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Infrared Spectroscopy of Complex Oxides of Phase Separated Manganites and Electron Doped Cuprates

Permanent Link: http://ufdc.ufl.edu/UFE0021888/00001

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Title: Infrared Spectroscopy of Complex Oxides of Phase Separated Manganites and Electron Doped Cuprates
Physical Description: 1 online resource (148 p.)
Language: english
Publisher: University of Florida
Place of Publication: Gainesville, Fla.
Publication Date: 2008

Subjects

Subjects / Keywords: Physics -- Dissertations, Academic -- UF
Genre: Physics thesis, Ph.D.
bibliography   ( marcgt )
theses   ( marcgt )
government publication (state, provincial, terriorial, dependent)   ( marcgt )
born-digital   ( sobekcm )
Electronic Thesis or Dissertation

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Abstract: Our study examined the infrared optical properties of complex oxides of phase separated manganite thin films and electron-doped cuprates as a function of temperature and magnetic field, covering a range of doping on various substrates. The principal conclusion of this study for manganites is that low energy optical properties are sensitive to phase separation in manganites. The optical constants indicate a percolative type of insulator-metal transition and effective electron density analyzes indicate that with large cation disorder, the description of the optical conductivity is not amenable to mean field models of double exchange and Jahn-Teller distortions. The magneto-optic study of electron-doped cuprates indicate that the optical properties are unaffected by the application of magnetic fields of 31T.
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, 2008.
Local: Adviser: Tanner, David B.
Electronic Access: RESTRICTED TO UF STUDENTS, STAFF, FACULTY, AND ON-CAMPUS USE UNTIL 2010-05-31

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Source Institution: UFRGP
Rights Management: Applicable rights reserved.
Classification: lcc - LD1780 2008
System ID: UFE0021888:00001

Permanent Link: http://ufdc.ufl.edu/UFE0021888/00001

Material Information

Title: Infrared Spectroscopy of Complex Oxides of Phase Separated Manganites and Electron Doped Cuprates
Physical Description: 1 online resource (148 p.)
Language: english
Publisher: University of Florida
Place of Publication: Gainesville, Fla.
Publication Date: 2008

Subjects

Subjects / Keywords: Physics -- Dissertations, Academic -- UF
Genre: Physics thesis, Ph.D.
bibliography   ( marcgt )
theses   ( marcgt )
government publication (state, provincial, terriorial, dependent)   ( marcgt )
born-digital   ( sobekcm )
Electronic Thesis or Dissertation

Notes

Abstract: Our study examined the infrared optical properties of complex oxides of phase separated manganite thin films and electron-doped cuprates as a function of temperature and magnetic field, covering a range of doping on various substrates. The principal conclusion of this study for manganites is that low energy optical properties are sensitive to phase separation in manganites. The optical constants indicate a percolative type of insulator-metal transition and effective electron density analyzes indicate that with large cation disorder, the description of the optical conductivity is not amenable to mean field models of double exchange and Jahn-Teller distortions. The magneto-optic study of electron-doped cuprates indicate that the optical properties are unaffected by the application of magnetic fields of 31T.
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, 2008.
Local: Adviser: Tanner, David B.
Electronic Access: RESTRICTED TO UF STUDENTS, STAFF, FACULTY, AND ON-CAMPUS USE UNTIL 2010-05-31

Record Information

Source Institution: UFRGP
Rights Management: Applicable rights reserved.
Classification: lcc - LD1780 2008
System ID: UFE0021888:00001


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Iwouldliketothankmyadvisor,ProfessorDavid.B.Tannerforhismentoringthroughoutmygraduatecareer.Ithasbeenaprivilegetoworkwithhim.IwouldalsoliketoexpressmygratitudetomycollaboratorsDr.TaraDhakal,Dr.Amlan,Biswas,Dr.AlexanderZimmers,Dr.RichardGreeneandDr.Y.J.Wang.Myexperimentswouldnotevenhavestartedifnotforthehelpfromthefollowingpeople.MarcLink,EdStorchandBillMalphursfromtheMachineshop,GregLabbeandJohnGrahamfromCryoengineering,LarryPhelpsandRobHamersmafromtheElectronicsshop,andBrentNelsonandDavidHansenfromcomputermaintenance.Theenthusiasmanddedicationtheyshowedtotheirworkhasbeenalifelessonforme.Myfriends,toomanytolisthere,havemadelifeworthwhile.Ithankthemfortheirgenerosity.IwouldalsoliketothankmyMomandDad,whohavealwaysbeenthereforme. 4

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page ACKNOWLEDGMENTS ................................. 4 LISTOFTABLES ..................................... 7 LISTOFFIGURES .................................... 8 ABSTRACT ........................................ 13 CHAPTER 1INTRODUCTION .................................. 14 1.1OpticalPropertiesofManganties ....................... 15 1.2OpticalPropertiesofInhomogeneousSystems ................ 19 2FARINFRAREDMAGNETO-OPTICALSTUDYOF(La1yPry)0:67Ca0:33MnO3y=0.6,THINFILMONLaAlO3 23 2.1Introduction ................................... 23 2.2ExperimentalDetails .............................. 23 2.2.1ZeroFieldSpectra ............................ 25 2.2.1.1Substrateproperties ..................... 25 2.2.1.2Resistancemeasurements ................... 26 2.2.1.3Temperaturedependentreectance ............. 26 2.2.2MagneticFieldStudies ......................... 28 2.3Discussion .................................... 29 2.4Conclusions ................................... 31 3OPTICALSTUDYOF(La1yPry)0:67Ca0:33MnO3FILMSONNdGaO3 44 3.1Introduction ................................... 44 3.2ExperimentDetails ............................... 44 3.2.1SubstrateProperties .......................... 45 3.2.2ResistivityMeasurements ........................ 45 3.2.3TemperatureDependentReectance .................. 46 3.3OpticalConductivity .............................. 48 3.3.1ResistivityComparison:TransportvsInfrared ............ 50 3.3.2Eectiveelectronicdensity,Neff 51 3.4Conclusions ................................... 53 4INVESTIGATIONOFTHEELECTRICFIELDEFFECTTHROUGHPOLARIZEDFAR-IRREFLECTANCE .............................. 83 4.1Introduction ................................... 83 4.2ExperimentalDetails .............................. 85 4.3Results ...................................... 85 5

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.................................... 87 5MAGNETO-OPTICALSTUDYOFELECTRON-DOPEDPr2xCexCuO4 104 5.1Introduction ................................... 104 5.1.1OpticalProperties ............................ 106 5.1.2InfraredStudiesinMagneticField ................... 110 5.2ExperimentalDetails .............................. 112 5.3ZeroFieldSpectra ............................... 113 5.4MagneticFieldSpectra ............................. 114 5.5Discussion .................................... 114 5.6Summary .................................... 118 6CONCLUSIONSANDFUTURERESEARCH ................... 128 6.1Conclusions ................................... 128 6.1.1Manganites ............................... 128 6.1.2Cuprates ................................. 129 6.2FutureResearch ................................. 130 APPENDIX AREFLECTANCEOFA5000A(La1yPry)0:67Ca0:33MnO3,y=0.6FILM. .... 132 BTHINFILMANALYSIS ............................... 133 B.1DeterminationofSingleBounceReectionoftheSubstrate ......... 133 B.2MatrixFormalism ................................ 134 B.2.1FittingwiththeDrude-LorentzModel ................. 137 B.2.2FittingProcedures ........................... 139 REFERENCES ....................................... 141 BIOGRAPHICALSKETCH ................................ 148 6

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Table page 2-1Relativeerrorestimatefortheextractedopticalconductivity ........... 29 2-2ParametersforLaAlO3 42 2-3Parametersfor(La1yPry)0:67Ca0:33MnO3,y=0.6onLaAlO3 43 3-1ParametersforNdGaO3 78 3-2ParametersforLa0:67Ca0:33MnO3 79 3-3Parametersfor(La1yPry)0:67Ca0:33MnO3,y=0.4 .................. 80 3-4Parametersfor(La1yPry)0:67Ca0:33MnO3,y=0.5 .................. 81 3-5Parametersfor(La1yPry)0:67Ca0:33MnO3,y=0.6 .................. 82 5-1Relativeerrorestimatefortheextractedopticalconductivity ........... 115 7

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Figure page 1-1PhasediagramofLa1xCaxMnO3[ 3 ],and(La1yPry)0:7Ca0:3MnO3[ 6 ] ...... 21 1-2OpticalconductivityofLa0:7Ca0:3MnO3[ 14 ],Pr1xCaxMnO3x=0.4[ 26 ]and(La1yPry)0:7Ca0:3MnO3[ 16 ] ............................. 22 2-1TemperaturedependenttransmittanceofLaAlO3 32 2-2TemperaturedependentreectanceofLaAlO3.Insetshowscalculatedsinglebouncereectancefromthemeasuredreectanceat300K. ............ 32 2-3LorentzoscillatortsofLaAlO3reectance .................... 33 2-4ConductivityextractedfromtheLorentzoscillatorbesttsforLaAlO3 33 2-5Resistanceofthe(La1yPry)0:7Ca0:3MnO3,y=0.6lm,onLaAlO3.Thetopcurveindicatescoolingwhilethebottomoneisforthewarmingcycle ......... 34 2-6Temperaturedependentreectanceforthe(La1yPry)0:7Ca0:3MnO3y=0.6,lmfrom300Kto120K .................................. 34 2-7Temperaturedependentreectanceforthe(La1yPry)0:7Ca0:3MnO3y=0.6lmfrom120Kto12K .................................. 35 2-8Temperaturedependentfar-IRreectanceforthe(La1yPry)0:7Ca0:3MnO3y=0.6lm,below1000cm1. ................................ 35 2-9Lorentzoscillatortsofthe(La1yPry)0:7Ca0:3MnO3y=0.6lm,reectanceatselecttemperatures .................................. 36 2-10Conductivityofthe(La1yPry)0:7Ca0:3MnO3y=0.6lm,from300Kto120K. .. 36 2-11Conductivityofthe(La1yPry)0:7Ca0:3MnO3y=0.6lm,from120Kto12K ... 37 2-12EectiveelectronicdensityNeff(!c=0:5eV)asafunctionoftemperature. ... 37 2-13Magneticelddependentreectance(La1yPry)0:7Ca0:3MnO3y=0.6lmfrom0Tto18T. ....................................... 38 2-14FitsgeneratedbyvaryingonlytheDrudetermanditswidth. .......... 38 2-15Opticalconductivityasafunctionofeld. ..................... 39 2-16SquareoftheDrudeplasmafrequencyasfunctionoftemperatureandeld. ... 40 2-17Drudescatteringrateasafunctionoftemperatureandeld. ........... 40 2-18Zerofrequencydielectricconstantasafunctionofmetallicfractionfinatwocomponenteectivemediumapproximationmethod ................ 41 8

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.... 41 3-1ReectanceofNdGaO3at300Kand10K.ThedashedlinesaretstotheLorentzmodelforthedielectricfunction. .......................... 54 3-2Conductivityspectraat300Kand20KofNdGaO3 54 3-3Resistivityofallthelmsmeasuredforthecooling(downwardarrows)andwarming(upwardarrows). ................................... 55 3-4Reectanceat30cm1and160cm1asafunctionoftemperatureincomparisontothedcconductivityobtainedfromtransportmeasurements. .......... 56 3-5Reectanceat750cm1,2000cm1and4500cm1asafunctionoftemperatureincomparisontothedcconductivityobtainedfromtransportmeasurements. .. 57 3-6ReectanceofLa0:67Ca0:33MnO3between30-5000cm1forvarioustemperatures. 58 3-7ReectanceofLa0:67Ca0:33MnO3between30-1200cm1forvarioustemperatures 58 3-8Reectanceof(La1yPry)0:67Ca0:33MnO3,y=0.4between30-5000cm1forvarioustemperatures. ..................................... 59 3-9Reectanceof(La1yPry)0:67Ca0:33MnO3,y=0.4between30-1200cm1forvarioustemperatures. ..................................... 59 3-10Reectanceof(La1yPry)0:67Ca0:33MnO3,y=0.5between30-5000cm1forvarioustemperatures. ..................................... 60 3-11Reectanceof(La1yPry)0:67Ca0:33MnO3,y=0.5between30-1200cm1forvarioustemperatures. ..................................... 60 3-12Reectanceof(La1yPry)0:67Ca0:33MnO3,y=0.6between30-5000cm1forvarioustemperatures. ..................................... 61 3-13Reectanceof(La1yPry)0:67Ca0:33MnO3,y=0.6between30-1200cm1forvarioustemperatures. ..................................... 61 3-14FitstothemeasuredreectanceofLa0:67Ca0:33MnO3atselecttemperatures,between30-5000cm1. ............................... 62 3-15FitstothemeasuredreectanceofLa0:67Ca0:33MnO3atselecttemperatures,between30-1200cm1. ................................ 62 3-16Fitstothemeasuredreectanceof(La1yPry)0:67Ca0:33MnO3,y=0.4atselecttemperatures,between30-5000cm1. ........................ 63 3-17Fitstothemeasuredreectanceof(La1yPry)0:67Ca0:33MnO3,y=0.4atselecttemperatures,between30-1200cm1. ........................ 63 9

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....................... 64 3-19Fitstothemeasuredreectanceof(La1yPry)0:67Ca0:33MnO3,y=0.5atselecttemperatures,between30-1200cm1. ........................ 64 3-20Fitstothemeasuredreectanceof(La1yPry)0:67Ca0:33MnO3,y=0.6atselecttemperatures,between30-5000cm1. ....................... 65 3-21Fitstothemeasuredreectanceof(La1yPry)0:67Ca0:33MnO3,y=0.6atselecttemperatures,between30-1200cm1. ........................ 65 3-22OpticalconductivityofLa0:67Ca0:33MnO3atalltemperatures,between30-4500cm1. ......................................... 66 3-23OpticalconductivityofLa0:67Ca0:33MnO3atalltemperatures,between30-1200cm1. ......................................... 66 3-24Opticalconductivityof(La1yPry)0:67Ca0:33MnO3,y=0.4,from300Kto160K. 67 3-25Opticalconductivityof(La1yPry)0:67Ca0:33MnO3,y=0.4from160Kto20K. 67 3-26Opticalconductivityof(La1yPry)0:67Ca0:33MnO3,y=0.4,foralltemperatures,between30-1200cm1. ................................ 68 3-27(La1yPry)0:67Ca0:33MnO3,y=0.5,from300Kto140K. .............. 68 3-28(La1yPry)0:67Ca0:33MnO3,y=0.5,from140Kto12K. .............. 69 3-29Opticalconductivityof(La1yPry)0:67Ca0:33MnO3,y=0.5,foralltemperatures,between30-1200cm1. ................................ 69 3-30(La1yPry)0:67Ca0:33MnO3,y=0.5,from300Kto120K. .............. 70 3-31(La1yPry)0:67Ca0:33MnO3,y=0.5,from120Kto12K. .............. 70 3-32Opticalconductivityof(La1yPry)0:67Ca0:33MnO3,y=0.6,foralltemperatures,between30-1200cm1. ................................ 71 3-33TemperaturedependenceofthephononoscillatorstrengthsofLa0:67Ca0:33MnO3. 72 3-34TemperaturedependenceofthephononoscillatorstrengthsofLa1yPry)0:67Ca0:33MnO3,y=0.4. ......................................... 73 3-35TemperaturedependenceofthephononoscillatorstrengthsofLa1yPry)0:67Ca0:33MnO3,y=0.5. ......................................... 74 3-36TemperaturedependenceofthephononoscillatorstrengthsofLa1yPry)0:67Ca0:33MnO3,y=0.6. ......................................... 75 3-37TemperaturedependenceoftheDrudeplasmafrequency. ............. 76 10

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................................. 77 3-39Scalingcurvesforthemanganitelms. ....................... 77 4-1Resistancemeasurementsforthey=0.6lmwithstraightlinesindicatingthetemperatureregionwhereelectriceldwasapplied. ................ 89 4-2IVofy=0.6samplemeasuredduringtheexperiment. ............... 89 4-3Unpolarizedreectanceasafunctionofappliedeldat60K. ........... 90 4-4Polarizedreectanceasafunctionofappliedeldat60K(A). .......... 90 4-5Polarizedreectanceasafunctionofappliedeldat60K(B). .......... 91 4-6Polarizedreectanceasafunctionofappliedeldat60K(C). .......... 91 4-7Polarizedreectanceasafunctionofappliedeldat60K(D). .......... 92 4-8Unpolarizedreectanceasafunctionofappliedeldat58K. ........... 92 4-9Polarizedreectanceasafunctionofappliedeldat58K(A). .......... 93 4-10Polarizedreectanceasafunctionofappliedeldat58K(B). .......... 93 4-11Polarizedreectanceasafunctionofappliedeldat58K(C). .......... 94 4-12Polarizedreectanceasafunctionofappliedeldat58K(D). .......... 94 4-13Unpolarizedreectanceasafunctionofappliedeldat54K. ........... 95 4-14Polarizedreectanceasafunctionofappliedeldat54K(A). .......... 95 4-15Polarizedreectanceasafunctionofappliedeldat54K(B). .......... 96 4-16Polarizedreectanceasafunctionofappliedeldat54K(C). .......... 96 4-17Polarizedreectanceasafunctionofappliedeldat54K(D). .......... 97 4-18Unpolarizedreectanceasafunctionofappliedeldat52K. ........... 97 4-19Polarizedreectanceasafunctionofappliedeldat52K(A). .......... 98 4-20Polarizedreectanceasafunctionofappliedeldat52K(B). .......... 98 4-21Polarizedreectanceasafunctionofappliedeldat52K(C). .......... 99 4-22Polarizedreectanceasafunctionofappliedeldat52K(D). .......... 99 4-23Unpolarizedreectanceasafunctionofappliedeldat50K. ........... 100 4-24Polarizedreectanceasafunctionofappliedeldat50K(A). .......... 100 11

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.......... 101 4-26Polarizedreectanceasafunctionofappliedeldat50K(C). .......... 101 4-27Polarizedreectanceasafunctionofappliedeldat50K(D). .......... 102 4-28EMAcalculationforsamemetalfractionbutdierentshapefactor. ....... 102 4-29EMAcalculationfordierentmetalfractionbutsameshapefactor. ....... 103 4-30EMAcalculationfordierentmetalfractionandshapefactor. .......... 103 5-1ComparativeStructureofhole-dopedPCCOandelectron-dopedLSCO. ..... 119 5-2Electronandhole-dopedphasediagramasafunctionofdoping. ......... 119 5-3Dierenceinchargecarrieroccupationsbetweenholeandelectrondoping. ... 120 5-4Temperaturedependenttransmittancespectraandtsforx=0.11. ....... 120 5-5Temperaturedependenttransmittancespectraandtsforx=0.15. ........ 121 5-6Temperaturedependenttransmittancespectraandtsforx=0.17. ........ 121 5-7Temperaturedependenttransmittancespectraandtsforx=0.18. ....... 122 5-8Fielddependenttransmittancespectraforx=0.11. ................ 122 5-9Fielddependenttransmittancespectraforx=0.15. ................ 123 5-10Fielddependenttransmittancespectraforx=0.18. ................ 123 5-11Fielddependentreectancespectraforx=0.11. .................. 124 5-12Fielddependentreectancespectraforx=0.15. .................. 124 5-13Fielddependentreectancespectraforx=0.19. .................. 125 5-14Temperaturedependentopticalconductivityforx=0.11. ............. 125 5-15Temperaturedependentopticalconductivityforx=0.15. ............. 126 5-16Temperaturedependentopticalconductivityforx=0.17. ............. 126 5-17Temperaturedependentopticalconductivityforx=0.18. ............. 127 A-1Temperaturedependentreectanceofa5000Almfrom300Kto120K. ..... 132 A-2Temperaturedependentreectanceofa5000Almfrom120Kto11K. ..... 132 12

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1 ],wheretheapplicationofsmallmagneticeldschangestheresistivityofthesematerialsbymanyordersofmagnitude,hasalreadyleadthesematerialsfromthelaboratoryintobecomingpotentialcandidatesfornonvolatileMagneticRandomAccessMemory(MRAM)modules.Therichgroundstateswhichthesematerialsexhibitresultfromunusualspin,charge,latticeandorbitaldegreesoffreedom.Phasediagramsofnumerousmanganitefamiliesindicatethatthereiscompetitionbetweenvariousphasesattheboundariesleadingtointrinsicallyinhomogeneoussystems.ThisandthenextfewChaptersattempttostudytheinhomogeneityinthesephaseseparatedmanganitesystemsbymeansofopticalspectroscopictechniques.TheeldofmanganitesstartedwiththeseminalpaperofJonkerandVanSanten[ 2 ]wheretheexistenceofferromagnetisminmixedcrystalsofLaMnO3-CaMnO3,LaMnO3-SrMnO3,andLaMnO3-BaMnO3wasreported.ThegeneralchemicalformulaforthemanganeseoxidesisRE1xAxMnO3withRE3+arareearthtrivalentcationandA2+aalkalinedivalentcation.OxygenisinaO2state,andtherelativefractionofMn4+toMn3+isregulatedbyx.Manganitesexhibitvariousgroundstatesdependingonthecationdoping.Basedonmagnetizationandresistivity,theinferredphasediagramofLa1xCaxMnO3,[ 3 ](Figure1-1A)featureanumberofdistinctphaseswiththeferromagnetic(FM)phasebetweenx=0:17andx=0:5.TheCurietemperatureismaximizedatx=3=8andaprominentchargeordered(CO)statebetweenx=0:5andx=0:87canalsobeobserved.Forxedholedopingofx=0:33,whentheAcationLa3+issubstituted 14

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4 ].ThisdisorderintroducedbychemicalreplacementsintheA-sitesiscruciallyimportantindeterminingthepropertiesofmanganites[ 5 ].Thephasediagramof(La1yPry)0:7Ca0:3MnO3[ 6 ]showninFigure1-1B,indicatesthatasthePr3+concentrationincreases,thesystemgoesfromahomogeneousferromagneticmetaltoacantedantiferromagneticinsulator.Betweenthesetwoextremes,theneutrondiractiondatasuggeststhepresenceofmixedphaseswithmetallicandantiferromagneticcoexistenceforanarrowrangeofdoping.Recently,theimportanceofphaseseparationindeningthepropertiesofmanganiteshasreceivedalotofattention.Inthiscontext,thepresenceofintrinsicmixed-phasetendenciesin(La,Pr,Ca)MnO3havebeenseenbyUeharaetal.[ 7 ]usingtransport,magnetic,andelectronmicroscopytechniques.Theyobservedhysteresisbehavioroftheresistivity,signallingthepresenceofrst-order-likecharacteristicsinthesecompounds.FurtherevidenceforapercolationtypetransitionwasprovidedbymagneticforcemicroscopyimagesofthinlmsofLa0:33Pr0:34Ca0:33MnO3[ 8 ]. 9 ]hasshowndouble-peakstructuresbelow3eV.Thelowerenergypeakat0.5eVhasbeenattributedtoatransitionfromaJahn-Teller(JT)splitMn3+iontoaMn4+unoccupiedelectronicstate(sincethereisnoelectroninthatstate,thereisnoJTdistortion),whilethehigherfrequencypeakataround2.0eVwasattributedtoanintra-atomictransitionbetweenJTsplitMn3+levels.AnimportantconclusionofthisstudywasthatJTdistortionspresentatroomtemperature,maybeactiveatalldensitiesinthedopedmaterialsregardlessofthelow 15

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11 ].ThelowenergyopticalpropertiesofdopedcompoundssuchasNd0:7Sr0:3MnO3[ 12 13 ],La1xSrxMnO3[ 10 ],La1xCaxMnO3[ 14 ]showcommontrends,namelyanarrowDrudepeakandamid-IRabsorptionpeak.Themid-IRpeakispresentaround1.0eVwhoseweighttransferstosmallerenergiesasthetemperatureislowered.Inadditionithasbeenseenthattheeectiveelectronicdensity,indicatedbyNeff,changessubstantiallyevenintheferromagneticphaseofseveralmanganites.InfraredreectancestudiesofthephononmodesinLa0:7Ca0:3MnO3[ 15 ]haveshownthreemaininfraredactivemodespertinenttothecubicpervoskitestructureofmanganites.Asclassiedby3F1umodesofthepointgroupOh(m3m),theyaredesignatedasexternal,bending,orstretchingmodes,dependingonthetypesofcollectivemotions.TheexternalmoderepresentsavibratingmotionoftheLa(Ca)ionsagainsttheMnO6octahedra.ThebendingmodereectsaninternalmotionoftheMnandOionslocatedalongaparticulardirectionagainsttheotheroxygenionsinaplaneperpendiculartothedirection.ThismodeisstronglyaectedbyachangeintheMn-O-Mnbondangle.ThestretchingmodecorrespondstoaninternalmotionoftheMnionagainsttheoxygenoctahedronandissensitivetotheMn-Obondlength.OpticalConductivitymeasurementsforpolycrystallineLa0:7yPryCa0:3MnO3samplesobservedsystematicdecreaseinspectralweightbelow0.5eVwithincreasingPrconcentration[ 14 16 ].AsseeninasinglecrystalofLa5=8PryCa3=8MnO3(y=0.35)[ 16 ],apeakat1.4eVgrowsastemperatureisdecreasedfrom300KtilltheCurietemperature,Tc.BelowTc,theshiftofspectralweighttobelow0.5eVwasseenwiththeappearanceofadditionalabsorptionbandscenteredaround0.2eVand0.5eV.Evenatthelowesttemperatures,itwasseenthatthefeaturearound1.4eVremainedprominent. 16

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17 ].Thestudyconcentratedontheisotopeeectwherein16Ointhelmwassubstitutedby18O.Asafunctionoftemperature,theauthorsreportedadrasticsuppressionofthemid-IRspectralweightintheisotopesubstituted18Olm.Wenowturntothevariousinterpretationsputforthforthemid-IRabsorptionseeninmanganites.ThisdiscussionisalsorelevanttotheresultspresentedinthethirdChapterwherethemid-IRabsorptionbelow0.5eVissystematicallystudiedasafunctionofPrdoping.Okimotoetal.[ 10 ]claimedthatthespectralweightchangesshouldbeunderstoodinthespin-splitbandpictureinvolvingHundcoupling,ascontainedintheoneorbitalmodel.Themid-IRfeaturewasassignedtoanintrabandexcitationwithinanegband,whichwasmergedbelowTcfromtwospin-splitbands.Emphasizingtheimportanceoforbitaldegreesoffreedom,deBritoandShiba[ 18 ]attributedthemid-IRabsorptiontoaninterbandtransitionbetweentheegorbitalstates.Millisetal.[ 19 20 ]showedthatthedynamicJTinteractioncouldplayanimportantroleinthespectralweightchanges,andKaplanetal.[ 12 ]associatedthemid-IRfeaturetoaJT-typesmallpolaronabsorption.Theyconcludedthatthe1eVpeakwasduetoaMn3+toMn4+opticaltransition.Thistransitionwasseentobemediatedbythehoppingmatrixelementandwasshowntoberesponsibleforthemetallicconductivityintheferromagneticstate.Kimetal.[ 14 ],proposedthattheevolutionofthelowfrequencymid-IRfeatureatlowtemperaturesasduetoanincoherentabsorptionofalargepolaronstate,whoseexistencewaspredictedbyRoderetal.[ 21 ],withafromacrossoverfromsmalltolargepolaronstates.Themid-IRabsorptionbelowhasalsobeenattributedtophaseseparationscenarios[ 16 22 ].Thebroadwidthofthemid-IRbandisthoughttoindicatethepresenceofaninhomogeneousdistributionofactivesites[ 23 ]duetophaseseparationtendencies.Theargumentisthattheenergiesinvolvedintheopticalprocessesarecompatible 17

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24 ]wheretherelevanceofchargeorderingindeningthelowenergyopticalpropertiescanbeseen.IntheopticalconductivityofLa5=8PryCa3=8MnO3(y=0.35)[ 16 ],itwasseenthataabsorptionbandaround0.2eVand0.4eVappearsbelowTcinadditiontoapeakcenteredat0.8eV.The0.4eVpeakwasinterpretedasduetoachargedisorderedstatepresentbelowTcinthismaterialwiththe0.8eVpeakpresentevenatlowtemperaturewasassignedtoaCOphase.OpticalstudiesonLa7=8Sr1=8MnO3[ 25 ]and(La0:5Pr0:5)0:7Ca0:3MnO3thinlms[ 17 ]havealsosuggestedthatthemid-IRabsorptionwasduetophaseseparation.Figure1-2showsthelowenergyopticalpropertiesofmanganiteswithdierentgroundstatesasafunctionoftemperature.InFigure1-2A,theconductivityofLa0:7Ca0:3MnO3[ 14 ]isshownwherethelowtemperaturegroundstateisferromagneticmetallic.Figure1-2BshowstheopticalconductivityofPr1xCaxMnO3x=0.4,[ 26 ]whichisainsulatoratlowtemperatures.Andnally,Figure1-2CshowstheopticalconductivityofmixedphaseLa5=8PryCa3=8MnO3(y=0.35)[ 16 ].PhasecoexistencecanbeexplainedqualitativelybyanisotropiclatticestraindevelopedinmanganitesduetostrongJTelectroninteraction[ 27 ].NowintheCOstate,itiswellknownthattheanisotropicstrainisquitelargeduetoacooperativeJTdistortionandadz2orbitalordering.Ontheotherhand,inanearlyhomogeneousFMmetallicstate,theJTdistortionbecomessmall.AsTdecreasesbelowTc,theFMphasestartstogrow.IfasingleFMcrystallitenucleatesintoaCOphase,itwillbeunderalargestressfromthesurroundingCOcrystalsthatdiscouragesfurthergrowth.Thendomainsindierentpartsofthecrystalwillformwiththestraineldinrandomorientations,sotheinhomogeneousstraincannotbeeasilyreleased,leadingtophase 18

PAGE 19

28 ].Eectivemediumtheoriestrytodescribesuchsystemsintermsoftheaveragedielectricresponseoftheconstituentparticles.Solongasthescaleonwhichmeasurementsaremade(thewavelength)islargecomparedtothescaleofuctuationsofthedielectricfunction(theparticlesize),theinhomogeneousmediumappearsuniforminitsresponsetoexternaleldsandthusisamenabletodescriptionbyaneectivedielectricfunction.Theapproachdescribedhereisvalidforatwocomponentmediummadeupofsphericalgrains.Therstcomponenthasdielectricfunctionaandispresentwithvolumefractionfwhilethesecondhasbandtheremainingvolumefraction1-f.EMAtreatsallconstituentsinasymmetricwaybyregardinganindividualgrain(whichmaybeeithertypeofmaterial)asbeingembeddedinanotherwisehomogeneous'eective'mediumthatisassumedtopossesstheaveragepropertiesofthemedium.Whenplacedinanexternaleld,thegraininquestionwillbepolarized;TheelectriceldEpinsideaparticleinpresenceofatime-varyingeldEei!tisgivenby[ 29 ] 19

PAGE 20

4p 20

PAGE 21

PhasediagramofLa1xCaxMnO3[ 3 ],and(La1yPry)0:7Ca0:3MnO3[ 6 ] 21

PAGE 22

OpticalconductivityofLa0:7Ca0:3MnO3[ 14 ],Pr1xCaxMnO3x=0.4[ 26 ]and(La1yPry)0:7Ca0:3MnO3[ 16 ] 22

PAGE 23

23

PAGE 24

30 ].The(La1yPry)0:67Ca0:33MnO3(y=0.6)lmdescribedinthisChapterwasgrownonLaAlO3for16min(60nmthick).Temperaturedependentreectancemeasurements(300K-12K)ofboththelmandabaresubstratewereinvestigatedoverafrequencyrangeof30-4400cm1,usingaBruker113vFourierTransformInfraredspectrometerinconjunctionwithacontinuousHeowcryostat.Inthefar-infrared,thedetectorusedwasa4.2KbolometerfromIRLabs.Inthemid-IR,anmercurycadmiumtelluriumdetectorat77Kwasused.Reectanceofthelmwasmeasuredatanintervalofevery20Kbetween300Kand12K.Thetemperaturewasregulatedtobetterthan0.1KwithaLakeshore330Temperaturecontroller.Magneticeldstudiesinthefar-infraredwascarriedoutattheNationalHighMagneticFieldLaboratory(NHMFL).OurmeasurementsusedaBruker66v/sspectrometerandlightpipeopticstochannelthefar-infraredradiationthrougha18Tsuperconductingmagnet.Thesampleprobeusedinthissetupwasdesignedtoaccommodatemultiplesamplesduetothelargebore(about200)ofthesuperconductingmagnet.Thesampleweremountedonawheelwhichcouldberotatedineldfromthetopofthemagnet.Inthereectanceset-up,thedetectorwasplacedinsidethemagnet,abovethesamplewheelontheprobeitself,sothatinputlightreectingfromasamplecouldbedirectlychanneledintothedetector.AnAumirrorwasusedasareferencetocheckforinstabilitiesofthesystemduringmeasurement. 24

PAGE 25

31 ],alsodescribedintheAppendix. 2.2.1.1SubstratepropertiesThesubstrateLaAlO3wascharacterizedbybothtransmittanceandreectancemeasurements.Transmittancewasmeasuredat16temperaturesbetween300Kand12KasseeninFigure2-2.At300K,thetransmittanceisabout30%atthelowestmeasuredfrequencyof30cm1.Withincreasingfrequency,thereisalineardecreaseintransmittanceandataround100cm1,itdropstozero.Anincreaseinthetransmittancetoabout40%at10Kcanalsobeseenatthelowestmeasuredfrequency.Thetemperaturedependentreectancewasalsomeasuredfor16temperaturesbetween300Kand12KasshowninFigure2-3.Theinsetshowsthereectancemeasuredbelow100cm1for300K.Theupturninthemeasuredredcurveisduetoextrareectancefromthebacksurfaceofthesubstrate.Inordertogetthesinglebouncereectanceasshownintheinset,modiedFresnelformulae(describedintheAppendix)wasappliedtothetransmittanceandreectancespectra.Thereectanceat300Kand12Kshowninthemaingraphiscorrectedforbacksidereectancebelow100cm1.Thereisnotemperaturedependenceofthereectanceinthemeasuredspectralregion.Inthefar-IRtworestrahlenbandsbetween100cm1and600cm1areobserved.Thesubstratebecomestransparentabovetheplasmaminimum,ataround1000cm1. 25

PAGE 26

32 33 ]whichpredictavalueintherangeof23-26. 26

PAGE 27

e2Z!c01(!0)d!0(2{2)here!cistheuppercutointhefrequency.Vcellistheunitcellvolume,andm,istheeectivemass.InordertocalculatethetemperaturedependentNeff,thetemperaturedependentvolumeofthepseudo-cubicunitcellwasusedfromstructuralstudies[ 4 ].Additionally,!cwaschosentobe0.5eVandm=me,wheremeisthebaremassof 27

PAGE 28

12 16 17 22 ].Below120K,weseeanincreaseinthespectralweightbelow0.5eV,eventhoughtheresistivityisstillincreasing.ThisisanindicationofthemixedphasecoexistenceattemperaturesabovetheCurietemperature.AsthetemperaturegoesbelowtheCurietemperature,alargeincreaseinNeffcanbeseenwhichshowsnosaturationevenat12Ksuggestingthatmostofthelmmightbeaninsulatingstate. 34 ]canbeseenastheconductivitydata. 28

PAGE 29

1 1R(R R)(2{3)whereRcanbetakenasthedierencebetweenthemeasuredreectanceandthegeneratedreectance.Thusanestimateoftheuncertaintyofthecalculatedconductivityvaluescouldbeobtainedforthettingprocedure.Thefollowingtableillustratestherelativeerrorestimateforsomenominaltemperaturesat100cm1. Table2-1. Relativeerrorestimatefortheextractedopticalconductivity 8% (La1yPry)0:7Ca0:3MnO3,y=0.6Sample(12K) 6% (La1yPry)0:7Ca0:3MnO3y=0.6Sample(18T) 15% 30 ].Thegrowthofspectralweightbeforetheresistancedropindicatesmixedphasecoexistence,withmetallicdomainshavealreadystartedformingeventhoughtheyhavenotyetpercolated.BelowtheCurietemperature,percolationoccursandaclearincreaseinthereectanceassociatedwithantypicalfreecarrierresponseisseen.Howevertheincreaseissmallevenatthelowestmeasuredtemperatureof12K.ThesmallDrudeplasmafrequencyat12KindicatestheexistenceofamixedphaseinagreementwithtransportmeasurementswhichhaveseencoexistenceofCOIandFMMatlowtemperatures[ 34 ]inthinlmsonthesamesubstrate.ThiscanalsobeseenbytheconsiderableincreaseoftheDrudeplasmafrequencyonapplicationofamagnetic 29

PAGE 30

35 ].Thisphaseseparatednatureofthethinlmwasfurthercharacterizedintermsofaneectivemediumtheory.Assumingthe18TresponseasindicativeofaFMMstateandthe300Kresponsetocharacterizetheinsulatingnatureofthelm,thezerofrequencydielectricresponsewascalculated.TheformofEMAasreviewedintheintroductorysection,predictsametal-insulatortransitionatthecriticalvolumefraction(forsphericalgrains)of1 3.Thezerofrequencyeectivedielectricconstantwascalculatedusingthedielectricresponseofthe18Tand300KdataasusingEq.1-3.TheresultsasafunctionofthellingfractionisshowninFigure2-19.Thepeakin1(0)haspreviouslybeeninterpretedindierentways.AccordingtotheHerzfeldcriterion[ 36 ]valenceelectronsareconsideredtobelocalizedaroundnucleiandcontributetoatomicpolarizability.NeartheMItransition,thepolarizabilitydiverges,sothedielectricconstantshoulddiverge.Abovethetransition,therestoringforceofthevalenceelectronsvanishes,resultinginfreecarriers.Another 30

PAGE 31

37 ].Herethepolarizabilityofamediumisproportionaltosquareoflocalizationlength,i.e.,atypicalsizeofthelocalizedwavefunction.SincethelocalizationlengthdivergesneartheMItransition,1shoulddiverge.Additionally,theincreasein1hasbeenattributedtoincreaseintheeectivecapacitivecoupling[ 38 ]betweenthemetallicdomainswheretheanomalyisattributedtoanincreaseintheeectiveareaandadecreaseinthespacingbetweenthemetallicclusters.Theexperimentallydetermined1(0)values,bothasafunctionoftemperatureandmagneticeld,areplottedinFigure2-20.Itcanbeseenthatat60K,rightinthemiddleoftheresistancedrop,thereisapeakinthedielectricfunction.Thisclearlyindicatestheinsulatormetaltransitionat60Khappensthroughapercolationtypeofmechanism.Additionally,wealsoseethatevenatthelowesttemperatures,thevalueof1(0)ispositive.Apurelymetallicphasehasnegative1(0)becauseofthelargeeectoftheDrudeplasmafrequencyon1(0).Thisoccursinthesampleonlyonapplicationofeldsgreaterthan12Twherethe1(0)goesnegative.ThisaddscredencetotheconclusiondrawnfromtheDrudeplasmafrequencyanalysisthattheentirematerialnowismeltedintoametallicstate. 31

PAGE 32

TemperaturedependenttransmittanceofLaAlO3 TemperaturedependentreectanceofLaAlO3.Insetshowscalculatedsinglebouncereectancefromthemeasuredreectanceat300K. 32

PAGE 33

LorentzoscillatortsofLaAlO3reectance ConductivityextractedfromtheLorentzoscillatorbesttsforLaAlO3

PAGE 34

Resistanceofthe(La1yPry)0:7Ca0:3MnO3,y=0.6lm,onLaAlO3.Thetopcurveindicatescoolingwhilethebottomoneisforthewarmingcycle Temperaturedependentreectanceforthe(La1yPry)0:7Ca0:3MnO3y=0.6,lmfrom300Kto120K 34

PAGE 35

Temperaturedependentreectanceforthe(La1yPry)0:7Ca0:3MnO3y=0.6lmfrom120Kto12K Temperaturedependentfar-IRreectanceforthe(La1yPry)0:7Ca0:3MnO3y=0.6lm,below1000cm1. 35

PAGE 36

Lorentzoscillatortsofthe(La1yPry)0:7Ca0:3MnO3y=0.6lm,reectanceatselecttemperatures Conductivityofthe(La1yPry)0:7Ca0:3MnO3y=0.6lm,from300Kto120K. 36

PAGE 37

Conductivityofthe(La1yPry)0:7Ca0:3MnO3y=0.6lm,from120Kto12K EectiveelectronicdensityNeff(!c=0:5eV)asafunctionoftemperature. 37

PAGE 38

Magneticelddependentreectance(La1yPry)0:7Ca0:3MnO3y=0.6lmfrom0Tto18T. FitsgeneratedbyvaryingonlytheDrudetermanditswidth. 38

PAGE 39

Opticalconductivityasafunctionofeld. 39

PAGE 40

SquareoftheDrudeplasmafrequencyasfunctionoftemperatureandeld. Drudescatteringrateasafunctionoftemperatureandeld. 40

PAGE 41

Zerofrequencydielectricconstantasafunctionofmetallicfractionfinatwocomponenteectivemediumapproximationmethod Zerofrequencydielectricconstantasafunctionoftemperatureandeld. 41

PAGE 42

ParametersforLaAlO3 12K 722.3 739.6 183.7 184.8 3.9 2.0 897.2 904.6 429.2 428.5 1.3 3.2 57.3 107.2 495.2 496.7 5.6 18.0 51.3 593.7 5.8 358.5 354.3 652.7 653.2 19.2 10.7 137.7 110.8 686.7 682.6 33.3 38.2 4.4 Thickness 0.6mm 0.6mm 42

PAGE 43

Parametersfor(La1yPry)0:67Ca0:33MnO3,y=0.6onLaAlO3 12K 18T 9348.4 0 736.9 671.9 671.9 198.5 198.5 17.9 17.9 1478.3 1478.3 353.9 353.9 64.4 64.4 1470.7 1470.7 330.1 330.1 141.0 141.0 1631.7 1631.7 594.2 594.2 73.5 73.5 18181.0 2953.6 6813.9 11519.9 11519.9 4354 4354 2579 2579 9 9 Thickness 609.8A 609.8A 609.8A 43

PAGE 44

39 ]similartothatobservedinbulk(La1yPry)0:67Ca0:33MnO3.ButotherbulkpropertiesliketheresistivityanomalyatthechargeorderingtemperatureTCOdisappearinthinlmsduetothestraininducedbythesubstrate[ 30 ].Theeectofthermalexpansionofthesubstratealsoinduceschangesinthegroundstateofthinlms.Thusthelowenergyelectrodynamicswillshedlightonthecombinedeectofsubstrateinducedstrainandsubstitutionaldoping.ThisChapterexploresthisideawiththestudyoftheselmsopticalmeasurements. 34 ],thereisnegligiblelatticestrain(lessthan0.1%)makingitidealtogrowhighqualitythinlmswhicharehomogeneous.Allthelmsdescribedhereweregrownfor45mininanoxygenatmosphereof450mTorratagrowthrateof0.05nm/s.Thenominalthicknessofthelmswasaround135nm. 44

PAGE 45

32 33 ]isintherangeof20-23.FromtheLorentzmodel, 45

PAGE 46

7 ],theresistivitymeasuredat10Kdoesnotchangefromy=0toy=0.5.Itisseentorisesharplyfory=0.6ascanbeseenintheFigure.ForthemanganitelmwithPrconcentrationy=0.4,resistivitydatashownisfora8minwithnominallmthicknessof24nm,whereastheopticalmeasurementsweremadeona45minlmwherethenominalthicknessisaround135nm.HoweverithasbeenobservedthroughresistivitymeasurementsthattheferromagneticTcforthisparticularcompositiondoesnotchangesubstantiallywithvaryingthickness. 46

PAGE 47

47

PAGE 48

15 ].InLa0:67Ca0:33MnO3(Figures3-22and3-23),asystematicincreaseinseenbothintheDrudecomponentandthemid-IRabsorptionasthesystemgoestoitsferromagneticmetallicgroundstate.Thelargeasymmetricmid-IRbandinLa0:67Ca0:33MnO3hasbeeninterpretedasduetolargelatticepolarons[ 14 ]followingthetheoreticalinvestigationsofEminetal.,[ 40 ].Accordingtothetheory,acoherentbandofthelargepolaronshould 48

PAGE 49

49

PAGE 50

LCMO y=0.4 y=0.5 y=0.6 IR 0.21 0.95 1 3.6 Transport 1.5 3 0.8 150 Previously,thediscrepancybetweeninfraredandtransportresistivitymeasurementshasbeeninvestigatedforpolycrystallineLa0:7Ca0:3MnO3samples[ 41 ].TheyattributedtheincreaseobservedintransportasduetotheinuenceofintergranularresistanceseenpredominantintransportdcpropertieswhiletheIRresponsesmayreectintrinsicpropertiesofthegrains.Thekeyideaisthatwhenhighandlowresistiveregionsare 50

PAGE 51

41 ].However,intheIRfrequencies,anincominglighttakesanaverageoveralengthscalethatistypicallyanorderofl=n,wherelisthewavelengthofthelightandnistherefractiveindexofthematerial.Followingthislineofreasoning,andusingthefactthatphaseseparationiny=0.6samplesoccurswithanaveragegrainsizeofabout5-10m[ 34 ],wecanattempttoanswerthedierenceinresistivitydiscrepancy.Therefractiveindexofthey=0.6sampleat20Kwasfoundtobeabout13around100cm1.Withn=13,l=nbecomesabout7.7mat100cm1,whichisquitecomparabletothetypicalgrainsize.Thiscouldbepartoftheexplanationfortheresistancediscrepancy.AmoresubstantialreasonmaybethatintrinsicdisorderinducedbythehigherPrdopingcreatesmorescatteringchannelsforfreecarriersandsuppressesthetransportprocesses.SincetheIRresponseisnotsensitivetotheintergrainresistanceandprovidesintrinsicelectrodynamicpropertieswithinthegrains,theresistancebyinfraredmeasurementsislower. 14 ]usingameaneldtheorybyRoderetal.,[ 21 ].ThetheoryuseddoubleexchangeandJTdistortionsandshowedthatlatticeeectsreducethemagnetictransitionofthesematerials.Additionallytheyalsopredictedthatthemaximaltransition 51

PAGE 52

50[eB(x)]()(3{2)where()representsthepolaronicbandnarrowing.AssumingthattheIRabsorptionbelow0.5eVwasproportionaltothehoppingelementt,Kimetal.,[ 14 ],usedtheabovepicturetoanalyzetheeectiveelectronicdensitybelow0.5eV.Intheirstudy,theNeffcurvesfordierentPrdopingsampleswere'scaled'bytherespectiveCurietemperaturesresultinginasinglescalingcurve.Followingthisidea,thescalingcurveisplottedforthethinlmdataasshowninFigure3-39.Itisclearthatallsamplesfollowasinglescalingcurveexceptforthey=0.6sample.Forthepolycrystallinedata,thereweresmalldeviationsfromthescalingcurveforthelargerPrdopingsamples.Thisbehaviorisampliedinthinlms.Thisbehaviorseemstoberelatedtothedcresistivitybehavior,whereabroaderM-Itransitionexhibitsmixedphasebehavior.Itshouldalsobenotedthatthescalinganalyzeswasnotsatisedintheoxygenisotopeeectstudyof(La0:5Pr0:5)0:7Ca0:3MnO3thinlms[ 17 ].Interestingly,they=0.6curvecanbebroughtbacktothescalingcurveifweassumethattheactualtransitiontemperatureissuppressedby1.5timesthemeaneldtheoryexpectedvalue.ThisisindicatedastheTvalueinplot3-38.ThissuppressionofTc(x)ingeneralhasbeenpreviouslyattributedtothenarrowingoftheelectronicbandwidthduetoelectron-phononcouplingarisingfromthedynamicJahn-Tellerdistortion.AsseeninthecaseofRoderetal.,[ 21 ]andasindicatedbyMillisetal.,[ 43 ]andRodriguez-MartinezandAtteld[ 42 ],theelectron-phononcouplingarisingfromthedynamicJTdistortioncouldinducethebandwidthnarrowingandsuppressTcrapidly.However,ithasalsobeensuggestedthatmechanismsotherthantheelectron-phononcouplingcouldalsoexplainthesamebehavior[ 44 45 ].Inparticular,Radaellietal.,[ 4 ]observedthatthesuppressionofTcwasmoresensitivetothebandwidthnarrowing 52

PAGE 53

45 ].MonteCarlostudieselucidatingtheroleoftheantiferromagneticcorrelationJAF,[ 39 ]inthesuppressionofTcsawalinearrelationshipbetweenthemwithTcdecreasingasJAFwasincreased.Fromtheseresults,theyconcludedthatthechangeinthesuperexchangeinteractionstrengthbetweenthet2gelectronsoftheMnionsisoneofthemechanismsresponsibleforthesuppressioninTcobservedinLa0:7yPryCa0:3MnO3.TherollofJAFinstrainedthinlmsofLa0:7yPryCa0:3MnO3isunderinvestigation.Atthetimeofwriting,acompleteexplanationforthisTcsuppressionisstilllacking. 53

PAGE 54

ReectanceofNdGaO3at300Kand10K.ThedashedlinesaretstotheLorentzmodelforthedielectricfunction. Conductivityspectraat300Kand20KofNdGaO3

PAGE 55

Resistivityofallthelmsmeasuredforthecooling(downwardarrows)andwarming(upwardarrows). 55

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Reectanceat30cm1and160cm1asafunctionoftemperatureincomparisontothedcconductivityobtainedfromtransportmeasurements. 56

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Reectanceat750cm1,2000cm1and4500cm1asafunctionoftemperatureincomparisontothedcconductivityobtainedfromtransportmeasurements. 57

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ReectanceofLa0:67Ca0:33MnO3between30-5000cm1forvarioustemperatures. ReectanceofLa0:67Ca0:33MnO3between30-1200cm1forvarioustemperatures 58

PAGE 59

Reectanceof(La1yPry)0:67Ca0:33MnO3,y=0.4between30-5000cm1forvarioustemperatures. Reectanceof(La1yPry)0:67Ca0:33MnO3,y=0.4between30-1200cm1forvarioustemperatures. 59

PAGE 60

Reectanceof(La1yPry)0:67Ca0:33MnO3,y=0.5between30-5000cm1forvarioustemperatures. Reectanceof(La1yPry)0:67Ca0:33MnO3,y=0.5between30-1200cm1forvarioustemperatures. 60

PAGE 61

Reectanceof(La1yPry)0:67Ca0:33MnO3,y=0.6between30-5000cm1forvarioustemperatures. Reectanceof(La1yPry)0:67Ca0:33MnO3,y=0.6between30-1200cm1forvarioustemperatures. 61

PAGE 62

FitstothemeasuredreectanceofLa0:67Ca0:33MnO3atselecttemperatures,between30-5000cm1. FitstothemeasuredreectanceofLa0:67Ca0:33MnO3atselecttemperatures,between30-1200cm1. 62

PAGE 63

Fitstothemeasuredreectanceof(La1yPry)0:67Ca0:33MnO3,y=0.4atselecttemperatures,between30-5000cm1. Fitstothemeasuredreectanceof(La1yPry)0:67Ca0:33MnO3,y=0.4atselecttemperatures,between30-1200cm1. 63

PAGE 64

Fitstothemeasuredreectanceof(La1yPry)0:67Ca0:33MnO3,y=0.5atselecttemperatures,between30-5000cm1. Fitstothemeasuredreectanceof(La1yPry)0:67Ca0:33MnO3,y=0.5atselecttemperatures,between30-1200cm1. 64

PAGE 65

Fitstothemeasuredreectanceof(La1yPry)0:67Ca0:33MnO3,y=0.6atselecttemperatures,between30-5000cm1. Fitstothemeasuredreectanceof(La1yPry)0:67Ca0:33MnO3,y=0.6atselecttemperatures,between30-1200cm1. 65

PAGE 66

OpticalconductivityofLa0:67Ca0:33MnO3atalltemperatures,between30-4500cm1. OpticalconductivityofLa0:67Ca0:33MnO3atalltemperatures,between30-1200cm1. 66

PAGE 67

Opticalconductivityof(La1yPry)0:67Ca0:33MnO3,y=0.4,from300Kto160K. Opticalconductivityof(La1yPry)0:67Ca0:33MnO3,y=0.4from160Kto20K. 67

PAGE 68

Opticalconductivityof(La1yPry)0:67Ca0:33MnO3,y=0.4,foralltemperatures,between30-1200cm1. (La1yPry)0:67Ca0:33MnO3,y=0.5,from300Kto140K. 68

PAGE 69

(La1yPry)0:67Ca0:33MnO3,y=0.5,from140Kto12K. Opticalconductivityof(La1yPry)0:67Ca0:33MnO3,y=0.5,foralltemperatures,between30-1200cm1. 69

PAGE 70

(La1yPry)0:67Ca0:33MnO3,y=0.5,from300Kto120K. (La1yPry)0:67Ca0:33MnO3,y=0.5,from120Kto12K. 70

PAGE 71

Opticalconductivityof(La1yPry)0:67Ca0:33MnO3,y=0.6,foralltemperatures,between30-1200cm1. 71

PAGE 72

TemperaturedependenceofthephononoscillatorstrengthsofLa0:67Ca0:33MnO3. 72

PAGE 73

TemperaturedependenceofthephononoscillatorstrengthsofLa1yPry)0:67Ca0:33MnO3,y=0.4. 73

PAGE 74

TemperaturedependenceofthephononoscillatorstrengthsofLa1yPry)0:67Ca0:33MnO3,y=0.5. 74

PAGE 75

TemperaturedependenceofthephononoscillatorstrengthsofLa1yPry)0:67Ca0:33MnO3,y=0.6. 75

PAGE 76

TemperaturedependenceoftheDrudeplasmafrequency. 76

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NeffvsTemperature. Scalingcurvesforthemanganitelms. 77

PAGE 78

ParametersforNdGaO3 10K 300K 10K 50.0 281.6 193.0 91.2 301.5 303.5 1.8 12.3 2.6 56.0 25.7 377.7 254.9 116.9 120.4 320.8 321.4 3.2 0.5 19.1 9.4 405.6 503.0 536.1 543.9 173.9 173.3 345.0 343.9 5.1 8.4 9.5 3.2 43.8 317.9 212.6 195.6 356.1 356.2 2.1 9.0 2.8 77.6 219.6 159.4 142.2 243.5 244.6 423.9 425.4 1.8 2.4 10.1 4.8 65.1 226.5 116.3 98.9 256.6 258.3 517.4 516.0 1.3 2.6 18.4 11.8 562.3 641.7 113.2 137.6 275.2 276.4 540.5 547.0 5.4 1.7 30.6 36.0 360.5 349.3 261.3 225.5 290.7 291.5 592.4 591.1 7.8 1.9 26.7 10.8 4.8 Thickness 0.5mm 0.5mm 78

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ParametersforLa0:67Ca0:33MnO3 280K 10173.8 0.0 349.1 822.6 723.4 167.4 165.0 40.9 6.2 1609.8 1058.3 337.0 341.1 176.2 19.2 314.4 373.6 19.0 288.6 247.5 522.6 520.7 11.6 4.9 1098.8 847.0 570.1 574.0 112.6 38.9 12305.3 1405.8 2132.5 6523.8 5817.2 2644.1 4599.6 5432.7 1004.7 13134.2 50156.3 6217.0 7024.1 3996.9 16383.5 8.7 Thickness 1360.9A 1360.9A 79

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Parametersfor(La1yPry)0:67Ca0:33MnO3,y=0.4 300K 20K 1689.3 183.1 106.0 1481.0 343.0 79.9 277.7 391.8 25.6 231.1 521.8 5.2 867.5 584.2 27.7 10354.2 2495.0 5947.5 9216.2 5008.8 3633.0 8.5 Thickness 1371.1 1371.1 80

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Parametersfor(La1yPry)0:67Ca0:33MnO3,y=0.5 300K 12K 873.4 178.8 85.3 1590.1 340.8 79.1 234.0 386.9 10.5 648.1 530.5 31.3 930.5 586.4 21.5 7508.1 1994.5 2971.5 20425.4 6059.4 6039.8 8.4 Thickness 1339.7 1339.7 81

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Parametersfor(La1yPry)0:67Ca0:33MnO3,y=0.6 300K 12K 1180.0 178.3 63.6 1807.6 333.1 83.2 351.7 385.2 12.8 514.8 522.7 16.5 1135.3 572.8 43.4 10191.4 3073.8 5610.4 11773.7 5063.4 3678.9 8.4 Thickness 1352.0 1352.0 82

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30 ].Thiseect,inducedbyanapplicationofanelectriceldtothesampleisadramaticchangeintheresistivityatconstanttemperature,inthephase-coexistenceregion.ThisphenomenonhaspreviouslybeenobservedinmanganitecrystalsofPr1xCaxMnO3(x=0.3)[ 46 ]whereanelectric-eld-inducedcollapseofthelow-temperature,electricallyinsulatingcharge-orderedstatetoametallicferromagneticstatewasseen.Studiesonaepitaxialthinlmof(Pr0:65La0:35)0:7Ca0:3MnO3foundaelectric-eld-inducedinsulator-metaltransition[ 47 ].Theauthorsspeculatedthattheelectriceldmightleadtothegrowthofmetallicclustersduetothepercolativenatureofthetransition.Asystematicstudyoftheeectontheelectriceldon(La1yPry)0:67Ca0:33MnO3thinlms[ 30 ]indicated,thatthemixedphaseshownoincreaseuntilathresholdvoltage,Vthisappliedtothesample.Increasingthevoltagefurthercausesaabruptincreaseinthecurrentthroughthelm.Thethresholdvoltagewasalsoseentodecreasewithdecreasingtemperature.Itwasalsoseenthatthesamplestayedinthelowresistancestateevenwhenthevoltagewasremoved.Onthetheoreticalside,usingadoubleexchangeHamiltonianwiththelong-rangeCoulombinteractionandtheelectriceldincluded,Guetal.,[ 48 ]investigatedtheelectric-eldeectinmanganites.Itwasfoundthattheelectriceldcansuppressthechargeorderingoftheantiferromagneticinsulatorandleadtothemetallicferromagneticstate.Inaddition,takingintoaccounttheintrinsicinhomogeneitiesinthemixedphasemanganites,theyshowedthroughnumericalsimulationsthatthethresholdvoltageneededtopercolatethesystemisreducedasthehighresistanceelementsdecreased,thusqualitativelyagreeingwiththeexperimentalresultsin[ 30 ]. 83

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2p (1g)a+(1gf) (1g)bandC=g 84

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85

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49 ]fordierentpolarizerpositionsalongandperpendiculartothenanotubeaxis.Herehowever,thetrendofnochangeisfurthersupportedinFigures4-18through4-22for52Kandgures4-23through4-27 86

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50 51 ]havebeenperformedwithappliedelectriceldinthemixedphaseregime.Garabinoetal.,[ 50 ]reportedthroughsimultaneousresistivityandmagnetizationmeasurementsthatnoappreciablechangeinthemagnetizationoccurredastheappliedeldwasincreasedbeyondthecriticaleldneededforthepercolationprocess.Inordertoexplainthetemperaturedependenceofthethresholdappliedeld,theauthorssuggestedanappearanceofaconsolute-liketemperature(temperaturebelowwhichtwocomponentsgivehomogeneousresponse)inthemixed-phaseregionthatshouldproduceanomaliesinmanystaticanddynamicpropertiesatatemperatureclosetothresholdappliedeld.Theiranalysisleadtoadivergenceofthelowfrequencydielectricconstantwhichtheyattributedtotheaccumulationofconductingchargesattheinterfaceintheboundarybetweentwophasesatthecriticalpoint.Thevoltage-eldinducedpercolationprocessintheabsenceofanincreaseinfwasinterpretedtobealamentarytypeprocesswiththisscenariobeingcomparedtothedielectricbreakdownofaninsulator,whereconductingdefectsincreasewithincreasingappliedeldtonallyproduceapercolativepath.Adivergingdielectricfunctionwouldleadtoachangeinthemeasuredreectance,butthishasbeenseennottobethecaseintheaboveexperiment.Toclarifythismatterfurther,wesimulatedthereectanceusingthegeneraleectivemediumapproachdescribedintheintroduction.Itcanbeseenthatanincreaseinthemetalfractionfwouldleadtoalargechangeinthereectance.Similarlyadrasticchangeintheshapeofthemetallicdomaininresponsetotheappliedelectriceldwouldcauseconsiderableanisotropyintheabsorptionleadingagaintobigchangesinthereectance.ThiscanbeseeninFigures4-28,4-29and4-30whereamodelreectancecalculation 87

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50 ]. 88

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Resistancemeasurementsforthey=0.6lmwithstraightlinesindicatingthetemperatureregionwhereelectriceldwasapplied. IVofy=0.6samplemeasuredduringtheexperiment. 89

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Unpolarizedreectanceasafunctionofappliedeldat60K. Polarizedreectanceasafunctionofappliedeldat60K(A). 90

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Polarizedreectanceasafunctionofappliedeldat60K(B). Polarizedreectanceasafunctionofappliedeldat60K(C). 91

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Polarizedreectanceasafunctionofappliedeldat60K(D). Unpolarizedreectanceasafunctionofappliedeldat58K. 92

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Polarizedreectanceasafunctionofappliedeldat58K(A). Polarizedreectanceasafunctionofappliedeldat58K(B). 93

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Polarizedreectanceasafunctionofappliedeldat58K(C). Polarizedreectanceasafunctionofappliedeldat58K(D). 94

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Unpolarizedreectanceasafunctionofappliedeldat54K. Polarizedreectanceasafunctionofappliedeldat54K(A). 95

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Polarizedreectanceasafunctionofappliedeldat54K(B). Polarizedreectanceasafunctionofappliedeldat54K(C). 96

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Polarizedreectanceasafunctionofappliedeldat54K(D). Unpolarizedreectanceasafunctionofappliedeldat52K. 97

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Polarizedreectanceasafunctionofappliedeldat52K(A). Polarizedreectanceasafunctionofappliedeldat52K(B). 98

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Polarizedreectanceasafunctionofappliedeldat52K(C). Polarizedreectanceasafunctionofappliedeldat52K(D). 99

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Unpolarizedreectanceasafunctionofappliedeldat50K. Polarizedreectanceasafunctionofappliedeldat50K(A). 100

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Polarizedreectanceasafunctionofappliedeldat50K(B). Polarizedreectanceasafunctionofappliedeldat50K(C). 101

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Polarizedreectanceasafunctionofappliedeldat50K(D). EMAcalculationforsamemetalfractionbutdierentshapefactor. 102

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EMAcalculationfordierentmetalfractionbutsameshapefactor. EMAcalculationfordierentmetalfractionandshapefactor. 103

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52 ]spurredextensiveresearchprovidingacomparativestudytotheirmorefamouscounterparts,thehole-dopedcuprates.Eventhoughconsiderableprogresshasbeenmadeinunderstandingmanyofthepropertiesofbothhole-dopedandelectron-dopedcuprates,thepairingmechanismresponsibleforsuperconductivityisnotclear.Below,abriefoverviewoftheimportantfeaturesofhigh-Tccupratesisgiven.Superconductivityoccurswhentheparentantiferromagnetic(AF)insulatingcompoundsareinjectedwithchargecarrierseitherthroughcationsubstitution(eg.La2CuO4!La2xSrxCuO4),orchangingtheoxygenconcentration(La2CuO4!La2xCuO4+).Thecopperoxide(CuO2)layersarethekeystructuralelementsresponsibleforsuperconductivity.EitherelectronsorholesareaddedtotheseCuO2layersbydopingoroxygenationtohelptriggersuperconductivity.Tobetterunderstandthebasicproperties,thecrystalstructuresoftworepresentativecupratesareshowninFigure5-1.Pr2xCexCuO4(PCCO)hasaT0structurewhereanoxygenatomismissingattheapicalsitesasseenfromthearrowintheFigure.Additionallytheout-of-planeoxygenatomsarenotchemicallybondedtothecopperatomsintheplanes,whichresultinasquarecoordinationfortheCuatom.Ontheotherhand,La2xSrxCuO4(LSCO)hasTstructurewherethecopperatomshaveoctahedralcoordination,surroundedbyfouroxygenatomsinthea-bplane,andtwoapicaloxygensalongthecaxis[ 54 ].Bothstructuresarebody-centeredtetragonal,spacegroupI4/mmm(D174h)[ 53 ].Thesematerialsconsistoftwotwo-dimensionalcopper-oxygenlayer(CuO2)intheunitcell,deningthea-bplane,withthecaxisbeingperpendiculartotheplane.HoledopingoccursinLSCOwhenLa3+cationsaresubstitutedbySr2+cations.Intheelectron-dopedcaseinPCCO,substitutingPr3+byCe4+addsextraelectronstotheCuO2planes. 104

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55 ]calculationspredictsthatthisstatetobeagoodmetal,insharpcontrasttothelargechargetransfergapobservedintheundopedcompounds.AspinpolarizedversionofLDAalsofailstocapturetheantiferromagneticnatureoftheundopedcompounds[ 56 ].Thisfailureismainlyduetobandtheoryignoringtheon-siteCoulombrepulsionUinthesesystems.SincetheelectronicbandwidthWisnarrowerthanthemagnitudeofU,theconductionbandsplitstoformalargegapoftheorderofUwhichisaround4eV.Ondoping,thereisasuppressionofAFcorrelationsleadingtoasuperconductingstate.Figure5-2showsagenericphasediagramofthecuprates.Onthemuchstudiedhole-dopedside,superconductivitysetsinatx=0.05andlastsupto0.30,whiletheelectron-dopedcuprateshaveanarrowerrangeofdopingsforwhichsuperconductivityexists.ThepersistenceoftheAFregionintheelectron-dopedcupratesisstronglyrelatedtothesuppressionofthesuperconductingstate.Figure5-3providesanintuitivevisualizationinthisregard.Onholedoping,thechargecarriersareintroducedonoxygen2porbitalswhichpromoteferromagneticcouplingfortheCu2+ionsadjacenttothepartiallyemptyoxygenorbital,thusresultinginsignicantspinfrustrationsintheCuO2planes[ 57 ],asschematicallyillustratedforaspecicdoping.TheresultingstrongspinuctuationsaretheprimarycausefortherapiddeclineoftheNeelstatewithincreasingholedoping.Ontheotherhand,electrondopinginn-typecupratestakesplaceinthed-orbitalofCu,givingrisetospinlessCu+-ionsthatdilutethebackgroundantiferromagneticCu2+-Cu2+couplingwithoutinducingasstrongspinfrustrationsasthoseinthep-typecuprates[ 58 ],asshownintheFigure.Hence,theNeelstatesurvivesoveralargerrangeofelectrondoping,incontrasttothep-typecuprates,whereasthe 105

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59 60 ].Onfurtherdopingtotheoverdopedrange,conventionalFermiliquidphysicsisseen.Ontheelectron-dopedside,alargeenergypseudogapinseenintheunderdopedmaterials[ 61 ]whichcontinuestilloptimaldoping.Theincreaseinfreechargecarriersinthesystemondopingmodiestheelectronicstructureoftheinsulatinghosts,leadingtoagradualdevelopmentofcoherentDrude-like(metallic)response[ 68 ].Ithasbeenshownthatthesuperconductingresponseprimarilycomesfromthiscoherentresponse.Theincreaseinthesuperuiddensityondoping[ 62 ]hasbeencorrelatedtoanincreaseofthetransitiontemperatureinmanyfamiliesofcuprates.ThisisencapsulatedinthecelebratedUemuraplot[ 63 ]whereitwasreportedthroughmagneticpenetrationdepthmeasurementsthatintheunderdopedregimefordierentfamiliesofcuprates,auniversallinearrelationshipexistsbetweenthetransitiontemperature,Tcandns=mwherensisthesuperuidcarrierdensityandmistheeectivemassofthechargecarriers. 64 { 66 ].Therearealsoexoticinterpretationstotheobservedpropertiesintermsofquantumprotectorate[ 75 ]orideasbasedontheexistenceofaquantumcriticalpointinthehighTccuprates[ 76 ]. 106

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107

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77 ] 78 ]andtotherenormalizedscatteringrate1 1 79 ]andnestedFermiliquidpictures[ 80 81 ].Italsooccursinthed-wavetheoriesofthesuperconductivity[ 82 83 ],wheretheimaginarypartoftheselfenergyforfrequenciessmallerthancuto!cisoftheform, 108

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84 ]andBi2Sr2CaCuO4[ 86 ].Inthetwocomponentmodel,thecontributiontotheinfraredconductivityisassumedtoarisefromtwotypesofchargecarriers:freecarrierswhichgiverisetotheDrude-likecomponentatzerofrequency,withatemperaturedependentscatteringrate,andboundcarrierswhichaccountforthebroadmid-IRband[ 87 ].Inthisapproach,asseenin[ 88 ],almostallofthefreecarrierscondenseintothesuperuidbelowTcwhilethemid-IRcarriersremainunaectedbysuperconductivity.Thedielectricfunctioninthiscaseis, 88 ]hasbeenseenthusraisingquestionsaboutthevalidityofthetwo-componentapproach.Theonecomponentpicturealsorunsintoproblemswhentryingtoexplainthesmallpercentageofnormalcarriersformingthesuperuidcondensate.Thisleadstoanpredictionfortheelectron-phononcouplingparameter4,whichisinconsistentwiththatobtainedthefromfrequencydependenceofthequasiparticledamping. 109

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89 ].Inoptics,josephsonvortexdynamicswereprobedinthec-axismagneto-reectancemeasurementsonLSCO[ 90 ].Inprobingtheab-planeopticalpropertiesofYBCOinhighelds[ 62 ],nosignatureforanyinducedeectat4.2Kwasfoundbutahightemperaturemagneto-opticeectwasobservedwhichwasexplainedtobeduetothethermalmotionofthevorticesinatypetwosuperconductor.Recentlytherehavealsobeenattemptstoquantifytheeectofmagneticeldontheelectron-bosoncouplingfunction2F(!)[ 91 ].Theauthorsusedthechangesseenthroughneutronscatteringtoplaceanupperboundon2F(!).Theythenback-calculatedtheexpectedreectancechangesineldsupto18Tandpredictedamaximumof10%changeat18T.Sincenochangeineldwasobservedwithinthesignaltonoiseof2%,theyconcludedthattheelectron-bosonspectralfunctionisweaklycoupledtomagneticexcitations.Inhole-dopedcuprates,theuppercriticaleldsneededtodestroysuperconductivityareoftheorderofhundredsofTeslamakingitunfeasibleatthepresenttimetoinvestigatethenormalstatepropertiesinthesesystems.Ontheotherhand,intheelectron-dopedcase,sincetheHc2'sareoftheorderofafewTesla,itispossibletoaccessthenormalstatebelowTcandquantifythenatureofthetruegroundstateinelectron-dopedsystems.Followingisabriefsummaryofthemainopticalpropertiesofelectron-dopedcupratesinzeroeld.Opticalpropertiesofelectron-dopedcuprateshavebeeninvestigatedbyanumberofpeople,[ 61 85 ]oftheab-planeopticalpropertiesofelectron-dopedcuprates.ThemainconclusionofthedopingdependentstudywasthatinunderdopedcrystalsofNd2xCexCuO4(fromx=0.05-0.10)thereisastronggaplikefeatureintheoptical 110

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61 ]attributedthislargeenergypseudogaptotheAFcorrelationsintheCuO2plane.Inaddition,theenergyscaleofthisgapwasseentobethesameasinARPESmeasurements[ 92 ]where,inthespectraoftheunderdopedregime,apseudogapwasobservedataround(=2;=2)inthetwodimensionalfermisurface.HencetheyconcludedthatthegapseeninopticswasthesameasobservedinARPES.Incontrast,inhole-dopedcuprates,asignatureofthepseudogaphasneverdirectlybeenseenintheab-planeopticalspectra.Thereappearsaknee,however,intheopticalscatteringrateath=8kbTcwhichhasbeenattributedtocomplexinteractionsbetweenthesuperconductinggap,thepseudogapandthebosonmodethatdominatesthetransportscatteringprocesses[ 93 ].OtheropticalstudiesonthinlmsofPCCO[ 94 ]extendedthestudytooverdopedmaterials.Theyproposedaspindensitywavemodeltoexplaintheappearanceofthelargeenergypseudogapseenintheunderdopedmaterials.Inadditiontheopticalconductivitywasmodeledinatightbindingapproach[ 95 ]wheretheenergydispersionrelationwas 111

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103 ].TheprocessinvolvedusinganExcimerlaser(wavelength248nm)toirradiateceramicpelletsofvariouscompositionsofPCCOatapressureof200mTorrofN2Owhichwasusedasthereactivegas.Theplumefromtheirradiatedpelletswasfocussedontosubstratesheldat850oCwhiledepositingthelms.Theannealingtimewasbetween0-2min.Thesampleswerethencooledtoroomtemperatureinthechamberinavacuumof105Torrwithin2h.FourlmsonLSGOwithdopingsx=0.11(nonsuperconducting),x=0.15(optimallydoped,Tc=19.23K),x=0.17(overdoped,Tc=12.3K)andx=0.18(Tc=7.6K)wereprepared.OnthesubstrateSTO,threelmsofcompositionx=0.11(nonsuperconducting),x=0.15(optimallydoped,Tc=20K)andx=0.19(Tc=6K)weresynthesized.Temperaturedependent(10-300K)transmittancemeasurementswereperformedbetween1000-5000cm1fortheLSGObasedlmsusingaBruker113vFourierTransformspectrometerequippedwithacontinuousowheliumcryostat.Thedetectorusedwasamercurycadmiumtelluriumoperatingat77k.StudiesinmagneticeldwerecarriedattheNationalMagneticFieldLaboratory(NHMFL)inTallahassee,FL.ThemeasurementsinvolveduseofaBruker113vspectrometerequippedwithlightpipeopticstochannelthelightthroughthemagnet.Superconductingmagnetswereusedtoaccesseldsupto18Twhereasresistivemagnetsallowedustoreacheldsupto33T.[ 104 ]Duetothelargeboreofthesuperconductingmagnet(2-inchdiameter),thesampleprobecouldaccommodate 112

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96 ].Thispreventsmeasuringthetransmittanceofthelmsbelowthisfrequencyrange.Figure5-4showsthetransmittanceoftheunderdopedsample.Asignicanttemperaturedependenceisseen.Withdecreasingtemperature,thetransmissionbelow2600cm1increasesconcomitantlywithdecreaseabove2600cm1.ThedashedlinesaremodeltstothetransmittanceusingtheDrude-Lorentzformofthedielectricfunctionusingmultilayerthinlmoptics(SeeAppendix).Thesuperconductinglms,startingwiththeoptimallydopedone,showsystematicdecreaseintransmittanceasthetemperatureisloweredfrom300Kto10Kasseenin 113

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114

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T T'1 2 (5{11)whereTcanbetakenasthedierenceintransmittancebetweenthemeasuredtransmittanceandthegeneratedtransmittance.Thusanestimateoftheuncertaintyofthecalculatedconductivityvaluescouldbeobtainedfromthettingprocedure.Thefollowingtableillustratestherelativeerrorestimateforsomeallthesamplesat!=1300cm1. Table5-1. Relativeerrorestimatefortheextractedopticalconductivity 15% 17% 10% 8% .InFigure5-14,theopticalconductivityofx=0.11sampleisshown.Weseeacharacteristichump-dipstructure,wherespectralweightbelow2700cm1decreaseswhilespectralweightabove2700cm1increases.ThischaracteristicsuppressionoflowfrequencyspectralweightandupturninhighfrequencyissimilartowhatisobservedintraditionalspindensitywavesystemslikeCr[ 97 ]. 115

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98 ],butthishasnotbeenseeninopticalconductivityderivedfromreectancemeasurements.Transmittancemeasurementsaremuchmoresensitivetosmallchanges,sothefeatureseenintheconductivityspectrumcouldbeascribedtotheexistenceofaweakgapinthesystem.Howeverthelargeerrorsbarsduetothettinginthisspectralrangeunambiguously,simultaneousreectancemeasurementsareneededtoinordertoremovetheuncertaintiesintroducedduetothettingprocedurespreventusfromconrmingtheexistenceofagapstructureinthissample.Thex=0.17(Figure5-16)andx=0.18(Figure5-17)samplesshowincreasingconductivityinthemid-IRwithoutanysignofdecreaseintheirspectralweights.Thecorrelateswiththedisappearanceofthegapintheoverdopedlms.Thesezeroeldtransmittancespectraattesttothegoodqualityofthelmsandareconsistentwithpreviousresults.Nowweturntothemagneticeldresults.Theabsenceofanychangeineithertransmittanceorreectanceispuzzling.Theinsensitivityinhigheldshastwoislookedatintwospectralregions.1.Thelargeenergygapinsensitivitytomagneto-transmissioninthemid-IR2.Thefar-IReldinsensitivityseeninreectance.Weexploretherstresultanditsimplicationsbelow.Inpreviousstudies,thex=0.11,nonsuperconductingsamplehasshowntemperaturedependenttransferofspectralweightfromthemid-IRtotheDrudepeakatzerofrequency.NowwithmagneticeldsuppressingtheDrudepeak,thereisnoresultanttransferofspectralweighttothemid-IRregime.Inadditiontheenergyofthemaximumeldof33Tisabout5meV,whereastheantiferromagneticuctuationJisoftheorderofthegap,about100meV.Thiscouldsuggestthattheuppereldsof33Taccessedintheseexperimentsaretoolowtobringaboutaspectralweighttransferinthespingap. 116

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99 ]foundthatlongrangeorderedAFMvanishesneartheSCdomeboundary,x=0.13.TheyclaimthatSCandAFMdonotcoexistandthatthequantumcriticalpointoccursatx=0.13,whichdiersfromtheresultsasobtainedfromrecentHallmeasurements[ 100 ]whereanonlinearHallresistivityathigheldaboveoptimaldoping.ThisbehaviorwasinterpretedqualitativelyintermsofaspindensitywaveinducedFermisurfacerearrangement.IftheAFMandSCcoexistbelowTc,thenthedestructionofsuperconductivitybyapplyingeldsgreaterthanHc2inoptimaldopedsamplesshouldshowclearsignaturesintransmittanceasindicatedabove,butthisisnotthecase.Thisissueisfarfromsettledandthedatapresentedhereprovidesinputforvariousscenariosputforthtoexplaintheexistenceofquantumphasetransitionsinthissystem.Incaseofoverdopedsamplesx=0.17andx=0.18,theirHc2'sareverysmall,theresultofturningthesesamplescompletelynormalwouldaddspectralweightfromthedeltafunctionandthisshouldspreadouttonitefrequencies,butnosuchchangeisobservedinthemid-IR. 117

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101 ].Thisgapdecreasesbyabout10%whenthelmisdrivencompletelynormalineldsupto33TalongwithbroadeningoftheZeroBiasConductancepeak(ZBCP).Currentlythereiscontroversyabouttheoriginofthisweaknormalstategap.Themagneto-opticalreectanceforbothx=0.15andx=0.19inthefar-IRshowednochanges.Inanycasetheseresultspointtoaqualitativedierenceinthegroundstatefeatureswhencomparedtohole-dopedmaterialswhichhavecompetingorders[ 89 ]. 118

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ComparativeStructureofhole-dopedPCCOandelectron-dopedLSCO. Electronandhole-dopedphasediagramasafunctionofdoping. 119

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Dierenceinchargecarrieroccupationsbetweenholeandelectrondoping. Temperaturedependenttransmittancespectraandtsforx=0.11. 120

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Temperaturedependenttransmittancespectraandtsforx=0.15. Temperaturedependenttransmittancespectraandtsforx=0.17. 121

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Temperaturedependenttransmittancespectraandtsforx=0.18. Fielddependenttransmittancespectraforx=0.11. 122

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Fielddependenttransmittancespectraforx=0.15. Fielddependenttransmittancespectraforx=0.18. 123

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Fielddependentreectancespectraforx=0.11. Fielddependentreectancespectraforx=0.15. 124

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Fielddependentreectancespectraforx=0.19. Temperaturedependentopticalconductivityforx=0.11. 125

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Temperaturedependentopticalconductivityforx=0.15. Temperaturedependentopticalconductivityforx=0.17. 126

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Temperaturedependentopticalconductivityforx=0.18. 127

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128

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50 ].Itisalsoconsistentwithmagnetizationmeasurementswhichdonotseeanyincreasebyapplicationofanelectriceldatxedtemperature. 129

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130

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131

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Temperaturedependentreectanceofa5000Almfrom300Kto120K. Temperaturedependentreectanceofa5000Almfrom120Kto11K. 132

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31 ] tan=2 cd(B{5)Thesearegeneralequationsthatincludeinterferenceeectsduetothesubstrate.Forthecasewheretheperiodicinterferencefringesareremovedeitherbyalowresolutionmeasurementorthroughsmoothingoftheacquireddata,theaveragescanbefoundbyintegratingEqs.(1)and(2)yieldoverd,togive, 133

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~n0Ei0~n0Er0=~n1Ei1+~n1Er1(B{12)Atthesecondinterface: 134

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135

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~nk=nk+ik=p 136

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d2t+d~x dt+!20=e~Eloc(~x;t) 137

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105 106 ].Sincethecomplexdielectricfunctionisgivenby, ~=1+4~e=1+4Ne2=m !20!2i!(B{34)theaboveformofthedielectricfunctioncanbegeneralizedtoincludefreecarrierdynamicsbysimplysetting!0=0.Astherearenodampingeectsonfreeelectrons,otherthancollisionsbetweenthemselvesorcollisionswithphononsorimpurities,wecanreplacethedampingtermbyaterm1/DwhereDsigniestheaveragerelaxationtimebetweencollisions.AdditionallypermittingvariableelectronicdensityNjanddierentresonantfrequencies!j,theDrude-Lorentzformulacanbewrittenas, 138

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107 ]calculatesamodelreectancebasedonthematrixequationsgivenabove.Itisaniterativeprogramwhichminimizesthe2betweentheacquireddataandthecomputedonebasedonamodiedleastsquaresroutineduetoBevington[ 108 ].Forthecaseofsubstrates,whichareinsulators,thedielectricfunctionwasmodeledwithjusttheLorentzterm.Forthelms,thecompleteformoftheDrude-Lorentzformwasused,withtheDrudepartaddedtoaccountforthefreecarrierresponse.Tocalculatetheoptimalparametersforthesubstrateisrelativelystraightforward.Therststepcaneitherconsistofparameters(!pj;!j;j)whichcanbeguessed(forexample!jcanbeguessedtobeintherisingparttothereectance)orbetterinitialestimatescanbegotfromtheopticalconductivityspectraobtainedthroughKramers-Kroninganalysisofthesubstratereectance.Inthecasethecenterfrequencieswereguessedtobeintherisingpartofthereectancedata,verynarrowlinewidthsweregivenandtheprogramwasallowedtondoptimalvaluesfortheoscillatorstrengthwhilekeepingtheinitialguessofcenter 139

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140

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NaveenMargankuntewasborninIndiain1979.MostofhiseducationwasinasmallgoldminingtownofKolarGoldFields(KGF).AftercompletinghisB.Scinphysics,chemistryandmathematicsfromSt.JosephsCollegeinBangalore,hewentontopursuehismaster'sdegreeattheIndianInstituteofTechnologyinBombay(nowMumbai).Subsequently,hegotintograduateschoolattheUniversityofFloridaandjoinedProfessorDavidTanner'sgroupinhisthirdyearwherehelearnttheexperimentaltechniquesofopticalspectroscopyandusedittostudymanganitesandcuprates.Hisinterestsincludefoodandcricket. 148