit(orange)immediatelybehind. usingtheQuantumDesignMPMSSQUIDapparatuswillbediscussedfollowedbydataacquisitiontechniques. ThePLDprocesscomprisesalaser,atargetmaterialandatargetsubstrateasshowninFigure 2-1 .Thetargetmaterialisgenerallyabulkpelletofthedesiredmaterial,sometimesofthedesiredcompositionandsometimesofaslightlydierentcompositionwhichislatertunedbychangingthechamberpressureand/ortemperatureofthesubstrate.Thesubstrateisathin(inthiscase0.5mmthick)singlecrystalmaterialwhichisnearlylatticematchedtothedesireddepositionmaterialinordertoavoidstrainand 42

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2-2 Figure2-2. Thisphotographdepictsaplume(white)createdbythelaserstrikingthetargetmaterialontheright.Notethatthetipoftheouteredgeoftheplumeverynearlycoincideswiththeheater(red/orange,820C)wherethesubstrateismounted. Thesubstratepositionisoptimizedtocoincidewiththetipoftheplume.Inthisway,eachlaserpulseresultsinmaterialbeingdepositedonthelm|generallylessthanonemonolayerperpulse.Thesubstratetemperatureisoptimizedtoensurecrystallinegrowth.Inotherwords,theatomsmusthaveenoughthermalenergyonceonthesurfacetomovearoundandndthepositionoflowestenergy(potentialwell),thusallowingatomicallyatlayerbylayerdeposition.Theambientpressuredeterminesnotonlytheplumesize,butifthematerialbeingdepositedisanoxide,italsodeterminestheoxygencontent.Hence,inthiscase,theoxygenpressurealsorequiredaconsiderableamountofnetuningbyDr.Dhakal[ 25 ]. TheoptimumparametersforLPCMOgrowthonNGOweredeterminedthroughextensivetrialanderror[ 25 ]:Substratesweremountedontoasubstrateheaterwhich 43

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Standard-2x-raydiractometrywasusedtodeterminethecompositionandcrystalinityofthesamples[ 25 ].Thex-rayresultswereusedincombinationwithtransportandmagnetizationmeasurementstodeterminethequalityoftheLPCMOthinlms[ 25 ] 44

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Electronbeam(E-beam)patterningisabletoovercomethelowerlimitspresentedbytheUVphotolithographytechnique.Asnotedearlierhowever,thechallengeofpatterningwiththe(E-beam)istherelativelylowconductivityofLPCMOatroomtemperature.Depositingametallayeronthemanganitewasnotstraightforwardbecausebothchemicalanddryetchremovaltechniquesresultedinsurfacedamageandthusstructuraldamagetothemanganitesandhencealteredtransportproperties.Forinstance,evenifanetchthatdoesnotaectmanganitesisusedtoremovethemetals,thesurfaceofthemanganiteisdamagedfromoxygenlosstothemetal.Thoughmetalssuchasgoldwhichdonotoxidizeeasilywereutilized,nosuitableselectivegoldetchwasfound:Alletchesusedforthisstudydamagedthemanganitethinlm.AnotherchallengewithE-beampatterningwasthesubsequentetchingoftheexposedregionsusingwetordryetchesandassociatedcomplicationswithwalldamagetotheultranarrowbridge. 45

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IndirectanalogytoanE-beamsystem,theGaionbeamrequiresfocusingandthesamplecanessentiallybe`viewed'bybombardingGaions(aswithelectronsforanelectronmicroscopeorphotonsinanopticalmicroscope).Thus,simplyfocusingtheionbeamorviewingasampleinthiswaycanresultinGaionimplantationinthedesiredsample.TheFIBisgenerallyusedforfabricatingsamplesfortransmissionelectronmicroscopywhicharecoatedwithaprotectivemetalliclayer,thusGaionimplantationisnotamajorissue.Inthethinmanganitelmsusedforthisworkhowever,itwasfoundearlyintheprojectthatGaionimplantationinthemanganitesresultedinalteredtransportpropertiesandnoinsulatortometaltransition. ToavoidGaionimplantationdirectlyintomanganites,wepatternedtheNGOsubstratesusingtheFIB.SinceNGOisinsulatingandthuspronetochargingproblemsfromtheGaionbeam,wedepositeda40nmto80nmthicklmoftransparentconductingnanotubes(CNT)incollaborationwithDr.A.Rinzler[ 35 ].SinceapristineandatomicallysmoothsubstratesurfaceisessentialforachievinghighqualityLPCMOthinlmsforourexperiments,theinertCNTthinlmswerebettersuitedasaconductinglayerforFIBpurposesthanconventionalmetals.BecauseCNT'sareinertwhenincontactwiththesubstrate,thesmoothsurfaceofthesubstrateispreserved.Itwasfoundthat 46

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2.2.1 .Mostofthemetalsreadilyavailableinourlaboratory(i.e.Al,Au,Cu)tendtooxidizetherebydepletingtheoxygeninNGOnearthesurfaceandchangingnotonlythesurfacechemistrybutthecrystalstructure,andresultinginundesirablesurfaceroughness.TheadvantagewithCNTsliesinthefactthattheydonotdepleteNGOsurfaceoxygenandcaneasilyberemovedwithalowpowerO2plasmawhichwasfoundtonotaecttheNGO. Figure2-3. TwotypicalscanningelectronmicrographsofatransparentconductingcarbonnanotubethinlmcoveringtheNdGaO3substrate,priortoFIBmilling. Figure 2-3 showsanSEMimageofatypicalsubstratecoatedwithaCNTlmpriortoFIBmilling.SmallrectangulargroovesorlinesdeningthedesiredbridgewidthasshowninFigure 2-4 weremilledintothecenterofthesubstrateusingtheDualBeam-FocusedIonBeamStrataDB235apparatusavailableattheUniversityofFloridaMajorAnalyticalInstrumentationCenter(MAIC),seeFigure 2-5 .The`dualbeam'featureoftheFIBisadditionallyusefulinavoidingGaioncontaminationsinceitconsistsoftwobeams:theGaionbeamandanE-beam.Bothbeamscanbefocusedatthesamepoint 47

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B C A.SchematicshowingrectangulargroovesintheNGOsubstrateetchedusingtheFIB.Thespacingofthegroovesdenesthewidth,d,ofthebridgetobefabricatedbetweenthem.B.Showsascanningelectronmicrograph(SEM)ofacarbonnanotubecoatedNGOsubstrateimmediatelyafterpatterningoftrenches1mdeep,40nmwidetodenethebridge(asopposedtogrooves,seeendofSection 2.2.3 ).C.AnSEMimageshowingdetailsofthegroovesdepictedinpartB.Thenanotubethinlmisvisible. thusallowingimagestobeobtainedwiththeminimallyinvasiveE-beamwhilemillingwiththeionbeam.Theionbeamfocusingsequencecanbeperformedatthesampleedge,farawayfromthedesiredpatternareaandtheE-beamcansubsequentlybeusedtodeneapatterningarea,avoidingGaioncontamination.Inthisway,theareasthatarenotdirectlybeingmilledwillavoidamajorinuxofGaions.Thelowestavailablebeamcurrentsettingsof1pAor10pAandabeamvoltageof30kVwasusedtominimizeGa`sidewall'contamination(i.e.Gaionswithenoughmomentumandenergyimplanting 48

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Figure2-5. TheDualBeam-FocusedIonBeamStrataDB235apparatusavailableattheUniversityofFloridaMajorAnalyticalInstrumentationCenter(MAIC).Photocourtesy,MAIC. AftersuccessfulFIBmilling,thesamplewasremovedandplacedinanAnatechSCE600Asher.AnO2plasmawasusedatapowerof600Wfor20minstoremovetheCNTthinlmbyoxidizingthecarbonnanotubes,resultinginCO2gas.Next,anLPCMOthinlmwasdepositedonthepatternedsubstrateusingthePLDsystemasdepictedinFigure 2-6 2-7 and 2-9 respectively. 49

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Schematicshowingtheetchedsubstrate(grey)beforeandafterLPCMO(red)deposition.ThesubstrategroovesaredeepenoughtoensureminimalLPCMOdepositiononthesidewalls,andthusminimalelectricalcontactbetweentheLPCMOonthesubstrateandthatdepositedwithinthegrove.Figurenottoscaleforclarity. Figure2-7. SchematicshowingLPCMO(red)depositedonetchedsubstrate(grey)beforeandafterthebridgeisdenedusingUVlithography.Figurenottoscaleforclarity. Figure2-8. Aschematic(nottoscale)depictingthefourcontactpadUVlithographymaskusedtoisolateanddenethebridgepriortowetetching. 50

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2-8 wasdevelopedusingtheAutocadsoftwarepackageinourlaboratoryandprintedbyPhotoSciences,Inc.Asnotedpreviously,thelowerlimitofresolutionwithourUVphotolithographysystemisapproximately1m.Thusamaskwithabridgewidthof3mwasdeveloped.AKarlSussMA-6ContactMaskAlignerwasusedtoalignthesubstratepatternwiththephotolithographymaskinsoftcontactmode.Thisparticularstep,giventhelowresolutionontheMaskAlignermicroscope,sometimesinvolvedseveralhoursoftediousandcarefulalignment.Oncealigned,thesamplewasexposedfor14secandsubsequentlydevelopedusingMicropositMF319developerfor10secandthenrinsedindeionizedwater.Figure 2-9 showsanopticalmicroscopeimageofasuccessfullyalignedanddevelopedbridgestructure.Notethatinthiscase,insteadofgrooves,1mdeep,40nmwidetrenchesweremilledwiththeFIBtodenethebridge,asatimesavingmeasure(narrowtrenchestakelesstimethanwiderectangulargrooves). Thenalfabricationstepinvolvesetchingtheexposed,unmaskedmanganiteusinganin-houserecipeforasolutionpreparedfromatitrationbetweenpotassiumiodideand10%hydrochloricacid.Sincethesolutionisunstableandtheetchratevarieswiththeageofthesolution,priortoetchingagivensamplesmallstripsofmanganitelmsonNGOareusedtodeterminetheexacttimeoftheetch.Etchtimingsrangefrom8sectooveraminute.Thusprecisetimingiscrucialsinceonesecondtoolongcanresultinetchingthroughthenarrowbridgeinthecenter. Oncesuccessfullyetched,thephotoresistmaskisremovedbysonicatingthesamplerstinacetoneforoneminutefollowedbyisopropanolandmethanolalsoforaminuteeachfollowedbynitrogengasblowdrying.AnopticalimageofacompletedmanganitebridgeisshowninFigure 2-9 B. 51

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B A.Opticalimageofa0.6mwideLPCMObridgealignedwithadevelopedphotoresistmask.Notethatinthiscase,insteadofgrooves,1mdeep,40nmwidetrenchesweremilledwiththeFIBtodenethebridge.AschematicofthelithographymaskusedisshowninFigure 2-7 .B.Opticalimageofa0.6mwideLPCMOcompletedbridge(denedwithrectangulargroovesinsteadoflines)afterasuccessfulwetetchandsubsequentremovalofthephotoresistmask. Figure2-10. AQuantumDesignproprietaryPPMStransportmeasurementpuck.TheleftimageshowsthebottomofthepuckandthecontactswhichplugintothePPMShardware.Therightshowsthetopofthepuck:Thegoldsquareinthecenteristhesamplespaceandthesmallcontactsalongtheperimeterareusedforelectricalconnectionwiththesampleusinggoldwires. 52

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2-10 whichconnectsthroughelectricalcontactsandwiringinourPPMSmeasurementsystem(describedinSection 2.5 below)tothemeasurementinstruments. ThedepositionoftheAlOxdielectricthinlmsisdescribedinSection 2.3.1 below.ThemetalelectrodedepositionforboththetopandbottomgatingelectrodesisdescribedinSection 2.3.2 .AphotolithographytechniquesimilartotheproceduredescribedinSection 2.2.3 abovewasusedtodenethebottomgateandthetopgatesuchthatthegatewasalignedwiththebridgewithminimaloverlapwiththemeasurementleadsasshownschematicallyinFigure 2-11 53

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TheschematicaboveshowsthebridgecappedwithalayerofAlOxfollowedbyathinmetallayer(Aushown)suchasAuorAlactingasthegate. placeofNGOwillalterthestrainandthusthepropertiesoftheLPCMOlm,thusNGOismostdesirableinordertostudytheLPCMOinitsleaststrainedform.Toovercomethisdiculty,anovelcapacitancestructurewherethematerialundertest,LPCMO,comprisedoneoftheelectrodesofanelectrode-insulator-electrodecapacitorstructureasshowninFigure 2-12 ,wasdevelopedbyDr.RyanP.Rairigh,apreviousmembersoftheHebardlab.FollowingDr.Rairigh'sgraduation,theremainingsampleswerefabricatedbymyselfonlmsdepositedbyDr.TaraDhakal.Notethatincontrast,aconventionalcapacitorgeometrycomprisesametal{(materialundertest){metalconguration.Throughextensivecircuitmodelingandanalysisoftheunconventionalcapacitorstructure,detailedinChapter 6 ,thepotentialdropparalleltotheplaneofthelmwasisolatedfromthevoltagedropperpendiculartotheplaneofthelm.Inthisway,itwasdeterminedthattheinsulator-to-metalphasetransitionwithintheplaneofthelmoccursatadierenttemperaturethanthephasetransitionperpendiculartotheplaneofthelm.Thephase 54

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Figure2-12. Aschematic(nottoscale)depictingallthelayersofthecapacitorstructurewithLPCMOasoneoftheelectrodesandacircularlydenedAlthinlmasthesecondelectrode. TheLPCMOtrilayercapacitorstructurecomprisedofanAlOxdielectriclayertoppedwithametalelectrode.TheAlOxwasdepositedusingRFmagnetronsputteringandametalevaporationchamberwasusedtodepositanAlelectrodeasdescribedinSections 2.3.1 and 2.3.2 respectivelybelow. 55

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Figure2-13. AschematicoftheAlOxdepositionsystem,Hamedonsystemdescribedinthetextisshownandthepartslabeled. Formetals,adcvoltageisgenerallyutilizedsincetheconductingtargetprovidesashunttogroundfortheaccumulatedchargefromthebombardingions.Insulatingmaterialshoweverdonotprovideaconductingpathtogroundandquicklybecomeionizeddeectingfurtherionbombardmentandthushindersputtering.Inthiscaseanacdrivingvoltage(13.56MHz,radiofrequence{rf)isused.Aschematicofourhome-builtdepositionchambernicknamedHamedonisshowninFigure 2-13 Afterpulsedlaserdeposition(Section 2.1 ),thehighqualityLPCMOlmswithacleansurfacewereloadedinHamedonviaaload-lock.Thesystemwasevacuatedusing 56

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2-14 Figure2-14. Thisopticalimageshowsametalcapacitortopelectrode(circular)withtwogoldwireleadsattachedusingsilverpaint.Numerousreectionsintheimagemaydiverttheeye,althoughthecircularelectrodeisclearlydened. Thermalevaporationisabasicmetaldepositiontechniqueinvolvingtheuseofasmalltungsten(W)heatingelementorlament(seeFigure 2-15 )whichholdsthedesiredmetal,inthiscaseAl.Whenahighcurrentisappliedacrosstheheatingelement,joule 57

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Figure2-15. TungstenthermalevaporationboatusedfordepositingAltopelectrodes.BoatsofothershapesandsizeswereusedforothermetalssuchasAu,Ag,Cu,etc. Forthepurposesofthisexperiment,anAllmof60nmthicknesswasthermallyevaporatedontotheLPCMO{AlOxstructureatarateof0.6nm/secachievedusingcurrentsof30Ato40Aacrossthetungstenboat,withabasepressureontheorderof107Torr.Contactstothemetaltopelectrodesweremadeusing0.00125"guagegoldwire.Microtippedtweezerswereusedtobendthewireintoaloop(10mdiameter)ononeendanddippedinsilverpaintandquicklyremoved.Withamicroscopicdropofsilverpaintsuspendedonthewireloop,thewirewasmanuallyplacedonthetopelectrodesothatthepaintwasconnedtothetopelectrode.Afterthepaintsolventsdried,thegoldwirewasbondedtotheAlwithalayerofsilverparticles.Figure 2-14 showstwowireloopsattachedwithpainttothetopofa1.5mmdiametercapacitortopelectrode. 58

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Thissamplesummarytableonlyliststhesamplesforwhichdataisshowninthesubsequentchapters(labeledinthelastcolumn).Thecolumnlabeled`Type'identieseachsampleaseitheranunpatternedthinlm(lm)orapatternedbridge(bridge).Sincethe100mscaleismuchlargethanthephaseseparationscale,sampleS2aisconsideredathinlm.S2bandS2chavebeenconsecutivelypatternedintoincreasinglynarrowerbridgesfromthesameinitialsample:S2a. SampleTypeIn-planedimensionsFilmthicknessChapters S1bridge3mx10m30nm 3 S2alm100mx3mm30nm 4 S2bbridge2.5mx8.0m30nm 4 S2cbridge0.6mx8.0m30nm 3 4 5 S3bridge2.5mx8.0m10nm 4 S4bridge0.4mx4.5m30nm 5 S5lm5.0cmx5.0cm60nm 6 S6lm5.0cmx5.0cm30nm 6 S7lm5.0cmx5.0cm60nm 6 S8lm5.0cmx5.0cm90nm 6 thedetailedmeasurementswerecarriedoutononlyafewtypicalsamples(asthoselistedhere)duetopracticalissuessuchastimeconstraintsandavailableresources.Aquantitativeaverageofpropertiessuchasthemagnetoresistancecannotbemeasuredforthebridgesamples,sinceeachsamplediersfromtheothersquantitatively,thoughallpossessthesamequalitativetransportfeaturesandproperties.ThisdiscrepancyismostlikelyduetoinhomogeneouschemistryoftheLPCMOthinlmswithinthenarrowbridge. 2.5.1 below.InSection 2.2.4 detailsofthebasicelectriceldgatingsetuparepresentedandSection 2.5.3 providesadescriptionofthethreeterminalcapacitancesetup.AlldctransportmeasurementswerecarriedoutbymyselfwhilethecapacitancemeasurementswerecarriedoutincollaborationwithfellowHebardlabmembers,Dr.Rairigh,SefTongayandPatrickMickel.Whilethemanganitecolossal 59

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Fourcontactresistancemeasurementcircuitdiagramshowingallinstrumentsutilized. Thoughthemeasurementofthemanganitebridgeswasessentiallytwoterminal,tominimizethecontactresistance,thefourterminalmeasurementsetupwasutilized.Thismeasurementcongurationisessentiallytwoterminalbecausethetwoleads(forvoltageandcurrent)ateitherendofthebridgeareshortedviathemacroscopicleads.Sincemostofthesamplesmeasuredhadresistancesontheorderof106to109,inmostcaseswesuppliedcurrentandmeasuredvoltage.Currentintherange106Ato1012AwasappliedusingaKeithley220currentsourceacrossthecurrentleadslabeledinFigure 2-16 60

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2-16 usingaKeithley182orthenewerKeithley2182aNanovoltmeter.Often,thecurrentsupplyandvoltmeterweresubstitutedwiththeKeithley236SourceMeasureUnitwhichcansimultaneouslysupplyandmeasurebothvoltageandcurrent.MeasurementsthatinvolvedsourcingvoltageandmeasuringcurrentwereoftencarriedoutwiththeKeithley236. Figure2-17. Twoterminalsource-voltage,measure-currentcircuitdiagramshowingallinstrumentsutilized.Thesampleresistanceismuchgreaterthanthe10kprotectionresistorshown.TheprotectionresistorservedasacurrentlimiterforthesensitiveSRS70currentpreamplierintheeventofanunexpectedcurrentincreaseacrossthemanganitebridge.Thusthevoltagedropacrosstheprotectionresistorisnegligiblecomparedtothesamplebeingmeasured. ThoughtheKeithley236sucedformostvoltagesourcingmeasurements,somemeasurementsthatrequiredmoreaccuratelowlevelcurrentreadingswhensourcingavoltagewerealsomadeusingtheStanfordResearchSystems(SRS)570CurrentPreamplierwithexcellentnoiselteringcapabilities,andaKeithley182Nanovoltmeter. 61

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2-17 .HeretheSRS570inputisheldatvirtualgroundandthereadingisconvertedtoavoltagewhichcanbereadatthevoltmeteroutputandmanuallyconvertedtoacurrentvalueusingthescalesdenedonthepreamplier. Circuitdiagramforelectriceldgatingmeasurementshowingallinstrumentsutilized. Figure 2-18 showsaschematicofthemeasurementsetupusedtoeldgatethemanganitebridges.Inthiscase,resistanceacrossthebridgewasmeasuredasdescribedinSection 2.5 above.However,aKeithley2400SourceMeasureUnitwasusedtosupplythegatevoltagewithrespecttogroundasindicatedinthegure.Notethattoavoid 62

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2-19 :Theautobalancingbridgecircuitry,theprecisionfrequencygeneratorandthedetector. Figure2-19. ThreeterminalcapacitancebridgeschematicadaptedfromtheAndeenHagerlingAH2700AUsersManual. Theunknowncapacitance,Cx(inthiscase,oursample)isconnectedasshownintheFigure 2-19 andeitheraparallel(shown)orseriescongurationofacapacitanceandresistance(Rx)isassumed.Todeterminethecapacitanceasmallamplitudeacsignalisgeneratedbythegeneratorandthebridgerunsit'sauto-balancingsequenceuntilthevoltageatthedetectorispreciselyzero.ThefactthattheratioofcoilsatTap1andatTap2isknownandthefactthatthevoltageatTap2isthesameasLeg4andthatatTap1isthesameasatLeg3isusedtodeterminetheprecisevaluesoftheunknownresistanceRxandcapacitanceCx. 63

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2-20 .Thecryostatconsistsofa7TsuperconductingmangetimmersedinliquidHe.Aliquidnitrogen(LN2)outerjacketprovidesathermalgradientbetweentheHeandtheambienttemperatureinthelaboratory.AvacuumjacketbetweentheHeandLN2aswellasbetweentheLN2andoutershellofthedewarprovidesaddedinsulation. Thesystemprovidesbuiltinandautomatedtemperaturecontrolswithuserinputthroughasoftwareinterface,QuantumDesign'sMultiview.ThePPMScanalsobecontrolledusingLabviewsoftwareandcaneasilybeinterfacedwithacomputerusingthebuilt-inGPIBconnectorsasdiscussedinSection 2.8 below.Forcooling,Hegasispumpedintothesamplechamberandusedtocoolthesampledownto4.2K,andcoolingdownto1.7Kisachievedbyllingthe`coolingannulus'withliquidHeandevaporating.Afeedbacksystemconsistingofheatersandthermocouplesisusedtopreciselycontrolthetemperatureofthesystembetween1.7Kand350K. SamplesareloadedintothePPMSonasamplepuckprovidedbyQuantumDesignandengineeredforthisparticularsystem,asshowninFigure 2-10 .ElectricalconnectorsonthepuckconnectinternallythroughthePPMSviaco-axialcableandterminateata`break-out'boxwithBNCconnectors,whichenableconnectivitywiththemeasurementinstruments. 2.6 butwithouttheouterLN2jacket.Thesampletobe 64

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SchematicofthePhysicalPropertiesMeasurementSystem(PPMS)dewar.DrawingadaptedfromtheQuantumDesignQD-6000HardwareManual. measuredwasinsertedandadjustedatthecenterofaplastic,transparentdrinkingstrawwhichwasmountedonasampleprobeandinsertedintotheMPMSsamplespace.SincetheSQUIDmagnetometerisadierentialtechnique,therelativelyfaintdiamagneticstrawsignalisnearlyinsignicantsincethedierentialtechniquerendersitabackgroundsignal. ThemagnetizationmeasurementswerecarriedoutinaHepurgedandevacuatedsamplespacebetween300Kand10K.TheMPMSsystemisinterfacedviaGPIB 65

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MagnetizationmeasurementoftheLPCMOlmontheparamagneticNGOsubstrate.Astheoverwhelminglylinearoverallshapeofthecurvedisplays,theparamagneticsubstratesignaldominates. connectiontoacomputerandcontrolledviatheQuantumDesignMultiviewsoftwarepackage.Figures 2-21 and 2-22 showmagnetizationdataforatypical300ALPCMOthinlm.Figure 2-21 showsthemeasuredsignalwiththedominant(linear)paramagneticNGOsubstratesignalandFigure 2-22 showstheLPCMOcomponentofthesignalafterthelinearparamagneticsignal(positiveslope|diamagneticmaterialshaveanegativeM(H)slope)issubtracted. Inadditiontomeasuringmagnetizationofthinlms,magnetizationmeasurementswerealsoperformedon1mwideLPCMOstripespatternedonNGOsubstratesasshowninFigure 2-23 (fabricatedusingthephotolithographytechniquesdescribedin 66

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AlinearttotheparamagneticsignalissubtractedfromthesignaltogivetheLPCMOferromagneticcontributionasshownhereforseveraltemperatures. Section 2.2.3 )whilesimultaneouslypassingcurrentthroughthestructure.Goldelectrodesweredeposited(Section 2.3.2 )onthetwoendsofthestripesasshownonthetoprightcornerofFigure 2-23 andthesamplewasmountedonacustomdesignMPMSsampleholderwithelectricalwiringforsimultaneouslyperformingmagnetizationmeasurementsandelectricaltransportmeasurements.AtypicalmagnetizationcurveafterremovaloftheparamagneticNGObackgroundsignalisshowninFigure 2-24 67

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Opticalimageofmultiple1mwideLPCMOstripes(lightercolor).ThetoprightcornershowstheAuelectrodes,slightlyoutoffocus. Figure2-24. Magnetizationdataformultiple1mwideLPCMOstripes 68

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TheLabviewdataacquisitionprogramswereinsomecasesmodicationsofprogramswrittenbypreviouslabmembersbutinmostcasesbrandnewprogramswrittenbymyself.AlldatawereanalyzedusinganumberofsoftwarepackagesincludingOriginLab,MicrosoftExcelforlesscomplexanalysis,Mathematicaandanumberofsharewareplottingprogramsfreelyavailable. Lastly,itshouldalsobenotedthatChapters 3 4 6 havepartiallybeenreproducedfromworkpublishedinscienticjournalsinaccordancewithcopyrightlaws.Afootnoteinthebeginningofeachchapterprovidestherelevantcitationandinformation.Inthisrespect,inaccordwiththeconventionalstandardsandtrendsofscienticjournalpublications,thesechaptersandalsoChapter 5 whichisbeingadaptedforanupcomingpublication,havebeenpresentedinpluralorcollectiverstpersonratherthantheobjectivestyleofwrittingemployedinChapters 1 2 and 3 69

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Toclarifytheexactroleoftheworkcarriedoutbyallindividualsincludingmyselfmentionedinthischapter,belowisalistoftheworkpresentedinthefollowingchapterswithashortnotelistingthecontributionsofeachindividual. Chapters TaskContributorContribution 2 to 6 LPCMOlmsDr.T.DhakalInitialthinlmdeposition 2 to 6 LPCMOlmsG.SinghBhallaSubsequentthinlmdeposition 2 bridge/lmmagnetizationmeasurementsG.SinghBhallaAllmagnetizationmeasurements 3 4 5 bridgefabricationDr.S.SelcukInitialnanofabricationtraining,specically,E-beam,FIB 3 4 5 bridgefabricationG.SinghBhallamodicationofinitialnanofabricationtechniques,developmentofalltechniquesusedtoday,includingsubstrateetching,CNTconductinglayers 3 4 5 bridgefabricationB.LiuCNTlmcoating 3 4 5 bridgetransportmeasurementsG.SinghBhallaAlltransportmeasurements 6 capacitorfabricationDr.RairighDevelopmentofuniquecapacitancegeometry 6 capacitorfabricationG.SinghBhallaFabricationofsubsequentcapacitors 6 capacitorfabricationS.TongayTrainedbymyselfonAlOxandmetaldeposition 6 capacitancemeasurementsDr.RairighDiscoveryofcolossalmagnetocapacitance(CMC);allworkonscalinglawcollapse 6 capacitancemeasurementsG.SinghBhallaThicknessdependenceofCMCvs.CMRpeaks. 6 capacitancemeasurementsS.TongayTrainedbymyselfonmeasurementsinvolvingthicknessdependenceofCMCvs.CMRpeaks. 6 capacitancemeasurementsP.MickelTrainedbymyselfoncapacitancemeasurements;analysingscalinglawcollapsewithinDebyemodel. 70

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2 ,designedtoexploitthemicrometerscalephaseseparationintocoexistingferromagneticmetallicandanti-ferromagneticinsulating(AFI)regions.Fabricatingbridgeswithwidthssmallerthanthephaseseparationlengthscalehasallowedustoprobethemagneticpropertiesofindividualphaseseparatedregions.First,neartheCurietemperature,amagneticeldinducedmetal-to-insulatortransitionamongadiscretenumberofdomainswithinthenarrowbridgesgivesrisetoabruptandcolossallow-eldmagnetoresistancestepsatwelldenedswitchingelds.Further,inthedynamicphaseseparationtemperaturerange,ourexperimentsrevealthatbecauseofthenarrowwidthofthebridges,alternatinginsulatingandmetallicregionsformalongthebridgelength.Withinthistemperaturerange,weobservetheclassicsignaturesoftunnelingmagnetoresistanceacrossthenaturallyoccurringintrinsicAFItunnelbarriersseparatingadjacentferromagneticregionsspanningthewidthofthebridges.Inotherwords,thebridgeessentiallyresemblesamagnetictunneljunction.Thepresenceofintrinsictunnelbarriersintroducesanalternativeapproachtofabricatingnovelnanoscalemagnetictunneljunctions.Themagneto-transportpropertiesofthebridgesbelowthephaseseparationtemperaturerangewillbediscussedinChapter 4 71

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36 37 ]orbicrystalline[ 38 ]lms,andacrossthinlminsulatorssandwichedbetweenferromagneticmetallic(FMM)electrodesintrilayerormultilayercongurations[ 39 ]. Utilizinganaltogetherdierentapproach,weexploitthemicrometerscaleintrinsicphaseseparationinLPCMO,which,asdescribedinChapter 1 ,resultsfromacompetitionbetweentheferromagneticmetallic(FMM)andinsulatingstateswithcomparablefreeenergies.WhenLPCMOthinlmsarereducedindimensionstonarrowbridgesofwidthsmallerthantheindividualphaseregions,alternatinginsulatingandFMMregionsspanthebridgewidthandthesamplesexhibittheclassicalsignaturesoftunnelingmagnetoresistance(TMR).Further,amagneticeldinducedinsulator-to-metal(IM)transitionamongadiscretenumberofregionsgivesrisetoabruptandcolossalLFMRstepsthatareanisotropicwithrespecttomagneticeldorientation. RecentobservationsofdiscreteresistivitystepsonsuchbridgesofthemixedphasemanganitesPr0:65(Ca0:75Sr0:25)0:35MnO3andLPCMOprovideevidenceofalternatingFMMandinsulatingregionsspanningthefullwidthofthestructure[ 40 { 42 ].However,spin-polarizedtunnelingacrosssuchintrinsicinsulatingregionswasnotconsidered.Belowwedescribetheexplicitroleofspin-polarizedcurrentsonmagnetotransportinsubmicronstructureswhereintrinsicinsulatingtunnelbarriers[ 43 ],resultingfromphaseseparationdominate. 1.3.3 and 1.3.4 ,isparamagneticatroomtemperatureandundergoesastructuraltransitiontoachargeorderedantiferromagneticinsulating(AFI)phasebelowabout240K[ 44 45 ].AtypicalR(T)curveforour(La0:5Pr0:5)0:67Ca0:33MnO3thinlmsgrownonNdGaO3substratesisshowninFigure 3-1 72

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1 butcertainlyraisesquestionsastothenatureofthetransition(rstordervs.secondorder).Furtherexperimentationbeyondthescopeofthepresentworkisneededtoconrmthis. Figure3-1. 2-1 .Herethebluecurvedepictscoolingandtheredcurve,warming. 2 73

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25 ].Duetothedynamicnature(seeSection 1.3.3 )ofthephasecoexistence,belowTIMOtheFMMandinsulatingregionsarenotpinnedbutevolveinshapeandsizewithchangingtemperature,asconrmedbyimaging[ 10 46 ]andtime-dependentrelaxationmeasurementsofresistivity[ 44 ].Next,belowwhatisoftenreferredtoastheblocking[ 44 ]orglasstransition[ 45 ]temperatureTG,(withTIMO>TGaslabeledinFigure 3-2 ),thesampleispredominantlyinasinglephaseferromagneticstate[ 25 ]characterizedbylongrelaxationtimeconstants.Itiswithinthephasecoexistencetemperaturerange,TIMO>T>TG,thatweobservetheanisotropicLFMRandTMReectsacrosssubmicrometerwidebridgesfabricatedfromLPCMOthinlms.AnapproximatephasediagramforLPCMOisshowninFigure 1-6 2 ,tofabricatethebridges,werstdepositedsinglecrystalline,epitaxial,30nmthick(La0:5Pr0:5)0:67Ca0:33MnO3(LPCMO)lmsonheated(820oC)NdGaO3(110)substratesusingpulsedlaserdeposition.Next,usingacombinationofphotolithographyandafocusedionbeam(FIB),bridgesrangingfrom100nmto1minwidthwerefabricated.AnSEMimageofatypicalsampleisshowninFigure2,inset.Pressedindiumdotsandgoldwirewereusedtomakecontacts.Resistance(R)measurementsweremadebysourcing+/-1nADCandmeasuringvoltage.AmagneticeldwasappliedthreeconsecutivetimesateachtemperaturealongthreedirectionsHz,HxandHywithrespecttothecurrentowIxasdepictedinFigure2,andrampedat25Oe/s.Thesampleidentities,aslistedinChapter 2 ,table 2-1 arenotedinthegurecaptions. 74

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Temperature-dependentresistanceofsampleS1(seetable 2-1 ,a2.5mwidebridge(blue)andS2(table 2-1 )a0.6mwidebridge(green)patternedfrom30nmthickLPCMOthinlmsrevealtheevolutionofpronouncedsteplikechangesandtheinsulator-to-metaltransitiontemperature(seetext)asthebridgewidthbecomescomparableto(2.5m),andthensmallerthan(0.6m)themicron-sizeregionsofco-existingAFIandFMMphases.Ascanningelectronmicrographofa0.2mwidebridge(withtheprotectivepolymerandmetallayersstillpresent)takenshortlyaftertheFIBprocessisshownintheinsettogetherwiththeorientationsoftheappliedelds:Hx,HyorHz

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3-2 (bluecurve,comparewithFigure 3-1 ),smallstepsaccompanyingtheIMtransitionbegintoappear,sincethebridgewidthisnowontheorderoftheindividualphaseseparatedregions[ 40 ].Signicantdeviationsintheresistivityareobservedforbridgesofwidthlessthan0.9m,whereinmostcasestheinsulatortometaltransitiontemperature,(TIM=64Kforthe0.6mwidebridge)shiftstoalowervalue.Weattributethistodimensionallylimitedpercolation(Figure 3-2 ,greencurve)fromthreetotwodimensions.Ahighresistance,temperatureindependentstatebeginstoappearbelowTG=48K.HerewediscussdataintherangeTIMO>T>TGfora0.6mwidebridgewithmagnetoresistancepropertiesthataretypicalofbridgeswehavefabricatedbelow0.9minwidth.TheTMRandcolossalLFMReectsoccurwithinthelargescalephaseseparationtemperaturerangeTIMO>T>TGandceasetoexistforTT>TIMwithTIM=64Khowever,weobserve(Figure 3-3 )colossal(hundredfold)eld-inducedresistancechangesatwell-denedanisotropicswitchingelds.Thetemperaturerangefortheselargeresistancechangescoincideswiththerangewherethemaximumcolossalmagnetoresistive(CMR)eectinourunpatternedlmsisobservedasshowninFigure 3-4 .Here,thehighresistancevalues(108)correspondtolimitedconductionthroughinsulatingregionswhichwithincreasingeldareeithercompletelyremovedorabruptlyshrinktoformremnant(lowerresistance)tunnelbarriersseparating 76

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Fortemperatures,T>TIM,repeatedmagneticeldsweepsattheindicatedtemperatures(73K,70,67K,64K)revealreproduciblehysteretictemperature-dependentcolossalresistancejumpsthataremoresensitivetoin-plane(Hx,Hy)ratherthanperpendicular(Hz,arrowswithsolidheads)elds.DataforsampleS1c,table 2-1 ferromagneticregionsspanningthebridgewidth.Theinsulatingregionsmaynotbefullyremovedforthe2Teldsshowninthegure,sincetheunpatternedthin-lmresistivityisnotachievedunlessaeldashighas5Tisapplied.ComparisonofourresultswiththeparentcompoundPr0:67Ca0:33MnO3suggeststhatwithdecreasingtemperature,thereisareductioninthefreeenergyoftheFMMphase,andtheregionsofinsulatingphaseundergoarst-orderphasetransitionresultinginaconcomitantcolossalresistancedrop[ 47 ].Inlikemanneradistributionofsuchrst-orderhysteretictransitionsover 77

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25 ]asshowninFigure 3-4 andincrystalsoftheparentcompoundPr0:67Ca0:33MnO3[ 47 ]. Figure3-4. Unpatternedthinlm(S1a,table 2-1 )R(H)datainrangeTIM>T=120K>TIMO.ThelowtohigheldtransitionsaresmoothwhencomparedtothebridgedatainFigure 3-3 .AdistributionoftherstordertransitionsshowninFigure 3-3 overmanydomainsmayaccountforthis. Ifthecrystallineanisotropyofathinlmisnegligible,thenthedemagnetizationeldsarisingfromshapeanisotropygiverisetoagreatersensitivityofthemagnetizationtoin-planecomparedtoout-of-planeappliedelds.Inourbridges,magnetoresistanceisaectedinthesameway;theeld-inducedchangesinthebridgeoccurmorereadily 78

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3-3 .ThemagneticanisotropyoftheCMReectmanifestsitselfmoredramaticallyinnarrowbridgesthaninthinlms,possiblyduetothelackofnumerousisotropicplanarconductionpathsavailableinlms.Lastly,thesensitivityoftherst-orderphasetransitiontothermaluctuations[ 47 ]islikelytobeenhancednearTIM,thusaccountingfortheunusualasymmetrictransitionsobservedattheboundarytemperature,TIM=64K,belowwhichsingle,irreversiblecolossaltransitionstoapredominantlyFMMstateoccur(T=57K). 10 44 45 ],theAFIphaseismetastablewithrespecttoappliedmagneticeldsastheFMMphasebecomesenergeticallyfavorable,partiallyasaresultofsubstrateinducedstrain[ 32 ](seealsoSection 1.3.4 ).Figure 3-5 illustratesthiseectat57K.InitiallyuponincreasingHy,R(Hy)dropsnearlyfourordersofmagnitudeandexhibitssharpsteps[ 25 47 ],resultingfromanincrementalconversionoftheinsulatingphasestoFMM.TheFMMregionsincreaseinsizeandvolume,separatedbyshrinkingAFIregionsalongthebridgelength.Figure 3-5 (insetfor57K)showsamagniedversionofthelow-resistanceregion.Herewenotethedistinctformationoflow-eldpeaks(3.5%MR)indicatingthatthesmallamountofinsulatingphasepresentbetweenthegrowingferromagneticregionactsasatunnelbarrier.ItisusefultocompareregionsofalternatingAFIandFMMphasealongthelengthofthenarrowbridgestomicroscopicanalogsoftheinsulatingandFMMmultilayers.Justastunneling-magnetoresistance(TMR)isobservedinsuchfabricatedspin-polarizedtunneljunctions[ 39 ],tworesistancestatesareseenforeldsweepsthroughzeroineachdirection:ahighresistancestateforantiparallelspinalignment("#)andalowresistancestateforparallelalignment("").Asnotedinprevioustheoreticalworks[ 48 79

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],TMRacrosscoexistingAFIandFMMregionsinphaseseparatedmanganitesmayhelpexplainsomeoftheobservedtransportpropertiesofbulkcrystals.Forinstance,thesmallloweld'notches'inR(H)forunpatternedthinlmswithinthedynamicphaseseparatedtemperaturerange(seeFigure 3-6 )maybeamanifestationofTMRbetweenferromagneticregionsseparatedbyAFItunnelbarriers. TheevolutionofTMRacrossthephaseseparatedregionsisbetterunderstoodbystudyingR(Hy)isothermsobtainedbelowTIM.ThemainpanelofFigure 3-7 showstheevolutionofthelow-eldTMRdemonstratingspin-dependenttunnelcouplingofadjacentFMMdomainswithloweringtemperature.ForthecoolingrunshownintheinsetofFigure 3-7 ,TMRremainedat10%for48K
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FortemperaturesaboveTBandbelowTIM,metamagnetictransitionsofthe0.6mwidebridge(SampleS2cintabel 2-1 )terminateinapredominantlylow-resistanceferromagneticmetal(FMM)statethatexhibitstunnelingmagnetoresistance(TMR).(a)Metamagnetictransitionat57KofaZFCsampleshowingapronouncedresistancedropatHz=6kOeandsubsequententranceintoalow-resistancephasethatisstablewithrespecttorepeatedeldsweepsbetween20kOe.TheinsetdepictsschematicallythecoalescenceofFMM(white)regionsattheexpenseofinsulating(black)regionswithappliedeldsorloweringtemperatures,witharectangularoverlaydepictingthe0.6mbridge.(b)MagnicationoftheTMRregion. 81

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2-1 )at50Kshowslow-eld`notches'.Thisfeaturemayresultfromadistributionoftunnelingmagnetoresistanceacrosstheinsulatingandmetallicregionswithinthephaseseparatedsample. stateconsistsofthininsulatingAFIregionsthatarestabilizedattheferromagneticdomainboundary,aphenomenonrelatedtothereduceddimensionsofthesample.Uponapplicationofaeld,theinsulatingstripedomainwalls,whichactliketunneljunctionsandcomprisetheremainingAFIphase,areextinguishedasspinsinneighboringdomainsalignresultinginsharpresistancedropsandauniformferromagneticregionspanningtheentirebridge.ThusTMR,whichrequiresstabletunneljunctionbarriers,isneverobservedwithinthistemperatureregion. 82

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Waterfallplotofrepeatedmagneticeldsweeps(sampleS2c,table 2-1 )inthetemperaturerange,TB
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84

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2 ),theintrinsicinsulatingregionsbecomethinenoughtoallowdirectelectrontunnelinginthesub-micrometerwideLPCMObridges.Tunnelingacrosstheseintrinsictunnelbarriers(ITBs)resultsinmetastable,temperature-independent,high-resistanceplateausoveralargerangeoftemperatures.UponapplicationofamagneticeldontheorderoftheLPCMOcoerciveeld,ourdatarevealthatthetunnelbarriersareextinguishedresultinginsharp,colossal,low-eldresistancedrops.Ourmagnetoresistanceresultscomparewelltotheoreticalpredictionsofmagneticdomainwallswhichcoincidewiththeintrinsicinsulating(AFI)phase,resultinginanovelkindofstripedomainwallwhichallowsdirectelectrontunneling. 1 ,inhole-dopedmanganitessuchasLPCMO[ 1 ],thebalancingofelectrostatic[ 51 ]andelastic[ 52 ]energiesinadditiontocompetingmagneticinteractionsmayleadtocoexistingregionsofferromagneticmetallic(FMM)andinsulatingphases[ 10 46 53 ].TheoreticalcalculationsbyD.I.Golosov[ 53 ]showthatuponreducingthedimensionsofsuchasystem,anincreaseintheeasy-axismagneticanisotropyandadecreaseinelectrostaticscreeningcancreateconditionswhichfavorphaseseparationattheferromagneticdomainboundariesresultinginnovelinsulatingstripedomainwallswhichallowdirectelectrontunneling[ 53 { 56 ].ThemanganiteLPCMOprovidesuniqueopportunitiesforexploringtheformationofsuchuniquedomainwallsdue 43 ]. 85

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46 52 ].Weusecurrent-voltage(IV)measurementstoshowinthischapterthatwhenLPCMOthinlmsarereducedindimensions(i.e.nanobridges),theydoindeedexhibittheclassicsignaturesofdi-rectelectrontunnelingacrossITBsseparatingadjacentFMMregions.Further,colossalloweldmagnetoresistance(MR)measurementssuggestthattheITBscoincidewithferromagneticdomainwalls,implyingthattheferromagneticdomainstructureinLPCMOismodied. 53 ].ThisresultsinanabruptchangeinmagnetizationbetweenneighboringFMMdomainsseparatedbyastripedomainwallincontrasttoclassicalferromagnetswherethedirectionofmagnetizationchangesovermlengthscalesnearadomainboundary[ 57 ].AccordingtoGolosov'stheory,in2Danupperlimittothelmthicknessforstripedomainwallformationensues.Although,narrowbridgegeometriessuchasourswerenotconsideredinGolosovscalculations,thecalculationscanbeextentedtoreducingdimensionsfrom2Dto1Dasinourbridgesandthushaveaneectsimilartoreducinga3Dbulksampletoa2Dthinlm.(Asdiscussedbelow,thismayexplainstripedomainwallformationwhenreducingourbridgesfrom2.5mto0.6mforthe30nmthicklms,eventhoughtheFMMstateinthe2.5mbridgesshowsnearlybulk-liketransportproperties.) 46 ](COI)andtheparamagnetic 86

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29 { 31 ].BelowTIM,LPCMOthinlmsgrownonNdGaO3areinapredominantlyferromagneticstate[ 25 ],butremainclosetoanenergeticallyfavorable,phaseseparatedstate.Thusasmallchangeinthedistributionofvariousenergyscalesinthesystem(i.e.electrostatic,magnetic)cantipthescalemakingphaseseparationenergeticallyfavorableagain.ChangingdimensionsasmentionedintheworkbyGolosovisjustonewaytoperturbsuchasystem.Additionally,aslightchangeinthechemistryanddopingofthe(La1yPry)0:67Ca0:33MnO3,(y=0.5)thinlmsusedinthisexperimentcandrasticallyalterthisphasecompetition[ 44 46 ].Finally,fromrecentliteratureweknowthatthenecessityofintrinsicphaseseparationforstripedomainwallformationisapparentwhenconsideringrecentmeasurementsofnotchedbridgesonnon-phaseseparatedLa0:67Sr0:33MnO3whichdidnotshowthepresenceofhighlyresistivedomainwalls[ 58 ]. 3 hasbeenusedforthemeasurementspresentedinthisChapter.Thoughothernarrowbridgesmeasuredhavesimilarproperties,thecriticaltemperaturesvaryfromsampletosample,thusmakingadirectcomparisonofthedatashowninthischaptertothatofotherchaptersnontrivial.Fordetailsonsamplefabricationandmeasurementtechniquesforthissection,pleaserefertoChapter 2 ,specicallySection 2.2 .TheappliedelddirectionsareshowinFigure 3-2 andinFigure 4-1 below.Thesampleidentities,aslistedinChapter 2 ,table 2-1 arenotedinthegurecaptions. 4-1 showsR(T)dataforalmpatternedintoabridgegeometryof2.5mwidth,whichisontheorderofindividualdomainlengthscales[ 10 46 ].Inthiscase,R(T)emulatesunpatternedthin-lmbehavior(grey)withtheexceptionofsmallstep-likefeatures[ 40 ]belowtheinsulator-to-metalpercolationtransitiontemperature,TIM=100K[ 59 ].However,asshowninChapter 3 ,whenthebridgewidthisreducedto0.6m, 87

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2-1 ),the2.5m8mbridge(black)orsampleS2bandthe0.6m8mbridge(green)orsampleS2crespectively.AFCcurveforthe0.6m8mbridge(blue)isalsoshown.Insulator-metaltransitions(TIM)forthetwobridgesareindicatedbytheverticalcolor-codeddashedlines.Lowerinset:schematicofthefour-terminalcongurationalongwiththeappliedelddirections.Upperinset:scanningelectronmicrographofthe0.6mwidebridge. 88

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3 [ 40 41 60 ]. 4-1 ceaseandanearlytemperature-independentresistanceinasupercooledstatedominates.ThoughmagnetizationmeasurementsonunpatternedepitaxialLPCMOthinlmsconrmafullyferromagneticmetallic(3:8B=Mn)statebelow50K[ 25 ],itispossiblethatthenarrowgeometryofthebridgefavorstheformationofaninsulatingstate.However,thetemperaturerangeofapproximately50KoverwhichthishighresistanceplateauoccurscannotbeexplainedbysuchascenariosinceanyhoppingtransportassociatedwiththeinsulatingCOIphaseinLPCMO[ 44 61 ]wouldshowapronouncedresistanceincreasewithdecreasingtemperature.Additionally,theresistance,R5108,ofthezero-eld-cooled(ZFC)temperatureindependentplateauisveordersofmagnitudelargerthanthequantumofresistanceh=2e2=12:9k.Bythescalingtheoryoflocalization[ 62 ]thelargeresistancevalueimpliesthatforalldimensions,theT=0statemustbeaninsulatorwithinniteresistance,contrarytoobservation(downto2K).Wethereforeconcludethattransportacrossthe0.6mwidebridgeistemperature-independentdirecttunnelingthroughITBscomprisingatomicallythininsulatingregions. 4-1 ).SimilarbutrelativelysmallandsmoothdropsinRareobservedinbulkandthin-lmLPCMOsamples,thoughthemechanismisunclear[ 10 ].TounderstandthisdropinresistanceuponFW,werecall 89

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10 44 ].However,belowTB40K,theblocking[ 44 ]orthesupercoolingglasstransition[ 45 60 ]temperature,thephaseseparatedregionsare`frozen'inplace[ 44 45 60 ].Thus,uponwarmingupagainintothedynamicstateaboveTB,thephaseseparatedregionsandthusthemetastableITBsarenolongerfrozeninspace,possiblygivingwaytoeld-enhancedFMMconversionofITBsresultinginacolossalresistancedrop. 4.5.1DirectTunnelingofElectronsacrossIntrinsicTunnelBarriers 4-1 )isduetoITBs,wemeasuredcurrent-voltage(I-V)curvesat5K,10K,and15KasshowninFigure 4-2 .BynumericallydierentiatingtheI-Vcurveat15K,thedierentialconductance(dI/dV-V)curveshowninFigure 4-3 isobtained.AssumingoneITBinthebridge,thesolidredcurvewasttedtothedatausingtheequation,dI/dV=+3V2,giving=9.8(1)109Sand=1.0(1)106S/V2.UsingSimmons'model[ 63 ]andthevaluesforand,wecalculatetheaveragebarrierheight 64 65 ].UnlikeGBshowever,ITBsaremetastableanduponapplicationofaeld,bulkvaluesarerecoveredinthebridge,conrmingtheabsenceofGBsinourstructure.ThissimilarityinresultsmayimplythatathinregionoftheinsulatingphaseformsattheGBwhichallowselectrontunneling. 4-2 couldalsobeduetocurrent-inducedJouleheating,whichforLPCMOcanbeconfusedwithmeltingofthechargeorderedstate[ 66 ].Thusif,at5Kanincreaseinthecurrentowingthroughthesampleraisesthetemperatureofthesampletosay15Kandatthesametimegivesrisetothe 90

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2-1 )atthethreeindicatedtemperaturesallmeasuredduringonecoolingcycle. observednonlinearity,thenthedataat15Kwheretheheatingeectforthesamecurrentwouldpresumablybelessshouldexhibitadierentnonlinearity.Theoverlapping(temperature-independent)IVcurvesshowninFigure 4-2 conrmthatthisisnotthecase. AdditionalevidencesupportingtheabsenceofJouleheatingisshowninFigure 4-4 ,showingplotsofthetemperature-dependentresistancetakenattheindicatedcurrents.InagreementwiththepositivecurvatureoftheIVcurvesofFigure 4-2 ,theresistancedecreaseswithincreasingappliedcurrent.Moreimportantly,TIMincreaseswithincreasingappliedcurrent,incontrasttothebehaviorfoundbySacanelletal.whereadecrease 91

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dI/dV-Vcurveat15Kwithat(redcurve)totheSimmons'modelforarectangularbarrierforsampleS2a(table 2-1 ). inTIMwithincreasingappliedcurrentisattributedtoJouleheating[ 66 ].Theoveralldecreaseinresistancewithincreasingappliedcurrentmayresultfromanelectric-elddriveninsulatortometaltransition[ 67 ]orincreasedferromagnetismresultingfromspinpolarizedtransport[ 68 ]amongotherscenarios[ 25 66 69 ].Thiseectinmanganites,whichwillbediscussedinChapter 5 ,explainsthedierenceintheresistancevaluesinFigure 4-2 mainpanelandtheinset.Forinstance,IVcurvesweremeasuredatxedtemperaturesintherange45Kto5Kusingappliedcurrentsupto1nA,thusdrivingthesampleintothe1nAcurrent-cooledstateshowninFigure 4-4 .Ontheotherhand,asamplecooledto15Katzeroappliedcurrenthasanirreversibleresistancechange(seeforexample,Figure 5-2 )uponmeasuringtheinitialIVcurveasseeninunpatternedthinlmsofLPCMO[ 25 ]anddiscussedinChapter 5 forthebridges.SubsequentIV

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2-1 ).TheresistanceclearlydecreaseswithincreasingappliedcurrentwhileTIMincreaseswithincreasingappliedcurrent.ThisisincontrasttothebehaviorfoundbySacanelletal.whereadecreaseinTIMwithincreasingappliedcurrentisattributedtoJouleheating[ 66 ] measurementsrevealreproducibleandreversiblemeasurementsalongthelowerresistancepath(notshown)[ 25 ]. 4.2.1 ,themagneticeldrequiredforthecollapseoftheITBwillcoupletotheintrinsicmagneticanisotropyofthethinlm.SensitivityofITBstomagneticelddirectionisveried 93

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ZFCandFCresistancetransitionsarelabeledbytheelddirectionsdenedwithrespecttobridge(or,sampleS2a(table 2-1 ))orientationinFig 4-1 .Inset:Rmeasuredat5Kwhenthebridgeiscooledinseparaterunsattheindicatedelds. inFigure 4-5 withasubsetofthemeasuredeld-cooledR(T)tracesforthethreeeldorientations(Hx,HyandHz)illustratedschematicallyinFigure 4-1 .Theinsethighlightsthecoolingelddirectionaldependenceat5K.Here,afteraresistanceof107isreached,coolinginaslightlyhighereldresultsinanabrupthundredfolddropinresistance,suggestingarapidandsuddendisappearanceoftheITB.Clearly,thein-planeeldsHxandHyaremoreeectivethanHzincouplingtothemagnetizationtoreachthelowresistanceFMMstate(R<105).Theseobservationsofanisotropiceld-inducedITBextinctionshowacouplingoftheITBswiththemagneticeasyaxiswhichlieswithinthe 94

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1 ].Themagneticeldvaluesrequiredtoreachthelowresistancestateareontheorderof1kOe,whichthoughmuchgreaterthanthemeasuredcoerciveeldinunpatternedlms,arenotatypicalfornarrowferromagneticwires[ 70 ].TheanisotropicMRassociatedwiththeITBsthussuggeststhattheymayindeedcoincidewiththeFMMdomainboundariesforminginsulatingstripedomainwalls.Thenecessityofintrinsicphaseseparationforstripedomainwallformationisapparentwhenconsideringrecentmeasurementsofnotchedbridgesonnon-phaseseparatedLa0:67Sr0:33MnO3whichdidnotshowthepresenceofhighlyresistiveITBs[ 58 ]. Figure4-6. 2-1 )zero-eld-cooledto15K,measuredattheindicatedvaluesofHz 95

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4-6 forsampleS2a(table 2-1 )normalizedtothevoltage,Vmax,measuredatmaximumappliedcurrent.Thelegendshown(lowerright)inFigure 4-6 applies. walls.ThisnotionisconrmedinFigure 4-6 wherethemagneticelddependenceoftheI-Vcurvesobtainedat15Kisshown.AsHzincreases,thecurvatureoftheI-Vcurveschanges(Figure 4-7 ).Foreldssucientlylargeenoughtodrivethebridgeintoalowresistancestate(9kOeinFigure 4-5 ),theI-Vcurvesbecomelinear(Figure 4-7 )suggestingITBextinction. 4.7.1Competingphasesandstrainsensitivityin(La,Pr,Ca)MnO3 1 ,singlecrystalsofthemanganiteLPCMO,whichareparamagneticinsulatorswithapseudo-cubicstructureatroomtemperature,undergoasuddenmartensitic-typestructuraltransitionwithintheparamagneticinsulating(PMI)backgroundtoanantiferromagneticcharge-orderedinsulating(COI) 96

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29 44 46 ].TheCOIphaseremainsnearlyconstantinvolumefractiondowntolowtemperaturesandanadditionalinsulatingphase,oftenreferredtoasthecharge-disorderedinsulating(CDI)phaseisalsopresentinbulksinglecrystalsbelowTCO[ 29 { 31 ].AsimilarCOI-CDI-FMMphasecompetitionisexpectedinthethinlms,althoughsubstratestrainwhichmodiesthemanganitestructure,canalsomodifythephasefraction.TheCDIregions(whicharestructurallysimilartoandthuspossiblyaremnantofthepseudo-cubicparamagneticphase)become,incontrasttotheCOIphase,predominantlyferromagneticuponloweringtemperature.MagnetizationmeasurementsofLPCMOthinlmsconrmanearlyfullyFMMstateforTlessthantheblockingtemperature,TB[ 25 ].TheremainingCDIphasewhichcoexistswiththeFMMandCOIphasesissometimesattributedtoaccommodationstrain[ 31 ]resultingfromstructuraldierencesbetweentheCOIandFMMphases. Inadditiontoaccommodationstrainresultingfromintrinsicstructuraldistortions,thephasetransitionsintheLPCMOthinlmsdepositedonNGO(110)substratesstudiedherearealsosensitivetostrainresultingfromaslightlatticemismatchwiththesubstrate[ 71 ].Thein-planelatticeconstantsofNGO(110)favorthepseudo-cubicFMMandparamagneticphasesinLPCMO.ThuswesuspectthattheCOIphaseiseitherdestabilizedresultinginareducedvolumefractionandincreasedsensitivitytoappliedelds,or,completelydisfavoredinthe300A-thicklmsonNGOassuggestedbythelackofanyhystereticfeaturesinR(T)typicaloftheCOIphasenearTCO(typically200K)butratherasmoothincreasedowntoTIMasseeninourexperiment(Figure 4-1 ). 72 ].Inourbridgeswesuspectthatitisthestructuralstrainresultingfrommisalignedspinsin 97

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4-1 ),coupledwiththenarrowdimensionsofourstructures,whichmakesinsulatingstripedomainwallformationenergeticallyfavorable[ 53 ].AsignicantfeatureofthebridgetransportpropertiesisthatthetemperaturedependenceofresistancebelowTIMvariesforeachcoolingcycle(e.g.Figure 4-1 andFigure 4-2 showtwodierentzeroeldcoolingcycles).ThisvariationlendsfurthersupporttothenotionthatITBsformduetointrinsicstrainaccommodationratherthanlocaldefects.Hence,wesuspectthatthestrain-inducedCDIphaseplaysavitalroleintheformationofITBs. Figure4-8. PossiblemechanismsfortheformationofinsulatingdomainwallsinLPCMOthin-lmbridges.(a)Inthe2.5mwidebridgetheedgeshavenegligiblecontributiontotheresistivityofthebridgeduetotheformationofawideandcontinuousFMMregionatlowtemperaturesandhencetheresistivityofthewireisthesameastheunpatternedthinlm.(b)and(c)Inthe0.6mwidebridgetheedgesstabilizetheCDIandCOIphasesattheexpenseoftheFMMphase.InsulatingdomainwallsspanningthewidthofthebridgeareformedeitherduetothestrainstabilizedCDIphaseasshownin(b)oracombinationofCDIandCOIphasesasshownin(c). 98

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4-8 .InbothcasesweshowtheCOIphaseformingatthebridgeedgessinceithasbeenshowntheoreticallythatananti-ferromagneticinsulatingphaseisfavoredatthesurfacesofFMMmanganites[ 73 ].Alsoinbothcases,wedepictthestrain-inducedCDIphaseformingattheinterfacebetweentheFMMandCOIphases[ 29 ].IntherstscenariotheITBscomprisingtheCDIphaseresultfromstrainbetweentwoFMMregionswithmisalignedmagnetizations,whileinthesecondscenariotheCOIphasespansthebridgewidthandtheITBscomprisebothCOIandCDIphases.Ourexperimentscannotdistinguishbetweenthesetwoscenarios.ItispossiblethatsimilarmechanismsarepresentingranularLPCMOsampleswhere,reducingthegrainsizealsoleadstometastablestates[ 29 ],asnotedinSection4.5.1. 47 ],itispossiblethatthisadditionalinsulatingphaseisasmallamountofremnantCOIpresentwithinthebridge(panel(a)ofFigure 4-9 ).However,asecondpossibilityremains:asmallamountofCDIphaseundergoesametamagnetictransitiontoanFMMphaseastheeldisturnedonandthenrevertsbacktotheCDIstatewhentheeldisturnedoandthustheTMRisactuallyacrossthisremainingCDIregion(panel(b)ofFigure 4-9 ).ThelatterscenarioprovidesaplausibleexplanationforthelackofTMRbelowTB(Figure 3-7 )becausetheCDIphasedoesnotrecoverbelowTBwhentheeldisturnedoandthusthebridgestaysmetallic.Whenconsideringtheformerscenariohowever,itisalsopossiblethatbelowTBtheCOIphaseisnolongerfavoredduetosubstrateinducedstrain.Hence,applicationofa20kOeeldresultsinametallicstatewithnoremnantCOIphase,resultinginthelackofTMR. 99

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PossiblemechanismsfortheformationofintrinsictunneljunctionsinthetemperaturerangeTB
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2-1 ).Allbridgesfabricatedfrom10nmthicklmsshowedthesameproperties.Metastablestateswithhighsensitivitytoappliedeldscanbeseenatlowtemperatures,reminiscentofthe0.6mwidebridgeona30nmthicklm(seeFigure 4-1 ). 0.6mbridgesfabricatedfrom30nmthicklms.Figure 4-10 showslowtemperature,temperatureindependenthighresistancestatesseeninthe30nmthick,0.6mwidebridge.ThedependenceofITBformationondimensionalityiscurrentlyasubjectofinvestigation. 53 ].MagnetotransportstudiesofLPCMObridgestructures 101

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102

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1 ].Unlikewithamagneticeldhowever,anelectricelddoesnotproducemeasurablechangesinthemetallicphasefraction.Thereisthusspeculationaroundseveraldierentscenariosthatcouldpotentiallyproducecolossalchangesinresistancewithoutchangingthemagneticphasefraction.Scenariosrangefromjouleheating[ 74 ],adielectricbreakdownoftheinsulatingregions[ 75 ],achangeinshapeofthemetallicregions[ 76 ]orachangeinmagnetizationbetweenneighboringdomainsasaresultofdoubleexchange[ 1 ].Asinthepreviouschapters,herewestudytheelectroresistanceeectonthemicroscopiclevelinthephaseseparatedmanganiteLPCMOinanattempttocapturethephysicsandpinpointthescenarioorscenariosresponsiblefortheobservedbehaviorinunpatternedthinlmsandbulksamples. 1 ).AsdiscussedinChapters 3 and 4 ,whentheLPCMOthinlmsarepatternedintonarrownanometerwidebridges,duringthephaseseparationtemperaturerangealternatinginsulatingandmetallicregionscanformacrossthelengthofthebridge.Inbothchaptersweshowedveryclearevidenceofdirectelectrontunnelingbetweentwometallicregionsspanningthebridgewidthseparatedbyintrinsicinsulatingregions.InChapter 4 ,assumingarectangularbarrier,wewereabletoextractabarrierheightand 103

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2 ,Section 2.2 andalsotoChapter 3 .Inthischapterdataispresentedontwobridges:(i)SampleS2c(table 2-1 ),thesame0.6mwide,8.0mlongbridgediscussedinChapters 3 and 4 ,and(ii)SampleS4(table 2-1 ),a0.34mwide,4.0mlongbridgenotpreviouslydiscussed. 1 77 ]. ThesecondtypeofCEReectisanintrinsicelectroresistancethatresultsfromanelectriceldorcurrentapplieddirectlyacrossthemanganitesample.Inthiscase 104

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78 ].Withinacertaintemperaturerange,anappliedelectriceldinducesahystereticrstordertransitiontoalowresistancestate.Itisnotcompletelyclearweatherthecollapseisinducedbyanelectriceldoranelectriccurrentthoughrecentdata[ 79 ]pointtotheformerscenario.LikeLPCMO,PCMOisalsoinsomecontextsconsideredtobephaseseparatedbutrequiresexternalperturbationsinadditiontotemperature(suchaselectricormagneticelds)toundergoaninsulatortometaltransition.PCMOisphaseseparatedintochargeandorbitalorderedP21nmregionsanddisorderedPnmaregions.Inthelattercase,polaronmobilityissignicantlyincreasedsincechargecarriersforma`liquid'orinteractingmobilepolarons.Withoutelectricormagneticeldapplication,transportmeasurementsrevealsmallpolaronhoppingconductioninPCMOdowntolowtemperatures[ 26 79 ].Ifasucientlyhighcurrentisappliedacrossthesample,transportmeasurementsrevealthatchargecarrierstransitiontolargepolaronhopping.Transportmeasurementssuggestacombinationofenhanceddoubleexchangeandanorder-disordertransitionassociatedwiththeCEReect[ 26 ]. ChemicallydopingthePCMOsampleswithLagivesLPCMOasdiscussedinChapter 1 ,andinducesaphasetransitionfromanominallychargeorderedstateatroomtemperaturetoadisorderedferromagneticmetallicstateatlowtemperatures.Thetransitiontemperaturesdependontheexactstoichiometryofthesample.AlthoughtherootcauseoftheCEReecthasnotbeenstudiedinLPCMO,inanalogytotheCEReectinPCMOdescribedabove,onemaysuspectameltingofthechargeorderedstate 105

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5.4.2 asummaryoftheformerscenarioandotherproposedideasontheoriginofCERinphaseseparatedmanganitesispresented.InSection 5.5 ourexplorationsoftheCEReectonthenanoscaleinLPCMOarepresentedandthebarrierparametersextractedfromourdataarecomparedtovaluesobtainedfromtheliterature. 26 79 ],(ii)jouleheating[ 74 ],(iii)lamentaryconductionordielectricbreakdownoftheinsulatingregions[ 75 ],(iv)dielectrophoresismodelorspacialreorientationoftheinsulatingandmetallicphase[ 76 ],or,(v)spindependentdomainreorientation[ 1 ]. InthecaseofLPCMO,anelectriceldinducedcollapseofthechargeorderedphaseinfavorofthedisorderedferrmomagneticmetallicphasewouldimplyanincreaseoftheferromagneticphasefractionwithinthelmorbulksample.Thisinturnwouldimplyahighersaturationmagnetizationofthethinlmwhichiscontrarytoobservation[ 25 75 ].Inthesecondjouleheatingscenario,thetemperatureofsampleincreasesduetolargecurrentdensities,changingtheeectivephasefractions.Inthiscase,theapparenttemperatureofthesampleasreadbyathermostatinthevicinityofthesampleisdierentthantheactualtemperature.Foroursamples,wehaveruledoutjouleheatingasdescribedindetailinSection 4.5.2 .Below,inSection( 5.5 ),ourtunnelingmeasurementsrevealthatthethirdscenarioabove(lamentaryconduction)canberuledoutwhilethedielectrophoresismodelmayindeedhelpexplaintheCEReectobservedinournanobridgesandthusperhapsalsoinphaseseparatedmanganites.Asalsodiscussedbelow,wecannothoweverruleoutthefthandnalscenarioofspindependentdomainreorientationswhichmayresultfromanenhanceddoubleexchangemechanisminducedbyhighercurrentdensities. 106

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25 ].Subsequently,thinlmspreparedidenticaltothisCERstudywerepatternedintonanometerwidebridgespresentedbelow.Itwasfoundthatwithinthephaseseparationtemperaturerangetheapplicationofanelectriceldresultedinanirreversiblechangetoalowerresistancestate.Despitethechangeinresistance,magnetizationmeasurementsdidnotrevealanincreaseintheferromagneticmetallicphasefractionwithinthelms.Thetransitiontoalowerresistancestateissmoothinthinlms,thoughwithawelldenedcriticalvoltage(orcurrent)asshowninFigure 5-1 .Current-voltage(IV)characteristicsforthis10mwideLPCMOlmrevealacleartransitiontoalowerresistancestateuponincreasingcurrent.TherelativeconcentrationsoftheLaandPrwerevariedtochangetherangeofphaseseparationtemperaturesanditwasfoundthatregardlessofthetemperaturewindow,theeectremainedthesameinalllmswithinthephaseseparationrange. Areversible,colossalCEReecthasbeenreportedinLPCMOlmswithFesubstitutionsattheMnsite[ 80 ].ThemechanismsfortheCEReectintheFedopedlmscomparedtoundopedLPCMOmaynotbewhollydierent.InundopedLPCMO,thechargeorderedphaseandtheferromagneticmetallicphaseareverycloseinfreeenergythoughwithloweringtemperature,themetallicphasehasanincreasinglylowerfreeenergy.ThisenergylandscapeiscertainlyalteredinthecaseofFedopedLPCMO.Inthiscasethemetallicphasemaynotbepreferredovertheinsulatingphase,justasinPCMOthinlms[ 26 ]. InthebridgesfabricatedfromLPCMOthinlms,theCEReectisevidentwhenmeasuringR(T)atdierentappliedcurrentsasshowninFigure 5-1 .TheseveralorderofmagnitudechangeinthelowtemperatureresistancewithappliedelectriceldcanwellbedescribedintheintrinsictunnelingframeworkdiscussedinChapter 4 107

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5.3 .ThetwobridgeswillbelabeledS0:6mandS0:34mforthe0:6mx8:0m(sampleS2c)and0:34mx4:0m(sampleS4)bridgesrespectively.NotethatS0:6mistwiceaslongasS0:34mwhichgivesrisetoanincreasedoverall 108

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sampleresistanceandthepossibilityofalargernumberofinsulatingandmetallicregionsspanningthebridgewidth. Figure 5-2 showsIVcharacteristicsat50KforS0:6mafterthesamplewascooledinazeroappliedcurrent(zeroappliedelectriceld).Notethatthiszero-electric-eld-cooling(ZFEC)conditionresultsindierentIVcharacteristicsasthosepresentedinSection 4.5.1 wherethesamplewascooledina1nAcurrentpriortomeasuringtheIVcharacteristics.Thusthesamplewasalreadyinalowresistancestateprior 109

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5-2 .Onceagain,clearstep-liketransitiontoalowresistancestatewithincreasingappliedcurrentsarevisible. themeasurementandthestepliketransitiontoalowresistancestateisnotvisible.InFigure 5-2 thebluecurvewasmeasuredatzeroappliedmagneticeld.Heresharpstep-liketransitionstoalowresistancestateareapparent.TheresistanceofthesamplecanalsobereducedwithanappliedmagneticeldasisapparentfromtheredcurveinFigure 5-2 .Acurrentinducedtransitiontoalowresistancestate,superimposedonthemagneticeldeectcanbeseen.Aeldof2T(inset)clearlyinducesaninsulatortometaltransitionacrosstheentirelengthofthebridge,thusgivingrisetoametallic,linearIVcurve. 110

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5-3 showsIVcurvesforS0:34mafter(ZFEC)to85K.ItisevidentfromcomparingthequalityofdataforS0:34mvs.S0:6mthatthedatafortheformerismoreappropriateforpurposesofanalysisgiventhefargreatersignaltonoiseratio.ThisfactisprobablyrelatedtothefactthatS0:6mistwiceaslonginlengthasS0:34mandthuscontainsperhapsonlyone,butcertainlyfewerinsulatingregionsalongthelengthofthebridge.S0:6mhowevershowsamuchmoredramaticCEReect.Inthisgure,theverticallylowerarrowforincreasingcurrent(increasingvoltage)showstherstlegofthecurveandatransitiontoalowerstateisveryclear.Beyondthersttransition,smallspikestoanevenlowerresistancestate(seetopleftquadrant,Figure 5-4 B)arevisiblethoughthesampledoesnotmakeacompletetransitiontothatlowerstate. B EachbranchofthetheZFECIVcurveforthe0.34mwidebridgeshowninFigure 5-3 wasrstdierentiatedandthederivativewasttothequadraticSimmons'model.A.showsthedI/dVvs.Vplotforthecenter(red)numericallygeneratedtshowninB.B.showsnumericaltsusingtheSimmons'modeltoeachbranchoftheIVcurveobtainedat85Kforzeroappliedmagneticeldandcooledinzeroappliedelectriceld. ToanalyzethedatashowninFigure 5-3 ,eachsegmentoftheIVcurvewasdierentiatednumericallywithrespecttovoltageandttotheSimmons'model(seeSection 4.5.1 fordetails)withthebarrierheightandwidthsetasfreeparameters.ExcellenttstotheSimmons'model(dI=dVV2)wereobtainedforvoltagesbelow 111

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5-4 AshowsadI=dVcurveandquadraticttotheSimmons'modelforthecentralbranchoftheIVcurveshowninFigure 5-3 .Figure 5-4 BshowsthesimulatedIVcurvesforeachbranchoftheoriginal(ZFEC).NotethatthesimulatedIVcurveresultingfromthebottombranchofthebottomleft(third)quadrantdepictsastatethatwelldescribesthebriefdropsinresistance(orspikes)intherstquadrantsincetheyfallapproximatelyontheyellowcurve.ThebarrierheightsandwidthsderivedfromeachtarelabeledinthelegendofFigure 5-4 Bandarediscussedindetailinthenextsection. BarrierheightsandwidthsobtainedusingtheSimmons'modelforthe0.34mwidebridgeasafunctionofthecriticalelectriccurrentduringtheinitialincreaseofappliedcurrent(i.e.,rstquadrant|topright|bottomIVcurvebranch. Figure 5-5 showsaplotofbarrierheightandwidthasafunctionsofthecriticalcurrentrequiredtogotoeachstatealongtherstquarteroftheIVcurve(bottomcurve,rstquadrant)showninFigures 5-3 and 5-4 .Firstwenotethatthebarrierheights,whichareontheorder0.1eVareontheorderofthepolaronichoppingactivationenergyreportedintheparentcompoundPCMO[ 26 79 ]andalsofromourowncomplexanalysisoftheLPCMOdielectricproperties(unpublishedwork).Contrarytoexpectations,thebarrierheightappearstoincreasebyapproximately44%whilethebarrierwidthdecreasesbynearly18%.Intuitivelyandgiventhedecreasingresistance, 112

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WiththettothesimplerectangulartunnelbarrierusingSimmons'modelasarstorderapproximation,thedielectrophoresismodelmaybeinvokedforaconsistentexplanation.Inthiscase,priortoapplicationofanelectriceldorcurrentthenaturallyformedintrinsicinsulatingregionscanbeapproximatedas`imperfect',containingsmalldefectscentersintheformofferromagneticislandsorsmallmagneticpolarons.Uponapplicationofanelectriceldthesmallferromagneticregionsorpolaronicdropletswithintheinsulatingregionsmovetowardthemetallicregionsandcoalesce.Inthisway,thevolumeofneitherphasefractionincreasesbutratheritreordersspatially.Inthisway,theinsulatingregionscontainlessco-tunnelingorpinningcentersandincreaseinqualityandthusbarrierheightwhilethemetallicregionsarenowseparatedbyathinnerbarrierandarethusmorecloselyspaced.Thusqualitatively,thedielectrophoresismodelmayindeedcapturethedynamicsoftheCEReect. 4-6 forsampleS0:6mwerealsottotheSimmons'modelasshowninFigure 5-6 .Giventherelativenoiselevelforthissample,thebarrierheightsextractedfromthetstotheSimmons'modelwereontheorderoftheenergygapofPCMO,thoughratherhigh.Thismaybeduetothepresenceofseveraltunnelbarriersinseries,giventherelativelylongerlengthofthebridge. 113

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BarrierheightsandwidthsobtainedusingtheSimmons'modelforthe0.6mwidebridgeasafunctionoftheappliedmagneticeld. Again,withtheSimmons'modelasarstorderttoourIVcurves,aclearlydierenttrendinthebarrierwidthsandheightswithincreasingmagneticeldsisevidentthanfortheCEReect.Here,withincreasingappliedeld,thereisaclearreductionofthebarrierheights(86%)whilethebarrierwidthremainsrelativelyconstantwithasmallincreaseofapproximately16%.Thisdecreaseinbarrierheightcanbeunderstoodintermsofspincantingoftheantiferromagneticallyorderedinsulatingbarrierspinsinthedirectionoftheappliedmagneticeld.Thespincantingincreaseswithincreasingmagneticeldandthebarrierwidthreducesforthetunnelingelectronswhicharealsoorientedinthedirectionoftheeld.Thebarrierwidthhoweverremainsnearlythesameindicatingasuddencollapseoftheinsulatingbarrieratawelldenedcriticaleldratherthanagradualdecreaseinwidthwithincreasingferromagneticphasefraction. 1 ].Todepictsuchbarrierpropertiesmorerealistically,wearecurrentlyemployingamethodwhichmodelsthetunnelbarrierasadoublebarrier 114

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81 ].Theauthorsofthistechniquewereabletodeduceamildcorrelationintheirbarrierheightsandwidthsbyutilizingthistechnique.Asecondtechniquerequiresobtainingrmsroughnessvaluesoftheinterfaceandincorporatingtheroughnessaschangingbarrierwidthsofrectangularbarriers(approximatedasagaussiandistribution)withintheSimmons'model[ 82 ].Bothmodelsarepresentlybeingtestedfortheireectiveness.Thecurrentanalysisisaworkinprogress. 115

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6-1 and 2-12 ).Undercertainexperimentalconditionsthisunconventionalcongurationallowsforthesimultaneousmeasurementofelectricaltransportbothparallelandperpendiculartothelminterfaces.Althoughthefour-terminalVanderPauwmeasurementoftheLPMCOlmsprovidesunambiguousinformationabouttransportparalleltothelminterfaces,thetwo-terminalcapacitancemeasurementismoreproblematicsinceitincludescontributionsfrombothparallelandperpendiculartransport. Byusingcomplexcircuitanalysis,weshowthatthetwo-terminalperpendicularcontributiontoelectronictransportcandominateovertheparallelcontributionprovidedcertainexperimentalconstraintsaresatised.Whentheseconditionsaresatised,weshowusingthewell-knownMaxwell-Wagnermodelthattheperpendicularcontributionisresolvedintotwoseries-connectedparts:acontributionfromthereferenceAlOxcapacitorandacontributionfromtheintrinsicdielectricresponseoftheLPCMOlm.Wethenshowwithadditionaldataonlmsofdierentthicknesshowthesubstratestrain-inducedanisotropy,measuredbythedierenceintemperaturebetweentheresistancemaximaandcapacitanceminimadecreasesandapproachesbulklikebehaviorasthelmthicknessincreases. 59 ] 116

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83 { 88 ]havethesamebehavioroverawiderangeoftemporalandspatialscales.Atlowfrequency,correspondingtolonglengthscales,thevolumeofthephasediagramcollapsestoapointdeningthezero-eldIMpercolationtransitionintheperpendiculardirection.Thismethodthusalsoallowsforanovelprobeofphaseboundariesinthinlms,wheretheboundariesmaynotbestraightforwardtodetectwithdctransportmeasurements. 1 .Thedctransportmeasurementspresentedintheprecedingchapters(whichareanalogoustothoseperformedonthenarrowbridgespresentedinthiswork)arenotsensitivetoexactphasefractionsandthedielectricpropertiesoftheinsulatingphases.Inaddition,thedctransportmeasurementscannotdistinguishbetweentwodierentinsulatingphaseswhichwouldresultinthesamehoppingtransporttemperaturedependence.Acmeasurementtechniquesontheotherhandcandistinguishbetweendierentdielectricconstantsandphasefractionsusingcomplexanalysis.InthischapterweprobephaseseparationinLPCMOthinlmsbyanalyzingthedielectricresponseofthethinlmsembeddedinanunconventionalgeometryasdescribedinSection 2.3 .ThinlmsofSCEMssuchasLPCMOareoftengrownepitaxiallyonplanarsubstratesandtypicallyhaveanisotropicpropertiesthatareusuallynotcapturedbyedge-mountedfour-terminalelectricalmeasurements,whichareprimarilysensitivetoin-planeconductionpaths.Accordingly,thecorrelatedinteractions 117

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2 .Fortheparticularcapacitorstructurestudiedinthischapter,theLPCMOthinlmwas600AthickwhiletheAlOxdielectricwas100Athick. AsdescribedinSection 2.5.3 ,thecapacitancemeasurements(Figure 6-1 ,red)weremadeusinganAndeen-HagerlingAH2700ACapacitanceBridgeinaguardedthree-terminalmodeatsteppedfrequenciesrangingfrom50-20,000Hz.TwooftheterminalswereconnectedtothesampleleadsshownschematicallyinFigure 6-1 andthethirdtoanelectricallyisolatedcoppercansurroundingthesampleandconnectedtothegroundofthebridgecircuit.Mostofthemeasurementsweremadeusing25mVrmsexcitation,andlinearitywasconrmedatalleldsandtemperatures.ThebridgewassettooutputdataintheparallelmodeinwhichthesampleisassumedtobethecircuitequivalentofacapacitanceCinparallelwitharesistanceR(seeSection 6.4 ). ContactstothesampleweremadetothebaseLPCMOlmusingpressedindiumandtotheAlcounterelectrodeusingnegoldwireheldinplacewithsilverpaint.Silverpaintwasalsooccasionallyusedtomakecontacttothebaseelectrodewithnoconsequencetothecapacitancedataatallmeasurementfrequencies.TheseriescombinationoftheLPCMOparallelresistancewiththeleakageresistanceoftheAlOxdielectricwasfoundtobeimmeasurablylargewithalowerbound>1010determinedbyreplacingthesample 118

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Parallel(resistance)andperpendicular(capacitance)transportmeasurementsaremadeonthesameLPCMOlm.a,CrosssectionalschematicviewofthetrilayercapacitorstructurecomprisingtheLPCMObaseelectrode,theAlOxdielectric,andtheAlcounterelectrode.b,SemilogarithmicplotsofthetemperaturedependentresistancesR#"jj(T)(black)andcapacitancesC#"?(T)(red)fordecreasing(#)andincreasing(")temperaturesatzeroeldobtainedonthesamestructure.ThethingreenlinesaretstotheMaxwell-Wagnermodel(seeSupplementary)whichincorporatesR#"jj(T)asaninputandthereforeproducescapacitanceminimaattemperaturescoincidentwiththeresistancemaxima.At50kOe(blue)thecapacitancehasincreasedfromthezeroeldminimabyafactorof1000.c,SchematicrepresentationoftheLPCMOlmusingdistributedcircuitelements.Straineectsgiverisetoaresistancegradientintheperpendiculardirectionrepresentedschematicallybyanunequalspacingofequipotentialsurfaces(dashedhorizontallines)superimposedonacolorgradient[ 59 ]. 119

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6-1 ). Thefour-terminalresistancemeasurementsofdctransportparalleltothelminterfaces(Figure 6-1 ,black)weremadeusingevenlyspacedVanderPauwcontacts(notshowninFigure 6-1 )directlyconnectedattheLPCMOlmedges.TocheckforanyfrequencydependenceintheparallelresistanceoftheLPCMOandassociatedcontactresistance,weperformedatwo-terminalacmeasurementbyapplyingasinusoidalvoltagetoallpairsoftheLPCMOcontactsandusedalock-inampliertosynchronouslydetecttheoutputofawidebandcurrentamplierthatprovidedareturnpathtogroundforthesamplecurrent.Thetwo-terminalresistancewasquitesimilartothefour-terminalmeasurement.Importantly,nofrequencydependenceintherange50-20,000Hzfortheresistancevaryingfrom1Kto20M(Figure 6-1 )wasdetected,thusassuringthatallthefrequencydependenceseeninthecapacitancemeasurementisduetoperpendicularratherthanparalleltransport.Inaddition,weestablishedinseparateexperimentsonsymmetricAl{AlOx{AlstructuresthatCAlOxhasnegligiblefrequencydispersionoverthesamefrequencyrange. 6-1 canhavebothparallelandperpendicularcontributionsfromcurrentsowingrespectivelyeitheralongtheLPCMOelectrodeortransversetothelmthroughthecapacitor.Sincethesecontributionscannotbedistinguishedinatwo-terminalmeasurement,itisnecessarywhenmeasuringcapacitancetoestablishconditionswheretheperpendicularvoltagedropdominatesovertheparallelvoltagedrop.Therearetwonecessaryrequirementstoassureadominantperpendicularvoltagedrop:(1)thedcleakagecurrentthroughtheAlOxdielectricisnegligibleand(2)themeasurementfrequencyisconstrainedtobewithinwelldenedupperandlowerboundsdeterminedbysampleproperties. 120

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6-1 ).Bylossycapacitancewemeanacapacitorthatdoesnotpassdccurrentbutdoesexperiencelossatacduetodipolereorientation.ThusthecombinationofC(!)shuntedbyR0isaleakycapacitorwhichdoespassdc.TheresistanceRSincludestheparallelresistanceRjjoftheLPCMOandanyresistanceassociatedwiththeLPCMOcontact.ThenegligibleresistanceoftheAlcounterelectrodeanditsassociatedcontactareincludedinRS. OurmeasurementsatdcestablishtheconditionsR0+RS>1010(Section 6.3 )andmaxfRSg=107(Figure 6-1 ),whichtogetherimplythatoverthewholerangeofdcmeasurementsmorethan99.9%ofthevoltageappearsacrossC.Attemperaturesawayfromtheresistancepeakthisgureofmeritimprovesconsiderably. Sincethecapacitancemeasurementsaremadeatnitefrequency,wemustconsiderthemorecomplicatedsituationofadditionalcurrentpathsandchooseconditionstoassurethatmostoftheacpotentialdropisacrossC(!).WedothisbyredrawingthecircuitofFigure 6-2 toincludetheaclossasaresistorR2(!)=1=!C2(!)(Figure 6-2 )whichdivergestoinnityatdc(!=0).TobesensitivetoLPCMOproperties,wedesiremostoftheaccurrenttoowthroughR2(!)andthereforechoosefrequenciestosatisfy therebydeterminingalowerboundon!. TheAHcapacitancebridgereportsthecapacitanceC0(!)andtheconductance1=R(!)oftheparallelequivalentcircuitshowninFigure 6-2 .UsingstraightforwardcircuitanalysiswerelatethemeasuredquantitiesC0(!)andR(!)tothecircuitparametersofFigure 6-2 bytheequations: 121

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Circuitdiagramsfacilitateunderstandingthesourcesoflongitudinalandperpendicularvoltagedrops.a,Circuitequivalentofthetwo-terminalmeasurementconguration(Figure 6-1 )whereRSistheseriesresistanceoftheLPCMOsampleandtheparallelcombinationofacomplex(lossy)capacitorC(!)witharesistorR0representstheimpedanceoftheLPCMOinserieswiththealuminumoxidecapacitor.Inthetwo-terminalconguration,thelongitudinalvoltagedropacrossRscannotbedistinguishedfromtheperpendicularvoltagedropacrosstheparallelcombinationofC(!)andR0.b,DecompositionofC(!)=C1(!)iC2(!)intoaparallelcombinationofC1(!)andR2(!)=1=!C2(!).c,CircuitequivalentforthecapacitanceC0(!)andconductance1=R(!)reportedbythecapacitancebridge.d,Maxwell-WagnercircuitequivalentfortheLPCMOimpedanceinserieswiththeAl/AlOxcapacitor.TheLPCMOmanganitelmimpedanceisrepresentedasalossycapacitorCM(!)shuntedbyaresistorRM.ThereisnoshuntingresistoracrossCAlOxbecausethemeasuredlowerboundonR0is10G,wellabovethehighestimpedanceoftheothercircuitelements. 122

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(R2(!)+RS)+(!R2(!)RSC1)2:(6{3) IfRSissmallenoughtosatisfytherelation thenequations 6{1 and 6{2 reducerespectivelytoC0(!)=C1(!)andR(!)=R2(!).Accordingly,thefulllmentoftheconstraintsimposedbyequations 6{1 and 6{4 assuresusthattheacdissipationisnotduetoleakageresistanceandthatthevoltagedropacrossRScanbeignored.Undertheseconditionsthemeasuredcomplexcapacitancehasreal,C0(!),andimaginary,C00(!)=1=!R(!),partsthatreectrespectivelythepolarizationandthedissipationplottedanddiscussedinSection 6.7 Theconstraintsofequations 6{1 and 6{4 nowbecome 1 wherewehavereplacedC1andC2bythemeasuredquantitiesC0andC00respectively.TheserelationsconvenientlyallowustoexperimentallydeterminetherangeoffrequenciesoverwhichRScanbesafelyignored,thusguaranteeingthattheequipotentialsatacareparalleltothelminterface(Figure 6-1 ).WeshowinFigure 6-3 theH=0temperaturedependenceoftheimpedancecomponents,1=!C0(!),1=!C00(!)measuredat500HzandRjjmeasuredatdc.ThecorrespondingtemperaturedependenceofC0(!)isshowninFigure 6-1 .Clearlytheconstraintsofequations 6{5 and 6{6 aresatised.Itisnotnecessarytoplotthethirdcomponentof 6{6 sinceC00(!)>C0(!)forallofourdataintheregionofcollapse(seeFigure 6-3 ).Wehaveveriedthattheconstraintsholdupto20kHzatallthetemperaturesandeldsusedtoconstructthephasediagraminFigure 6-8 .Forourlowestfrequencyofmeasurement(100Hz)wecalculateC00=0.16pFasalower 123

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Impedanceplotsverifythatthelongitudinalvoltagedropsarenegligiblecomparedtotheperpendicularvoltagedrops:TheH=0temperaturedependenceoftheimpedancecomponents1=!C0(!),1=!C00(!)measuredat500HzandRS=Rjjmeasuredatdc.Thehorizontaldashedlineat1010representsthelowerboundonR0.Comparisonoftherelativemagnitudesoftheseplotsshowsthatatalltemperaturestheconstraintsimposedbyequations 6{5 and 6{6 aresatised. 124

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6{5 cannotbesatised.Forallofourdata,C00(100Hz)ismorethanafactoroftenhigherandequation 6{5 isthussatisedforallofourlowfrequencydata. 6-2 .Theresultingexpression, revealsadielectricresponsedeterminedbytwotimeconstants,RMCAlOxandRMCM.As!increases,thecapacitancecrossesoverfrombeingdominatedbyCAlOxtoacapacitancedominatedbytheseriescombinationofCAlOxandCM.IfCMCAlOx,asitisovermuchofthedatarangeinFigure 6-1 andlikewiseforsimilardatatakeninhighmagneticelds,thenCinthehighfrequencylimitisequaltoCMandisthereforeadirectmeasureoftheLPCMOdielectricresponse.WetesttheselimitsinFigure 6-1 byevaluatingRefCMW(!)gat0.5kHz(greencurve)usingCM=CAlOx=104andRM=Rjj(T)#"(black)asinputs.CMisassumedtoberealforthiscalculation.TheMWmodelthusprovidesagoodqualitativeaccountofthetemperature-dependentcapacitance(Figure 6-1 ,greenline)forCMindependentoffrequencyandequalto104CAlOx.TheMWmodelalsoshowsgoodalignmentintemperaturebetweenthemaximumintheresistanceusedasaninputandthecalculatedcapacitanceminimum.Finally,wenotethatthelargeseries-connectedaluminumoxidecapacitorservesasareferencecapacitor,whichbyitspresencedecloaks 125

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6{6 isviolatedandRSbecomesvisible,introducinglongitudinalvoltagedropsthatcannotbedistinguishedfromtheperpendiculardrops. Inrealitythereisconsiderabledielectricloss,especiallyinthepresenceofmagneticeld,andCMisfrequencydependentandthereforecomplex.IfweforceCMintheMWcalculationtobecomplexwith,forexample,aDebyeresponse,thealignmentbetweentheresistancemaximumandthecapacitanceminimumdoesnotchange.TheCole-Coleplots(Figures 6-6 and 6-7 )aretheadditionalingredientsthatclearlycapturetheinterestingintrinsicdynamicsofscaleinvariantdielectricresponseassociatedwiththeinterplayofcompetingphasesasdiscussedinSection 6.7 Itisworthwhiletofurtherelaborateonintrinsicversusextrinsiceects.TheMWmodelisusuallyusedtoascertainthecontributionsofcontactsandinterfaceswhenthematerialofinterestissandwichedbetweentwoelectrodes[ 6 89 { 92 ].Incapacitorswiththickdielectrics,theinterfaceregionnexttoeitherelectrodecanhavedistinctlydierentpropertiesthantheinteriorbulk.SuchaheterogeneoussystemiswelldescribedintheMWmodelbytwoseries-connectedleakycapacitors.Ifoneoftheleakagecomponents,saytheinterface,ismagneticeldsensitiveandexhibitsmagnetoresistance(MR),thenthemeasuredmagnetocapacitance(MC)canbeaconsequenceoftheextrinsicpropertiesofaninterfacecontactratherthantheintrinsicpropertiesofthebulk.Intheunconventionalcongurationdescribedhere,theinterfacecontactisadispersionlessleak-freeAl{AlOxcapacitorasrepresentedschematicallyinFigure 6-1 ,andtheobservedMCisduetotheintrinsicpropertiesofthemixedphaseLPCMO.AnyinterfaceeectsbetweentheAlOxandtheLPCMOarenegligible,sincethefactorof1000changeincapacitance,whichincludestheregionwherepower-lawscalingcollapseisobserved,necessarilyinvolvestheentiremanganitelm.InadditionallextrinsiccontributionsfromcontactstotheLPCMOatthelmedges(Figure 6-1 )areincludedintheresistanceRS,whichaswehaveshownabove,canbeignoredwhenthefrequencyischosentosatisfytheinequalityofequation 126

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.Experimentally,thisinsensitivitywasfurthercheckedbyusingsilverpaintorpressedindiumforcontactsasdescribedinSection 6.3 Figure 6-4 showsthedependenceofT#"IM;jjandT#"IM;?ondforcoolingandwarmingaslabeledinthelegend.Forparalleltransporttheobservedincreaseoftransitiontemperaturescanbequalitativelyexplainedbytheeectofdimensionalityonpercolation.Sincepercolationin3Doccursatalowermetalfractionthanitdoesin2D,theIMtransitionincreaseswithincreasingdasisindeedobserved.ThisqualitativepictureiscomplicatedhoweverbythepresenceofastrainedlayeratthesubstrateinterfacewhichcontainsahigherfractionofFMMphase.Inthiscaseconductionintheparalleldirectionisfacilitatedbythepresenceofthehigherconductivitystrainedlayerwhereasintheperpendiculardirectionthecurrentpathsmustthreadregionscontainingagreaterproportionofinsulatingphase,hencethedierencebetweenT#"IM;jjandT#"IM;?.Thetemperaturedierences,T#"IM=T#"IM;jjT#"IM;?,forcoolingandwarmingareplottedversusdinFigure 6-5 .Wenotethattheanisotropydoesindeeddecreasewithincreasingd.ThusasdincreasestheIMtransitionmovestohighertemperatureandtransportbecomesmoreisotropicastheeectofthestrainedinterfacediminishes. Thelmsdiscussedabovewerepreparedfromthesametargetbutunderdierentconditionsthanthe600A-thicklmdiscussedinthischapter.Thedepositionconditions 127

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WithincreasingLPCMOthicknessdtheanisotropicIMtransitionsmovetohighertemperatures:Thetransitiontemperaturesassociatedwithresistancemaxima(squaresandcircles)andcapacitanceminima(triangles)areidentiedinthelegendandplottedasafunctionofdforcoolingandwarming.Thecapacitancedataforthethreedierentlmsaretakenat100Hzandsatisfytheimpedanceinequalitiesexpressedinequations 6{5 and 6{6 andshowninFigure 6-3 forthe600A-thicksample. (oxygenpressure=420mTorr,substratetemperature=820oC,depositionrate=0.5A/s)weredeterminedbyminimizingthetransitionwidthatanIMtransitiontemperature(T#IM;jj)thatisclosetothemaximumvalue(cooling)observedinbulkcompoundsofthesamecomposition.Thetargetwasthenconditionedwiththesamedepositionparametersformanyruns.Incomparingthetwo600A-thicklms,weseethatthetransitiontemperaturesT#IM;jj=117.7KandT"IM;jj=140.5Koftheoptimized600A-thicklmshowninFig. 6-4 areappreciablyhigherthanthecorrespondingtemperatures,T#IM;jj=95KandT"IM;jj=106K,ofthelmshowninFigure 6-1 .In 128

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WithincreasingLPCMOthicknesstheanisotropyasmeasuredbyT#"IM=T#"IM;jjT#"IM;?decreasestowardszeroandbulklikebehavior:ThedataforbothcoolingandwarmingcyclesateachthicknessareobtainedfromthedatashowninFigure 6-5 bysubtractingthetemperatureofthecapacitanceminimum(perpendiculartransition)fromthetemperatureoftheresistancemaximum.Theerrorbars,whichareontheorderofthesymbolsizeinFigure 6-5 ,aredeterminedbythetemperatureswhichgivea0.1%deviationateachextremum(resistancemaximumorcapacitanceminimum). addition,therespectiveanisotropiesforcooling(T#IM=1.5K)andwarming(T"IM=3.5K)oftheoptimized600A-thicklmaresignicantlysmallerthanthecorrespondinganisotropiesforcooling(T#IM=20K)andwarming(T"IM=15K)ofthesamethicknesslmshowninFigure 6-1 .TheseresultsshowthatourtechniquecanadvantageouslybeusedtocorrelateanisotropiesinLPCMOwithdepositionparameters.Weanticipatethatthiscapabilitywillbeapplicabletootherstrongly-correlatedcomplexoxidesystemsaswell. 129

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6-1 ,iscapturedinthetemperature-dependentcurvesshown.Thetwo-terminalC(T)measurementscorrespondtotherealpartC0(!)ofacomplexlossycapacitance,C(!)=C0(!)iC00(!),measuredatf=!=2=0:5kHz.AstemperatureTdecreasesfrom300K,theprevailinghightemperatureparamagneticinsulator(PI)phasegiveswaynearT=220K[ 87 ]toadominantCOIphase.MinorityphaseFMMdomainsappearandbegintoshortcircuittheresistanceriseasTcontinuestodecrease.AttheresistancepeaksthepercolativeIMtransitionfortransportintheparalleldirectionthroughFMMdomainsoccursattemperaturesT#IM;jj=95KandT"IM;jj=106Kwherethedown(#)/up(")arrowsindicatethecooling/warmingdirectionofthetemperaturesweep.BelowT#IM;jjtheFMMphaserapidlydominateswithdecreasingT,andRjjdecreasesbyfourordersofmagnitude. TheC(T)#"tracesreachplateausathighandlowtemperaturewheretheLPCMOisinitsrespectivePIandFMMstates,bothofwhichhavesucientlylowresistivitytoactasmetallicelectrodesinaMIMstructure.BetweentheCAlOx(T)plateaus,theC(T)#"tracesshowcapacitanceminima20Kbelowthecorrespondingresistancemaxima.AtperpendiculareldsH=50kOethecapacitance(bluecurve)hasincreasedbyafactorof1000abovethezero-eldminimum;colossalmagnetocapacitance(CMC)isclearlypresent.Theremnantcapacitancedipat50kOedisappearsat70kOeandthelineartemperaturedependenceC(T)=CAlOx(T)isidenticaltothatofseparatelymeasuredAl{AlOx{Alcapacitors.DeviationsofC(T)#"belowCAlOx(T)thusreectthecompetitionofFMMandCOIphases,anditisherewheretheCMCeectsoccur. InSection 6.4 weshoweddetailedanalysisofhowmeasurementofC(T)isnotacomplicatedwayofmeasuringR(T):WemodeledaresistanceRSinserieswiththeparallelcombinationofC(!)andadcresistanceR0,andestablishednecessaryand 130

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6-1 .WemodelC(!)usingaMaxwell-Wagner(MW)circuitequivalent[ 93 ]inSection 6.5 .ThequalitativeagreementshowninFigure 6-1 Bbetweenthecapacitancedata(red)andtheMWmodelcalculation(green)conrmstheappropriatenessoftheMWmodelashasalsobeenshowninrelateddielectricstudiesoftransitionmetaloxides[ 91 ],spinels[ 89 90 92 ]andmultiferroics[ 6 ]wherethematerialunderinvestigationistheinsulator(I)ofaMIMstructureratherthanthebaseelectrodeasdiscussedhere. TheMWanalysisusesthemeasuredRjjasaninputandthereforeenforcesanalignmentintemperature(Figure 6-1 B)betweenthemeasuredresistancemaximaandthecalculatedcapacitanceminima.Sincetheequipotentialsofthecapacitancemeasurementareparalleltothelmsurface,themisalignmentofthemeasuredcapacitanceminima(20KinFigure 6-1 B),canbestbeexplainedbyassumingthatRMintheMWcalculationshouldbetheperpendicularresistanceR?(T)ratherthanRjj(T).HencethemeasuredcapacitanceminimaareinalignmentwithputativeresistancemaximacorrespondingtopercolativeIMtransitionsinR?(T).TheIMtransitiontemperaturesintheperpendiculardirection,T#IM;?=77KandT"IM;?=91K,arethereforeequaltothetemperatureswherethecapacitanceminimaoccuratnoticeablylowervaluesthanthecorrespondingtemperatures,T#IM;jj=95KandT"IM;jj=106K,fortheRjj(T)maxima. Straineectsexplainthetwoseparatepercolationtransitions.TheLPCMOlmsweregrownonNdGaO3,whichisknowntostabilizethepseudocubicstructureoftheFMMphaseatlowtemperatures[ 94 95 ].Theeectofthesubstratediminishesawayfromtheinterface[ 94 ]asshownschematicallybytheshadinginFigure 6-1 C,wheretheLPCMOelectrodeisdepictedasaninniteRCnetworkcomprisinglocalresistancesr?andrjjrespectivelyperpendicularandparalleltotheinterface.Thesedistributed 131

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96 ].InthemeasurementofRjjthestrain-stabilizedFMMregion\shortsoutthehigherresistancestateoccurringawayfromtheinterfaceandpercolationoccursatahighertemperatureT#"IM;jjthanT#"IM;?asmeasuredbythecapacitanceminima.ForthickerlmsthetwoIMtransitionsconverge,asexperimentallyconrmedoverthethicknessrange300Ato900A(seeSection 6.6 ),toasinglevaluerepresentingisotropic3DpercolationofbulkLPCMOwiththetemperaturedierenceT#"IM=T#"IM;jjT#"IM;?approachingzero. 93 ].WeshowsuchaplotonlogarithmicaxesinFigure 6-6 atT=65K(warming)forthemagneticeldsindicatedintheinset.Asthefrequencyissweptfromlow(50Hz)tohigh(20kHz)ateacheld,C00(!)passesfromaregionwhereCAlOxdominates,subsequentlyreachesapeakvalueat!RMCM=1(verticalarrow),andthenentersthehighfrequencyregionwheretheintrinsicresponseofthemanganitedominatesandthedatacollapseontothesamecurve.Thelow-to-highfrequencycrossoverfromno-collapseofthedatatocollapseismagniedintheinset. AthighertemperaturesthedatacollapseismorestrikingasshownintheCole-ColeplotofFigure 6-6 B.Independentlyofwhethertheimplicitvariableisfrequencyf=!=2,TorH,thedielectricresponsecollapsesontothesamecurvewhentheremainingtwovariablesarexed(seeinset).As!increases,orequivalently,asTorHdecrease,C00approacheszeroandC0approachesaconstantC1representingthebaredielectricresponse.WendthatwhenC00isplottedagainstC0C1ondoublelogarithmicaxes,allthedatacollapseontoastraightline(inset)describedbytheequation 132

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Cole-Coleplotsrevealdatacollapseandpower-lawscalingofthedielectricresponse.a,ColeColeplotonlogarithmicaxesofdielectricdissipationC00(!)versuspolarizationC0(!)atT=65K(warming)forthemagneticeldsindicatedinthelegend.Ateacheldtheimplicitfrequencyvariablefrangesfrom100Hzto20kHz.Thecrossoverfromnon-overlappingtracesatlowfrequenciestodatacollapseathighfrequenciesismagniedintheinset.b,ColeColeplotforthesweepparametersandrangesindicatedinthelegend.Independentlyofwhethertheimplicitvariableisfrequency(blacksquares),temperature(redcircles)ormagneticeld(bluetriangles)thedatacollapseontothesamecurveregardlessoftheparameterbeingvaried.Thesesamedata,replottedasastraightorangelineintheinsetaftersubtractingasinglettingparameterC1,showpower-lawscalingcollapse(PLSC). 133

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6{8 isageneralizationofJonschersuniversaldielectricresponse,whichrequires=1anddescribeswellthehighfrequencydielectricresponseofmostdielectrics[ 97 ].Asshownbelow,thegeneralizedpower-lawscalingthatwehaveobservedwithrespecttothreeindependentvariables(!;T;H)isassociatedwithapercolationtransitioninwhichFMMandCOIphasesformclustersthatcompeteonself-similarlengthscales. Figure6-7. Cole-Coleplotonlinearaxeswithtemperature(cooling)astheimplicitvariableforf=500Hzandmagneticeldsidentiedinthelegend.Thewell-denedtransitionsonto/(oof)theorangePLSCline(magniedintheinset),whichisthesamelineshownintheinsetofFigure 6-6 ,denerespectivelytheupper/lowereld-dependentcriticaltemperaturesthatboundthePLSCbehaviorinfTHspaceshowninFigure 6-8 Theuniversalpower-lawscalingcollapse(PLSC)ofthedatadescribedbyequation 6{8 appliestoaregionoffTHspacewithboundariesthatcanbeaccuratelydeterminedfromCole-ColeplotswhichuseTastheimplicitvariableovertheentiretemperaturerange.Asanexampleofourprocedure,weshowinFigure 6-7 aCole-Coleplotonlinearaxeswithtemperature(cooling)astheimplicitvariableforf=500Hzandmagneticeldsidentied 134

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6{8 (seealsoFigure 6-6 inset)incommonwiththelowerpartoftheupperbranchtono-collapse(NC)behavior(lowerbranch).Astemperaturedecreasesontheupperbranch,thedatafollowanonpower-lawcollapse(NPLC)whichatwelldenedeld-dependentuppercriticaltemperatures,T#upper(H),mergeontotheorangelinerepresentingPLSCbehavior.AsTcontinuestodecreaseinthePLSCregion,thereisasecondcriticaltemperature,T#lower(H),markingthedemarcationpointsbetweenbranchesbyanalmost180changeinthedirectionofthetrajectoryasindicatedbythe`turnaround'arrowintheinset.Theseeld-dependentcrossoverpointspreciselydenec=T#Cmin(H)whereC0(H)isminimumandwhichbyourMWanalysishasbeenshowntobethesameasT#IM;?(H).Asimilaranalysisholdsforwarmingcurves. Theaccuratedeterminationofeld-dependentcriticaltemperatureboundariesateachfrequencyallowsustodelineatetriangular-shapedareasinTHspacewherePLSCisobeyedasshownforcoolinginFigure 6-8 .Thetwocriticaltemperatureboundaries,T#upper(H)andT#lower(H),aredeterminedbytheNPLC-to-PLSC(closedsymbols)andthePLSC-to-NCtransition(opensymbols).Forcomparisonweshow(crosses)theIMboundaryT#IM;jj(H),determinedfromthepeaksinR#jj(H).TheroughlyparallelosetfromthelowerboundaryT#IM;?(H)ofthePLSCphaseimpliesseparatepercolationtransitionsforR?andRjj.IncreasingthefrequencypushesT#upper(H),tohighertemperaturesandelds,thusincreasingthevolumeoffTHspacewherePLSCoccurs.ForanyTHregionboundedbyanuppercriticalboundarydeterminedatf=f0,PLSCisobeyedwithinthatregionforallff0.Thereforeasf0decreasesandthecorrespondinglengthscalesbeingprobedincrease,thecorrespondingTHregion,wherePLSCisobeyedforallff0,shrinkstoapointdenedbythetemperatureT#IM;?(H)=77KatH=0(markedbyXonFigure 6-8 )whereR?ismaximumandpercolationoccurs.Asimilarphasediagramshifted20Ktohighertemperaturesoccursforwarmingdata.Thenotionofpercolative 135

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PLSCholdsoverawideregionoffTHspaceandatlowfrequencyconvergestoapointdeningtheinsulator-metaltransitionT#IM;?(H=0).Thedeterminationofupper(solidsymbols)andlower(opensymbols)criticaltemperaturelines(cooling,Figure 6-7 )denetriangular-shapedregionsinTHspacewithinwhichPLSCholdsforfrequencieshigherthanthefrequency(labeled)atwhichtheupperboundaryisdetermined.AsfdecreasesthePLSCregionshrinkstoapoint(largeredX)thatmarksT#IM;?(H=0)andanchorsthelowercriticaltemperaturelineT#IM;?(H)wherethecapacitanceisminimum.ThecriticaltemperaturelineT#IM;jj(H)(green)determinedfromthepeaksinR#jj(H)isroughlyparalleltoT#IM;?(H)atatemperatureosetby20K. 136

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83 ]recognizesthatthepercolationtransitionasafunctionoftemperatureisdierentfromtheclassicpercolationproblemwhichdealswithconnectivityoccurringasafunctionofcompositionratherthantemperature.Thiscomplicationisreectedinnoisemeasurementsonthin-lm[ 98 ]andbulkcite24maisermanganiteswhichshownoisepeaksrespectivelyatpercolationtemperaturesdenedrespectivelybythemaximuminRandthemaximumindR=dT.OurresultsdonotdependonanexactidenticationofpercolationtemperaturebutareunambiguousinshowingthatthePLSC-to-NCtransitiontemperature(T#"IM)occursattheresistancepeak,whichforthepurposesofthispaperiscalledthe\percolationtransitiontemperature. Weexpectthatourmeasurementtechnique,whichadvantageouslyincludesinformationaboutdynamics,willndwideapplicationinstudiesofavarietyofanisotropicthin-lmsystemsincludingthosewherethepresenceofcompetingphasesisunderdebate.Candidatesforstudyincludelayeredmanganites[ 99 ],under-dopedhigh-Tcsuperconductors[ 2 ],electron-dopedcuprates[ 100 ]withanisotropicresistivityratios(c=ab)reported[ 101 ]tobeashighasafactoroftenthousand,andc-axisgraphitewhereresistivityratiosaretypicallyafactorofonethousand.Wehavealsodemonstratedthatourtechniquecanbesensitivetostrainatepitaxialinterfacesandthuscapableofdeterminingthroughthicknessdependencestudiesthecriticalthicknessforarelaxedtopinterface.ByincorporatinganLPCMOlmasthe`metal'(M)baseelectrodeofanMIMstructureandusinganultralowleakagedielectric(AlOx)fortheinsulatingspacer,wepreventthemetallicphaseoftheLPCMOfromshortingoutthemeasurementasitwouldifitwerethemiddlelayer(I)ofaconventionaldielectricconguration.Circuitanalysisshows,andexperimentdemonstrates,thatoverawelldenedfrequencyrangethelargeAl/AlOxcapacitoractsasabaselinereferencethat`decloaksormakesvisiblethemuchsmallercapacitanceoftheseries-connectedLPCMOlm. 137

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83 84 ].Afullunderstandingoftheseresultswillbeachallengetothecontrastingtheoriesofphaseseparationandcompetitioninmanganitesbasedonintrinsicdisorder[ 85 ],longrangestraininteractions[ 86 ],blockedmetastablestates[ 87 ]orthermallyequilibratedelectronicallysoftphases[ 88 ]. 138

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Inordertounderstandandstudyphaseseparationonthenanometerscale,inChapter 2 thetechniquesusedforfabricatingnarrowbridges(wires)ofnanometerwidthwhichallowthestudyoftransportacrossafewphaseseparatedregionswaspresented.Additionally,capacitancemeasurementswereperformedonLPCMObyutilizinganovelgeometrythathasallowedustoprobetheanisotropictransportpropertiesthatariseinultrathinlmsofnanometerthickness. Bymeasuringthetransportpropertiesofthenarrowbridgesasafunctionoftemperatureandmagneticeld,inChapter 3 evidenceofalternatinginsulatingandmetallicregionsspanningthebridgewidthalignedalongthelengthofthebridgewaspresented.First,evidenceofdirectelectrontunnelingbetweentwoormoreferromagneticmetallic(FM)regionsseparatedbyantiferromagneticinsulating(AFI)regionswas 139

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InChapter 4 itwasfoundthatattemperaturesbelowthephaseseparatedtemperature,rangewhentheunpatternedthinlmsamplesarenearlyfullyferromagneticmetallic,thenarrowbridgesincontrasthaveahighresistance.Current-voltagemeasurementspointtoadirecttunnelingphenomenonthussuggestingthatthemetallicregionsareseparatedbyverythinAFItunnelbarriers.Magneticeldmeasurementsrevealthatthebarriersaremetastablewithrespecttoverysmallelds(ontheorderofthemanganitecoerciveeld)andhaveananisotropythatisinagreementwiththeeasyaxisdirectioninunpatternedthinlms.Thedatathussuggestthepresenceofnovel,insulating,stripedomainwallswheretunnelingoccursacrossthedomainboundary,astheoreticallypredicted. InChapter 5 wediscusstheelectricalanalogofthecolossalmagnetoresistance(CMR)eect,thecolossalelectroresistance(CER)eectonthenanoscale.Ourcurrent-voltagemeasurementsreveal,asinbulk,ahysteresisandabreakdowntoalowresistancestatewithahighenoughappliedcurrent.Thebreakdownoccursinsharpstepswhileamuchsmoothertransitiontoalowerresistancestateisobservedinbulk.Weusedacombinationofcurrent-voltagemeasurementsandtstotheSimmons'modeltorevealthatwhileCMRresultsfromaphasetransitionoftheinsulatingregionstometallicregions,CERresultsfromaspacialreorganizationofthemetallicandinsulatingphasestominimizeenergyinthepresenceofanelectriceld. Lastly,inChapter 6 theeectsoflmthicknessinthenanometerrangeonphaseseparationin(La,Pr,Ca)MnO3thinlmswasinvestigatedviacapacitancemeasurements.Anunusualgeometryforfabricatingacapacitorstructurewasutilized,suchthatthe 140

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6 ,inthiswayitwasfoundthatthedielectricresponsedeviatesfromthe'universal'expressionbyanexponentthatisdierentfromunity,andthevalueofwhichdependsontheexactphaseofthe(La,Pr,Ca)MnO3.Thismethodallowsforanovelprobeofphaseboundariesinthinlms,wheretheboundariesmaynotbedetectablewithDCtransportmeasurements.Additionally,itwasfoundthatcapacitanceasafunctionoftimeshowsadierentphasetransitiontemperaturethanthetemperaturedependentresistancemeasurements.Thecapacitanceandresistancetransitiontemperaturesbegintoconvergeasthelmthicknessincreasesshowingtheeectoflmthicknessontwodierenttransitions:oneintheplaneofthelmandoneperpendiculartotheplaneofthelm. Someimmediateandongoingexperimentswhichdirectlyfollowfromtheworkpresentedcanbesummedupasfollows.Firstly,theasymmetricpeaksseeninourTMRmeasurementsinSection 3.6.2 implythatanexchangebiasmaybepresentbetweentheferromagneticdomainsandtheantiferromagneticinsulatingregionsthatseparatethem.Workiscurrentlyunderwayinprobingtheexchangebiasbyexploitingthefactthatexchangebiasgivesrisetoauniaxialanisotropy.Thehopeistocapturetheeectsoftheuniaxialmagneticanisotropybymeasuringmagnetoresistanceasafunctionofappliedmagneticeldanglewithrespecttothesamplesurface. 141

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3.6.1 .Preliminarycurrent-voltagemeasurementsinthistemperaturerangerevealsignaturesofcoulombblockadewithintheferromagneticdropletsseparatedbyinsulatingregions.ThisiscurrentlybeingstudiedusingtheelectriceldgatingmeasurementcongurationdescribedinSection 2.2.4 .Bygatingthebridgecontainingthecoulombblockadeddots(i.e.ferromagneticdroplets),wecanmodulatethechargingenergyofthedotsandthusthethresholdvoltagerequiredfortransportofelectronsintoandoutofthedots.Thistypeofchangeinthechargingpropertiesofthedotscanbeevaluatedusingcurrent-voltagecharacteristics.ItmaythusbepossibletocorrelatetheelectriceldeectseeninbulkwithsingleelectroncharginganddischargingofarraysofCoulombblockadedferromagneticdroplets. Lastly,theresultsfromtheunconventionalcapacitancegeometryarebeingutilized(incollaborationwithPatrickMickel)toanalyzethedielectricresponseusingcole-coleplotsandunderstandingtheresultsusingtheDebyerelaxationmodelformultiplephaseswithdierenttimeconstantspresentinourthinlms.ThisprocesshashelpedthusfartoidentifyaphasetransitionfromtheparamagneticinsulatingphasetothechargeorderinsulatingphaseinLPCMO.Thistypeofinsulator-to-insulatorphasetransitionisdiculttoassessusingtransportmeasurements,sincethetransportinbothinsulatorswillbeactiated.Suchanalysiscanbeutilizedinotherphaseseparatedsystemswherephaseseparationisstilladebatablescenario,todetermineifindeedphasefractionswithdierentdipolerelaxationtimeconstantsarepresent. Inadditiontotheworkinprogressmentionedhere,auniquecapacitancegeometryandnanofabricationtechniqueforfabricatingnanoscalebridgesandstructuresinphaseseparated,highlyinsulatingthinlms,anavenuewassetforthforinvestigatingphaseseparationincomplexoxidesystemsinanovelmanner.Inthefuture,suchtechniquesmayallowforprobesintootherphaseseparatedmaterialsorothercomplexoxide 142

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GuneetawasbornattheDelhiKentArmyHospitalinNewDelhi,IndiaonLohri,aNorthIndianholidaywhichfallsonJanuary13.BeinganocerintheIndianArmy,herfatherwasregularlypostedtodierentbasesthroughoutIndia.AsaresultshegrewuplivinginseveralcitieswithinIndiaincludingthecapitalNewDelhi,andseveralcitiesinareassuchastheHimalayanstateofJammu&Kashmir,inMaharashtraandalsoinherancestralstateofPunjab.Seekingabetterlife,whenshewas10shemovedwithherparentsandyoungersistertotheUnitedStateswheretheylivedrstinNewJersey,followedbrieybyCaliforniaandnallyOrlando,Floridawhereshenishedmiddleschoolandattendedhighschool.Theconstantchangeinscenery,cultureandlanguagewhilegrowingupevokedadeepsenseofcuriosityinGuneetaabouteverythingfromthevisualarts,philosophyandthephysicalworldtohistoryandtheevolutionoflanguages.Guneetahashadaninterestinthenaturalworldforasfarbackasshecanremember.Sherecallswonderingendlesslyabouttheinnerworkingsofatomsafterlearninginrstgradethattheywerethebuildingblocksofallthings.Aroundthesametime,catchingaglimpseofHaley'scometandwatchinganIndiansatelliteshootupintotheskysolidiedherfuturedream.ShediscoveredtheHebardlabwhileturninginalabreporttoherundergraduateAdvancedLabinstructor,Dr.ArthurF.Hebard,attheUniversityofFloridainGainesville.Afteronebriefglimpseofthepeculiarmachineryanditemsinhislab,shewasovercomebycuriosityandhooked.ShethusbeganworkingintheHebardlabasanundergraduatestudentandhereortsresultedintheirrstpublicationtogether.ShecontinuedtoworkforDr.HebardasagraduatestudentandhadtheopportunityofcloselycollaboratingwithDr.AmlanBiswasinworkingonherthesistopicofsizeeectsinmanganites.ShehasalsohadtheopportunityofconductingresearchinJapanincollaborationwithDr.HaroldY.Hwangonatopicofherchoosing,fundedbytheNSFEastAsiaandPacicSummerInstitute(EAPSI)duringthesummerof2008. 149

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