The Physics of Dilute Magnetic Alloys

276 Pages·2012·2.19 MB·English

by  Jun Kondo

ThePhysicsofDiluteMagneticAlloys
Available for the first time in English, this classic text by Jun Kondo describes the
Kondoeffectthoroughlyandintuitively.Itsclearandconcisetreatmentmakesthisbook
ofinteresttograduatestudentsandresearchersincondensedmatterphysics.
Thefirsthalfofthebookdescribestherudimentsofthetheoryofmetalsatalevelthat
isaccessibleforundergraduatestudents.Thesecondhalfdiscusseskeydevelopments
in the Kondo problem, covering topics including magnetic impurities in metals, the
resistance minimum phenomenon, infrared divergence in metals and scaling theory,
includingWilson’srenormalizationgrouptreatmentandtheexactsolutionbytheBethe
ansatz.AnewchapterhasbeenaddedcoveringadvancesmadesincetheJapaneseedition
waspublished,suchasthequantumdotandheavyfermionsystems.
jun kondo is Emeritus Professor of Toho University and Special Advisor at the
NationalInstituteforAdvancedIndustrialScienceandTechnology(AIST),Japan,and
a Member of the JapanAcademy. He is well known for solving the problem of the
resistance minimum phenomenon, now known as the Kondo effect. Theoretical and
experimentalstudiesinthisfieldcontinuetoday,andnewapplicationsforthetheoryare
stillbeingfound.

The Physics of Dilute Magnetic Alloys
JUN KONDO
MemberoftheJapanAcademy,Japan
Translatedby
ShigeruKoikegami,SecondLab,LLC
KosukeOdagiri,NationalInstituteofAdvancedIndustrialScienceand
Technology
KunihikoYamaji,NationalInstituteofAdvancedIndustrialScienceand
Technology
TakashiYanagisawa,NationalInstituteofAdvancedIndustrialScienceand
Technology
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©J.Kondo2012
Thispublicationisincopyright.Subjecttostatutoryexception
andtotheprovisionsofrelevantcollectivelicensingagreements,
noreproductionofanypartmaytakeplacewithoutthewritten
permissionofCambridgeUniversityPress.
Firstpublished2012
PrintedintheUnitedKingdomattheUniversityPress,Cambridge
AcatalogrecordforthispublicationisavailablefromtheBritishLibrary
LibraryofCongressCataloginginPublicationdata
Kondo,Jun,1930–
Thephysicsofdilutemagneticalloys/JunKondo;translatedby
ShigeruKoikegami...[etal.].
p. cm.
Includesbibliographicalreferencesandindex.
ISBN978-1-107-02418-2(hardback)
1. Dilutealloys. 2. Magneticalloys. 3. Kondoeffect. 4. Freeelectrontheory
ofmetals. I. Title.
QC176.8.M3K66 2012
538(cid:1).4–dc23 2012014479
ISBN978-1-107-02418-2Hardback
CambridgeUniversityPresshasnoresponsibilityforthepersistenceor
accuracyofURLsforexternalorthird-partyinternetwebsitesreferredtoin
thispublication,anddoesnotguaranteethatanycontentonsuchwebsitesis,
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Contents
Preface page ix
Translators’foreword xi
1 Atoms 1
1.1 Mean-fieldapproximationandelectronicconfigurations 1
1.2 Multiplets 3
1.3 Coulombandexchangeintegrals 10
1.4 Hartree’smethod 13
Referencesandfurtherreading 14
2 Molecules 16
+
2.1 TheH molecule 16
2
2.2 TheH molecule 19
2
2.3 Theconfigurationinteraction 22
2.4 Secondquantization 25
Referencesandfurtherreading 30
3 TheSommerfeldtheoryofmetals 32
3.1 Classificationofsolids 32
3.2 TheSommerfeldtheory 36
Referencesandfurtherreading 48
4 Bandtheory 49
4.1 Theperiodicstructureofcrystals 49
4.2 Bloch’stheorem 52
4.3 Anapproachstartingfromthefreeelectronpicture 55
4.4 TheBlochorbitalasalinearcombinationofatomicorbitals 59
4.5 Metalsandinsulators 61
4.6 TheWigner–Seitztheory 63
v
vi Contents
5 Magneticimpuritiesinmetals 69
5.1 Localchargeneutrality 69
5.2 Thesphericalrepresentation 72
5.3 Chargedistributionandthedensityofstates 78
5.4 Virtualboundstates 80
5.5 TheAndersonmodelI 84
5.6 TheAndersonmodelII 90
5.7 TheCoulombinteraction:UHF 97
5.8 ExpansioninpowersofU 104
5.9 s–dinteraction 106
5.10 Casewithorbitaldegeneracy 115
Referencesandfurtherreading 119
6 Theinfrareddivergenceinmetals 120
6.1 TheAndersonorthogonalitytheorem 120
6.2 Mahan’sproblem 124
6.3 ThethermalGreen’sfunction 127
6.4 ThermalGreen’sfunctionsinthepresenceoflocalpotentials 130
6.5 Thepartitionfunctioninthes–dproblem 132
6.6 TheNozières–deDominicissolution 134
6.7 Calculationofthepartitionfunction 136
6.8 Ascalingapproach 140
Referencesandfurtherreading 143
7 Wilson’stheory 144
7.1 Wilson’sHamiltonian 144
7.2 Perturbativeexpansions 150
7.3 Numericalcalculations:scaling 154
7.4 Susceptibilityandspecificheat 159
Referencesandfurtherreading 164
8 Exactsolutiontothes–dproblem 165
8.1 Aone-dimensionalmodel 165
8.2 Thethree-bodyproblem 168
8.3 Symmetricgroups 175
8.4 TheN-electronproblem 176
8.5 Antisymmetrization 179
8.6 Theeigenvalueproblem 182
8.7 Theintegralequation 185
8.8 Thegroundstate 187
8.9 Susceptibility 188
Contents vii
8.10 Universality 192
8.11 Theexcitedstates 195
8.12 Freeenergy 199
8.13 Specificheat 204
Referencesandfurtherreading 208
9 Recentdevelopments 209
9.1 Thespin-fliprate 209
9.2 Theheavyelectrons 211
9.3 Quantumdots 214
Referencesandfurtherreading 217
Appendices 218
A MatrixelementsbetweenSlaterdeterminants 218
B SpinfunctionforN-electronsystems 221
C Fourierexpansionofthree-dimensionalperiodicfunctions 224
D Proofofeq.(5.29) 225
E RelationsbetweenGreen’sfunctions 226
F ExpansionoffreeenergytoorderJ2 228
G Calculationofg± 234
H Feynman’stheorem 236
I Eliminationofadjacentpairs 237
J Proofofeq.(6.80) 239
K Transformationfromplane-waverepresentationto
spherical-waverepresentation 240
L Derivationofeq.(7.33) 241
M Derivationofeq.(7.35) 241
N Solutiontotheeigenvalueproblemin§8.6 243
O Wiener–Hopfintegralequation 253
P Analyticcontinuationofeq.(8.82) 255
Q Rewritingeqs.(8.115)and(8.116) 256
Index 259