Magnetic Oxides

473 Pages·2009·6.616 MB·English

by  Gerald F. Dionne (auth.)

Magnetic Oxides
Gerald F. Dionne
Magnetic Oxides
123
GeraldF.Dionne
MassachusettsInstituteofTechnology
244WoodStreet
Lexington,MA02420
[email protected]
ISBN978-1-4419-0053-1 e-ISBN978-1-4419-0054-8
DOI10.1007/978-1-4419-0054-8
Springer NewYorkDordrechtHeidelbergLondon
LibraryofCongressControlNumber:2009935694
(cid:2)c SpringerScience+BusinessMedia,LLC2009
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Printedonacid-freepaper
SpringerispartofSpringerScience+BusinessMedia(www.springer.com)
Theauthordedicatesthisbookto
Rev.HughMcPhee, S.J.,
formerDean ofScienceat LoyolaCollege
inMontreal,
who onceadviseda liberalartsstudent
thatsciencecouldoffer aclearer window
ontheworld.
Preface
Theinspirationsforthisbookprobablybeganin1961whenIleftapromisingcareer
as a semiconductordeviceengineerin the Rte 128 cauldronof the Boston area to
pursuea newchallengeatthe McGillUniversityEatonElectronicsResearchLab-
oratory.Three yearslater I wrote a Ph.D. thesis on paramagneticresonanceand3
yearsafterIwasaddingtothatexperienceasaStaffMemberwithMITLincolnLab-
oratory, where the scope of my obligations gradually broadened from microwave
magnetic resonance to the physics and chemistry of ferrites and related magnetic
oxidesystems.Atthetimeofthiswriting,Icontinuethereasaresidentconsultant
andalsoasa researchaffiliatewith theMITDepartmentofMaterialsScienceand
Engineering.
Magnetic resonance has played a vital role in the study of magnetism in ox-
idesandotherinsulatingcompoundsthatbeganduringWorldWarIIandflourished
globallyfora quartercentury.Duringthishalcyonperiod,textsonmagnetismbe-
came abundant as many of the pioneers took pen in hand to leave a treasure of
elegantly presented reference literature as the 1960s drew to a close. By the mid-
1970s, the once-fledglingfield of semiconductorelectronicsthat I had abandoned
wasoverwhelmingalmostallcompetingtechnologies,includingthosewithamag-
netic component. For the better part of the two decades between the end of the
Vietnam war and the discoveriesof high-temperaturesuperconductivityand giant
magnetoresistanceintransition-metaloxidesintheearly1990s,fundamentalinves-
tigationsofmagneticcompoundswerenearlydormant.
Thecontentandorganizationofthisvolumeareintendedtoservetwopurposes:
(1) bridging of the intellectual gap left by the 20 years of reduced inquiry into
magnetic phenomena, and (2) restoration of the molecular approach to the study
ofmagneticinsulatorsthatfunctionmorebylocalratherthanthecollectiveelectron
interactionsthataremorecharacteristicofmetalsandsemiconductors.
Thelevelofdiscussionpresumesthereadertohavesomefamiliaritywithatomic
physicsandbasic quantummechanics.Chapter1isanabbreviatedintroductionto
magnetism.Thediscussionbeginswithareminderofsomefundamentaldefinitions
and selected subjectsthatcan be foundin moststandardtextbooks.However,two
topicsaretreatedingreaterdepth.Agenericdescriptionofthequantumoriginsof
magneticexchangeintroducestheantisymmetryrequirementsofthehybrideigen-
states that determine the stabilization of parallel (metal) or antiparallel(insulator)
vii
viii Preface
spin alignment. This general theory is intended to support the later discussion of
superexchange that is approached with a model that is more specific to magnetic
oxides.Anintroductiontomagneticresonanceandrelaxationderivedfromclassical
Larmorprecessionservesasimilarpurposefortheexaminationofthebroadsubject
ofelectromagnetisminferrites.The physicsandchemistryofmagnetisminoxide
compoundsiscoveredinChaps.2,3,and4intermsoflocalizedionandmolecular-
orbitalmodelsofmolecularbonding.Chapter5addressesthesecondarymagnetic
phenomenaofanisotropyandmagnetostrictionfromthestandpointoflocalorbital
interactions with crystal fields and spin–orbitcoupling that producesself-induced
magnetoelastic effects. Traditional phenomenological theories are then reviewed
in preparation for the examination of electromagnetic properties in Chap. 6. In
Chaps. 7 and 8, magneto-optics and polarized spin transport that will be of in-
creasing importance in the age of molecular-scale structures are described in the
conceptualcontextoftheearlierchapters.
As the preparationof this monographdrawsto a close, I reflecton the journey
that brought me to this point. From the frequency of their citations, the reader is
certaintorecognizetherelianceontheseminalworksofJohnVanVleck,Maurice
Pryce,JohnGoodenough,andErnstSchlœmann,aswellastheclassictextbooksof
AlanMorrish,SoNshinChikazumi,CarlBallhausen,BenjaminLaxandKennethBut-
ton,andmanyothers.Therewerealsocollaborationswithacademia,industry,and
governmentthat are too numerousto list in anydetail. However,I cannotpass up
thisopportunitytoacknowledgetheguidanceofmydoctoralthesisadvisorGarnet
WoontonandhiscolleagueMauricePrycewhowasamostencouragingexternalex-
aminer.LincolnLaboratory’sradarleadersJohnAllen,CarlBlake,DonaldTemme,
and Roger Sudbury who supported me and my vigorouscolleagues Jerald Weiss,
JamesFitzgerald,DanielOates,andRussellWest(ofTrans-Tech,Inc.).Thenthere
was the mentorshipof JohnGoodenoughandBenjaminLax andthe MIT campus
affiliationswithMildredandGeneDresselhaus,andCarolineRoss.Finally,Imust
mentiontheassociationswithKristlHathaway,GaryPrinz,andStuartWolfofthe
USDepartmentsof theNavyandDARPA, andthe assistance ofElaineThamand
LaurenDanahyofSpringerUS.
Lexington GeraldF.Dionne
MA
Contents
1 IntroductoryMagnetism...................................................... 1
1.1 FundamentalConceptsandDefinitions ............................... 1
1.1.1 BasicElectrostatics............................................. 2
1.1.2 BasicMagnetostatics........................................... 3
1.1.3 DemagnetizationinUniformlyMagnetizedBodies.......... 4
1.1.4 DomainsinPartiallyMagnetizedBodies ..................... 6
1.2 InducedMagnetism..................................................... 8
1.2.1 DiamagnetismandParamagnetism............................ 8
1.2.2 TemperatureDependenceofSusceptibility................... 11
1.3 SpontaneousMagnetism ............................................... 15
1.3.1 ClassicalFerromagnetismandAntiferromagnetism.......... 15
1.3.2 SolutionsoftheBrillouin–WeissEquation ................... 16
1.3.3 QuantumOriginsoftheMolecularField ..................... 19
1.3.4 TheIsingApproximation...................................... 24
1.4 Gyromagnetism......................................................... 25
1.4.1 LarmorPrecessionandResonance............................ 26
1.4.2 PhenomenologicalRelaxationTheory ........................ 27
1.4.3 ComplexSusceptibilityTheory................................ 29
1.4.4 ResonanceLineShapes........................................ 33
Appendix1A Spin–LatticeContributiontoLinewidth ..................... 34
References....................................................................... 35
2 MagneticIonsinOxides ...................................................... 37
2.1 TheTransitionMetals.................................................. 37
2.1.1 ThePeriodicTable ............................................. 38
2.1.2 IronGroup3dnIons........................................... 40
2.1.3 RareEarth4fn Ions............................................ 42
2.1.4 4dnand5dnIons.............................................. 42
2.2 OxygenCoordinations ................................................. 43
2.2.1 CrystalSystemsandPointGroups ............................ 44
2.2.2 CubicSymmetry ............................................... 45
2.2.3 LowerSymmetries............................................. 47
2.3 CrystalElectricFields.................................................. 48
2.3.1 AngularMomentumStates .................................... 49
ix
x Contents
2.3.2 CrystalFieldHamiltonian ..................................... 50
2.3.3 HierarchyofPerturbations..................................... 54
2.3.4 Weak-FieldSolutions .......................................... 55
2.3.5 GroupTheoryandLowerSymmetry.......................... 64
2.3.6 StrongFieldSolutionsandTermDiagrams................... 68
2.3.7 Rare-EarthIonSolutions....................................... 71
2.4 OrbitalEnergyStabilization ........................................... 73
2.4.1 One-ElectronModel ........................................... 73
2.4.2 High-andLow-SpinStates.................................... 75
2.4.3 Orbit–LatticeStabilization(Jahn–TellerEffects)............. 79
2.4.4 Spin–Orbit–LatticeStabilization .............................. 82
2.5 CovalentStabilization.................................................. 88
2.5.1 Molecular-OrbitalTheory...................................... 89
2.5.2 DeterminantMethod........................................... 91
2.5.3 (cid:2) and(cid:3) BondsandtheMolecularOrbitalDiagram.......... 95
2.5.4 ValenceBondMethod.......................................... 99
Appendix2A HomonuclearMoleculeIon...................................102
Appendix2B Valence-BondDiatomicMolecule ...........................103
References.......................................................................105
3 MagneticExchangeinOxides................................................107
3.1 InterionicMagneticExchange.........................................108
3.1.1 Molecular-OrbitalExchangeApproximation.................109
3.1.2 Valence-BondSolutions .......................................113
3.1.3 SpinAlignmentinOxides .....................................119
3.1.4 FerromagnetismbySpinTransfer.............................121
3.1.5 Goodenough–KanamoriRules.................................125
3.2 Antiferromagnetism....................................................129
3.2.1 SuperexchangeandMolecularFields .........................129
3.2.2 MolecularFieldTheoryofAntiferromagnetism..............131
3.2.3 AntiferromagneticSpinConfigurations.......................135
3.3 AntiferromagneticOxides..............................................139
3.3.1 One-MetalOxides..............................................139
3.3.2 ABO andA BO Perovskites...............................140
3 2 4
3.3.3 TheMixed-ValenceManganiteAnomaly.....................143
Appendix3A AnalysisofM2CO2(cid:2)ExchangeInteractions................146
Appendix3B CurieTemperatureModelfor(La,Ca)MnO ................147
3
References.......................................................................149
4 Ferrimagnetism................................................................151
4.1 FerrimagneticOrder....................................................151
4.1.1 GenericFerrimagneticSystems ...............................152
4.1.2 MolecularFieldTheoryofFerrimagnetism...................153
4.1.3 MagneticFrustrationandSpinCanting.......................157
Contents xi
4.2 TheoryofSuperexchangeDilution....................................161
4.2.1 SuperexchangeEnergyStabilization..........................161
4.2.2 MolecularFieldCoefficients...................................164
4.2.3 SolutionforYttriumIronGarnet..............................165
4.3 FerrimagneticOxides...................................................168
4.3.1 SpinelFerritesAŒB (cid:4)O ......................................169
2 4
4.3.2 GarnetFerritesfc gŒa (cid:4).d /O .............................175
3 2 3 12
4.3.3 Rare-EarthGarnetFerrites.....................................180
4.3.4 Rare-EarthCantingEffect .....................................184
4.3.5 HexagonalFerrites .............................................190
4.3.6 Orthoferrites....................................................193
Appendix4A MolecularFieldAnalysisofLiZnTiFerrite .................193
Appendix4B High-MagnetizationLimits...................................195
Appendix4C BrillouinFunctionsinExchangeEnergyFormat............196
References.......................................................................197
5 AnisotropyandMagnetoelasticProperties.................................201
5.1 QuantumParamagnetismofSingleIons ..............................202
5.1.1 TheoryofAnisotropicgFactors...............................202
5.1.2 ConventionalPerturbationSolutions..........................205
5.1.3 TheSpinHamiltonianfor3dnIons ...........................209
5.1.4 TheCrystal-FieldHamiltonianfor4fn Ions..................210
5.2 AnisotropyofSingleIons..............................................212
5.2.1 3d1and3d6D-StateTriplet..................................213
5.2.2 3d4and3d9D-StateDoublet(J–TEffect)...................217
5.2.3 3d2and3d7F-StateTriplet...................................219
5.2.4 3d3and3d8F-StateSinglet...................................220
5.2.5 3d5S-StateSinglet.............................................222
5.2.6 4fn IonAnisotropy............................................226
5.3 MagnetocrystallineAnisotropyandMagnetostriction................228
5.3.1 PhenomenologicalAnisotropyTheory........................229
5.3.2 PhenomenologicalMagnetostrictionTheory .................231
5.3.3 DipolarPairModelofMagneticAnisotropy..................234
5.3.4 Single-IonModelofFerrimagneticAnisotropy ..............236
5.3.5 CooperativeSingle-IonEffects:Anisotropy..................241
5.3.6 CooperativeSingle-IonEffects:Magnetostriction............246
5.4 MagnetizationProcessandHysteresis.................................250
5.4.1 InitialPermeabilityandCoercivity............................251
5.4.2 AnisotropyFieldandRemanenceRatio.......................254
5.4.3 ApproachtoSaturation ........................................256
5.4.4 DemagnetizationandPermanentMagnets....................258
Appendix5A Four-LevelDegeneratePerturbationSolution
ford1....................................................................261
xii Contents
Appendix5B T Solutionford1inanExchangeField....................263
2g
Appendix5C OrbitalStatesofd5inaCubicField.........................265
Appendix5D AngularDependenceofCubicAnisotropyFields...........267
References.......................................................................269
6 ElectromagneticProperties...................................................273
6.1 MagneticRelaxation ...................................................274
6.1.1 NonresonantLongitudinalRelaxation ........................274
6.1.2 QuantumMechanismsofSpin–LatticeRelaxation...........278
6.1.3 PerturbationTheoriesofSpin–PhononInteraction...........286
6.2 GyromagneticResonanceandRelaxation.............................287
6.2.1 ParamagneticResonance.......................................288
6.2.2 FerromagneticResonance .....................................292
6.2.3 UniformPrecessionDamping .................................295
6.2.4 InhomogeneousResonanceLineBroadening.................297
6.2.5 Fast-RelaxingIonEffects......................................300
6.2.6 TheExchangeIsolationEffect.................................306
6.3 Exchange-CoupledModes(SpinWaves)..............................307
6.3.1 UniformPrecessionDecoherence(Degenerate
SpinWaves) ....................................................307
6.3.2 InstabilityThreshold(ClassicalApproximation).............311
6.3.3 InstabilityThreshold(NonlinearSpinWaves)................315
6.3.4 MagnetostaticModes ..........................................317
6.4 PermeabilityandPropagation..........................................318
6.4.1 Low-FrequencyLongitudinalPermeability...................318
6.4.2 High-FrequencyTransverseLimits............................322
6.4.3 Snoek’sLawConsiderations...................................324
6.4.4 CircularPolarizationandNonreciprocalProperties..........327
6.4.5 LinearPolarizationandFaradayRotation.....................332
Appendix6A TransversePermeabilityTensor..............................333
Appendix6B ClassicalInstabilityThreshold ...............................336
Appendix6C DomainWallSusceptibilityEquation........................338
References.......................................................................340
7 Magneto-OpticalProperties..................................................343
7.1 InfraredExchangeResonance .........................................344
7.1.1 ClassicalPrecessionModel....................................344
7.1.2 QuantumSpinTransitionModel ..............................346
7.1.3 ExperimentalExchangeSpectra...............................351
7.2 CombinedPermeabilityandPermittivity..............................352
7.2.1 The["](cid:2)[(cid:5)]TensorSolutions..................................352
7.2.2 PropagationParametersandFaradayRotation ...............353
7.3 Magneto-OpticalSpectra...............................................355
7.3.1 Electric-DipoleTransitions....................................355
7.3.2 YttriumIronGarnetSpectra(Paramagnetic) .................360