Verfügbarkeit: Quantum theory of magnetism

Quantum theory of magnetism:

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Hauptverfasser:	Nolting, Wolfgang 1944- (VerfasserIn), Ramakanth, Anupuru (VerfasserIn)
Format:	Buch
Sprache:	English
Veröffentlicht:	Heidelberg [u.a.] Springer 2009
Schlagworte:	Quantentheorie Magnetism Quantum theory Magnetismus
Online-Zugang:	Inhaltsverzeichnis
Beschreibung:	XIII, 752 S. graph. Darst.
ISBN:	9783540854159 9783540854166

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Datensatz im Suchindex

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adam_text	Contents 1 Basic Facts ..................................................... 1 1.1 Macroscopic Maxwell Equations ............................. 1 1.2 Magnetic Moment and Magnetization ......................... 7 1.3 Susceptibility ............................................. 13 1.4 Classification of Magnetic Materials .......................... 15 1.4.1 Diamagnetism .................................... 15 1 .4.2 Paramagnetism .................................... 15 1.4.3 Collective Magnetism .............................. 17 1.5 Elements of Thermodynamics ............................... 19 1.6 Problems ................................................. 22 2 Atomic Magnetism .............................................. 25 2.1 Hund s Rules ............................................. 25 2.1.1 Russell-Saunders (LS-) Coupling .................... 25 2.1.2 Hund s Rules for ¿5 Coupling ....................... 27 2.2 Dirac Equation ............................................ 28 2.3 Electron Spin ............................................. 34 2.4 Spin-Orbit Coupling ....................................... 40 2.5 Wigner-Eckart Theorem .................................... 45 2.5.1 Rotation ......................................... 45 2.5.2 Rotation Operator ................................. 47 2.5.3 Angular Momentum ............................... 48 2.5.4 Rotation Matrices .................................. 50 2.5.5 Tensor Operators .................................. 52 2.5.6 Wigner-Eckart Theorem ............................ 53 2.5.7 Examples of Application ............................ 55 2.6 Electron in an External Magnetic Field ........................ 56 2.7 Nuclear Quadrupole Field ................................... 62 2.8 Hyperfine Field ........................................... 67 2.9 Magnetic Hamiitonian of the Atomic Electron .................. 72 2.10 Many-Electron Systems .................................... 74 2.10.1 Coulomb Interaction ............................... 74 x Contents 2.10.2 Spin-Orbit Coupling ............................... 75 2.10.3 Further Couplings ................................. 76 2.11 Problems ................................................. 81 3 Diamagnetism ................................................. 85 3.1 Bohr-van Leeuwen Theorem ................................ 85 3.2 Larmor Diamagnetism (Insulators) ........................... 87 3.3 The Sommerfeld Model of a Metal ........................... 90 3.3.1 Properties of the Model ............................. 91 3.3.2 Sommerfeld Expansion ............................. 99 3.4 Landau Diamagnetism (Metals) ..............................104 3.4.1 Free Electrons in Magnetic Field (Landau Levels) ......104 3.4.2 Grand Canonical Potential of the Conduction Electrons .. 109 3.4.3 Susceptibility of the Conduction Electrons .............117 3.5 The de Haas-Van Alphen Effect .............................121 3.5.1 Oscillations in the Magnetic Susceptibility .............121 3.5.2 Electron Orbits in Magnetic Field ....................124 3.5.3 Physical Origin of the Oscillations ...................128 3.5.4 Onsager Argument .................................131 3.6 Problems .................................................134 References ......................................................136 4 Paramagnetism .................................................137 4.1 Pauli Spin Paramagnetism ..................................138 4.1.1 Primitive Theory of the Pauli Spin Paramagnetism .... 138 4.1.2 Temperature Corrections ............................141 4.1.3 Exchange Corrections ..............................142 4.2 Paramagnetism of the Localized Electrons .....................155 4.2.1 Weak Spin-Orbit Interaction ........................158 4.2.2 Strong Spin-Orbit Coupling .........................164 4.2.3 Van Vleck Paramagnetism ..........................166 4.3 Problems .................................................171 References ......................................................174 5 Exchange Interaction ............................................175 5.1 Phenomenological Theories .................................178 5.1.1 The Exchange Field ................................178 5.1.2 Weiss Ferromagnet ................................180 5.2 Direct Exchange Interaction .................................184 5.2.1 Pauli s Principle ...................................184 5.2.2 The Heitler-London Method ........................188 5.2.3 Dirac s Vector Model ...............................195 5.3 Indirect Exchange Interaction ................................200 5.3.1 Rudermann-Khtel-Kasuya-Yosida (RKKY) Interaction . 200 5.3.2 Superexchange ....................................209 Contents xi 5.3.3 Double Exchange..................................217 5.4 Problems.................................................226 References ......................................................231 6 Ising Model ....................................................233 6.1 The Model ...............................................234 6.2 The One Dimensional Ising Model...........................236 6.2. t Spontaneous Magnetization .........................236 6.2.2 One Dimensional Ising Model in External Field ........240 6.3 The Phase Transition of Two-Dimensional Ising Model ..........245 6.3.1 The Method of Proof ...............................245 6.3.2 Finite Ising Lattice with Special Boundary Conditions ... 247 6.3.3 Probabilities ......................................247 6.3.4 Realization Possibilities for the Polygons ..............249 6.3.5 Magnetization of the Finite Lattice ...................252 6.3.6 Thermodynamic Limit ..............................252 6.4 The Free Energy of the Two-Dimensional Ising Model ...........254 6.4.1 High-Temperature Expansion ........................255 6.4.2 Spin Products as Graphs ............................256 6.4.3 Loops ...........................................257 6.4.4 Directed Paths ....................................261 6.4.5 Matrix Mt ........................................264 6.4.6 Free Energy per Spin ...............................266 6.4.7 Curie Temperature Tc ...............................267 6.4.8 Specific Heat .....................................268 6.4.9 Spontaneous Magnetization .........................269 6.5 Problems .................................................270 References ......................................................271 7 Heisenberg Model ...............................................273 7.1 Model Hamiltonian ........................................273 7.1. 1 Spin Operators ....................................273 7.1.2 Model Extensions .................................279 7.2 Exact Statements ..........................................283 7.2.1 Mermin-Wagner Theorem ..........................283 7.2.2 One-Magnon States of a Ferromagnet .................291 7.3 Molecular Field Approximations .............................296 7.3.1 Ferromagnet ......................................297 7.3.2 Antiferromagnet ...................................303 7.3.3 Ferrimagnet ......................................317 7.4 Spin Waves ...............................................322 7.4. 1 Linear Spin Wave Theory for the Isotropie Ferromagnet . 322 7.4.2 Renormalized Spin Waves .........................329 7.4.3 Harmonic Approximation for Antiferromagnets ........336 7.4.4 Harmonic Approximation for a Ferromagnet with Dipolar Interaction .................345 Contents 7.5 Thermodynamics of S = 1 /2 Ferromagnet .....................351 7.5.1 Tyablikov Decoupling ..............................35 1 7.5.2 Spontaneous Magnetization .........................354 7.5.3 Thermodynamic Potentials ..........................359 7.6 Thermodynamics of 5 > I /2 Ferromagnets ....................361 7.6.1 Green s Functions .................................361 7.6.2 Spontaneous Magnetization .........................363 7.6.3 The Callen Method ................................371 7.7 Problems .................................................381 References ......................................................386 Hubbard Model ................................................387 8.1 Introduction ..............................................387 8.2 Model for Band Magnets ...................................388 8.2.1 Solid as a Many-Body System .......................388 8.2.2 Electrons in Narrow Energy Bands ...................389 8.2.3 Hubbard Model ...................................393 8.3 Stoner Model .............................................395 8.3.1 Stoner Ansatz (Ferromagnet) ........................395 8.3.2 Stoner Excitations .................................397 8.3.3 Magnetic Phase Transition ..........................398 8.3.4 Static Susceptibility ................................405 8.4 Exact Statements and General Properties ......................409 8.4.1 Mermin-Wagner Theorem ..........................410 8.4.2 The Infinitely Narrow Band .........................415 8.4.3 The Two-Site Model ...............................420 8.4.4 The Exactly Half-Filled Band ........................427 8.4.5 Strong-Coupling Regime ...........................431 8.4.6 Spectra] Moments .................................437 8.4.7 High-Energy Expansions ...........................439 8.4.8 Weak-Coupling Regime ............................441 8.4.9 Infinite Dimensions ................................444 8.4.10 Effective impurity^Problem ........................448 8.5 Magnetism and Electronic Correlations .......................451 8.5.1 Hubbard-I Approximation ..........................451 8.5.2 Interpolation Method ...............................454 8.5.3 Correlation Effects and Ferromagnetism ...............455 8.5.4 Criterion for Ferromagnetism ........................457 8.5.5 Static Susceptibility and Ferromagnetism ..............461 8.5.6 Spin-Dependent Band Shift .........................464 8.5.7 Quasiparticle Damping .............................470 8.5.8 Dynamical Mean Field Theory .......................475 8.5.9 Modified Perturbation Theory .......................479 Contents xiii 8.5.10 Curie Temperature, Magnetization and Static Susceptibility .....................................482 8.6 Problems .................................................485 References ......................................................490 A Second Quantization ............................................491 A.I Identical Particles ..........................................492 A.2 Continuous Fock Representation .............................494 A. 2.1 Symmetrized Many-Particle States ...................494 A. 2.2 Construction Operators .............................495 A. 2.3 Many-Body Operators ..............................497 A.3 Discrete Fock Representation (Occupation Number Representation) ........................................... 501 A.3.1 Symmetrized Many-Particle States ...................501 A. 3.2 Construction Operators .............................503 A.4 Examples ................................................506 A.4.1 Bloch Electrons ...................................506 A.4.2 Wannier Electrons .................................508 A.4.3 Density Operator ..................................509 A.4.4 Coulomb Interaction ...............................510 A.5 Problems .................................................511 В The Method of Green s Functions .................................515 B. 1 Linear Response Theory ....................................515 B.I.I Kubo Formula ....................................515 B.1.2 Magnetic Susceptibility .............................518 B. 1.3 Dielectric Function ................................520 B.2 Spectroscopies and Spectral Densities .........................523 B.3 Double-Time Green s Functions .............................528 B.3. 1 Definitions and Equations of Motion ..................528 B.3.2 Spectral Representations ............................531 B.3.3 Spectral Theorem ..................................534 B.3.4 Spectral Moments .................................536 B.3.5 Kramer s-Kronig Relations .........................537 B.3.6 Simple Applications ...............................539 B.4 The Quasiparticle Concept ..................................545 B.4. 1 Interacting Electrons ...............................545 B.4.2 Electronic Self-energy ..............................548 B.4.3 Quasiparticles .....................................551 B.4.4 Quasiparticle Density of States ......................555 B.4.5 Thermodynamics ..................................558 B.5 Problems .................................................559 С Solutions to Problems ...........................................563 Index .............................................................743
adam_txt	Contents 1 Basic Facts . 1 1.1 Macroscopic Maxwell Equations . 1 1.2 Magnetic Moment and Magnetization . 7 1.3 Susceptibility . 13 1.4 Classification of Magnetic Materials . 15 1.4.1 Diamagnetism . 15 1 .4.2 Paramagnetism . 15 1.4.3 Collective Magnetism . 17 1.5 Elements of Thermodynamics . 19 1.6 Problems . 22 2 Atomic Magnetism . 25 2.1 Hund's Rules . 25 2.1.1 Russell-Saunders (LS-) Coupling . 25 2.1.2 Hund's Rules for ¿5 Coupling . 27 2.2 Dirac Equation . 28 2.3 Electron Spin . 34 2.4 Spin-Orbit Coupling . 40 2.5 Wigner-Eckart Theorem . 45 2.5.1 Rotation . 45 2.5.2 Rotation Operator . 47 2.5.3 Angular Momentum . 48 2.5.4 Rotation Matrices . 50 2.5.5 Tensor Operators . 52 2.5.6 Wigner-Eckart Theorem . 53 2.5.7 Examples of Application . 55 2.6 Electron in an External Magnetic Field . 56 2.7 Nuclear Quadrupole Field . 62 2.8 Hyperfine Field . 67 2.9 Magnetic Hamiitonian of the Atomic Electron . 72 2.10 Many-Electron Systems . 74 2.10.1 Coulomb Interaction . 74 x Contents 2.10.2 Spin-Orbit Coupling . 75 2.10.3 Further Couplings . 76 2.11 Problems . 81 3 Diamagnetism . 85 3.1 Bohr-van Leeuwen Theorem . 85 3.2 Larmor Diamagnetism (Insulators) . 87 3.3 The Sommerfeld Model of a Metal . 90 3.3.1 Properties of the Model . 91 3.3.2 Sommerfeld Expansion . 99 3.4 Landau Diamagnetism (Metals) .104 3.4.1 Free Electrons in Magnetic Field (Landau Levels) .104 3.4.2 Grand Canonical Potential of the Conduction Electrons . 109 3.4.3 Susceptibility of the Conduction Electrons .117 3.5 The de Haas-Van Alphen Effect .121 3.5.1 Oscillations in the Magnetic Susceptibility .121 3.5.2 Electron Orbits in Magnetic Field .124 3.5.3 Physical Origin of the Oscillations .128 3.5.4 Onsager Argument .131 3.6 Problems .134 References .136 4 Paramagnetism .137 4.1 Pauli Spin Paramagnetism .138 4.1.1 "Primitive" Theory of the Pauli Spin Paramagnetism . 138 4.1.2 Temperature Corrections .141 4.1.3 Exchange Corrections .142 4.2 Paramagnetism of the Localized Electrons .155 4.2.1 Weak Spin-Orbit Interaction .158 4.2.2 Strong Spin-Orbit Coupling .164 4.2.3 Van Vleck Paramagnetism .166 4.3 Problems .171 References .174 5 Exchange Interaction .175 5.1 Phenomenological Theories .178 5.1.1 The Exchange Field .178 5.1.2 Weiss Ferromagnet .180 5.2 Direct Exchange Interaction .184 5.2.1 Pauli's Principle .184 5.2.2 The Heitler-London Method .188 5.2.3 Dirac's Vector Model .195 5.3 Indirect Exchange Interaction .200 5.3.1 Rudermann-Khtel-Kasuya-Yosida (RKKY) Interaction . 200 5.3.2 Superexchange .209 Contents xi 5.3.3 Double Exchange.217 5.4 Problems.226 References .231 6 Ising Model .233 6.1 The Model .234 6.2 The One Dimensional Ising Model.236 6.2. t Spontaneous Magnetization .236 6.2.2 One Dimensional Ising Model in External Field .240 6.3 The Phase Transition of Two-Dimensional Ising Model .245 6.3.1 The Method of Proof .245 6.3.2 Finite Ising Lattice with Special Boundary Conditions . 247 6.3.3 Probabilities .247 6.3.4 Realization Possibilities for the Polygons .249 6.3.5 Magnetization of the Finite Lattice .252 6.3.6 Thermodynamic Limit .252 6.4 The Free Energy of the Two-Dimensional Ising Model .254 6.4.1 High-Temperature Expansion .255 6.4.2 Spin Products as Graphs .256 6.4.3 Loops .257 6.4.4 Directed Paths .261 6.4.5 Matrix Mt .264 6.4.6 Free Energy per Spin .266 6.4.7 Curie Temperature Tc .267 6.4.8 Specific Heat .268 6.4.9 Spontaneous Magnetization .269 6.5 Problems .270 References .271 7 Heisenberg Model .273 7.1 Model Hamiltonian .273 7.1. 1 Spin Operators .273 7.1.2 Model Extensions .279 7.2 Exact Statements .283 7.2.1 Mermin-Wagner Theorem .283 7.2.2 One-Magnon States of a Ferromagnet .291 7.3 Molecular Field Approximations .296 7.3.1 Ferromagnet .297 7.3.2 Antiferromagnet .303 7.3.3 Ferrimagnet .317 7.4 Spin Waves .322 7.4. 1 Linear Spin Wave Theory for the Isotropie Ferromagnet . 322 7.4.2 "Renormalized" Spin Waves .329 7.4.3 Harmonic Approximation for Antiferromagnets .336 7.4.4 Harmonic Approximation for a Ferromagnet with Dipolar Interaction .345 Contents 7.5 Thermodynamics of S = 1 /2 Ferromagnet .351 7.5.1 Tyablikov Decoupling .35 1 7.5.2 Spontaneous Magnetization .354 7.5.3 Thermodynamic Potentials .359 7.6 Thermodynamics of 5 > I /2 Ferromagnets .361 7.6.1 Green's Functions .361 7.6.2 Spontaneous Magnetization .363 7.6.3 The Callen Method .371 7.7 Problems .381 References .386 Hubbard Model .387 8.1 Introduction .387 8.2 Model for Band Magnets .388 8.2.1 Solid as a Many-Body System .388 8.2.2 Electrons in Narrow Energy Bands .389 8.2.3 Hubbard Model .393 8.3 Stoner Model .395 8.3.1 Stoner Ansatz (Ferromagnet) .395 8.3.2 Stoner Excitations .397 8.3.3 Magnetic Phase Transition .398 8.3.4 Static Susceptibility .405 8.4 Exact Statements and General Properties .409 8.4.1 Mermin-Wagner Theorem .410 8.4.2 The Infinitely Narrow Band .415 8.4.3 The Two-Site Model .420 8.4.4 The Exactly Half-Filled Band .427 8.4.5 Strong-Coupling Regime .431 8.4.6 Spectra] Moments .437 8.4.7 High-Energy Expansions .439 8.4.8 Weak-Coupling Regime .441 8.4.9 Infinite Dimensions .444 8.4.10 Effective "impurity^Problem .448 8.5 Magnetism and Electronic Correlations .451 8.5.1 Hubbard-I Approximation .451 8.5.2 Interpolation Method .454 8.5.3 Correlation Effects and Ferromagnetism .455 8.5.4 Criterion for Ferromagnetism .457 8.5.5 Static Susceptibility and Ferromagnetism .461 8.5.6 Spin-Dependent Band Shift .464 8.5.7 Quasiparticle Damping .470 8.5.8 Dynamical Mean Field Theory .475 8.5.9 Modified Perturbation Theory .479 Contents xiii 8.5.10 Curie Temperature, Magnetization and Static Susceptibility .482 8.6 Problems .485 References .490 A Second Quantization .491 A.I Identical Particles .492 A.2 Continuous Fock Representation .494 A. 2.1 Symmetrized Many-Particle States .494 A. 2.2 Construction Operators .495 A. 2.3 Many-Body Operators .497 A.3 Discrete Fock Representation (Occupation Number Representation) . 501 A.3.1 Symmetrized Many-Particle States .501 A. 3.2 Construction Operators .503 A.4 Examples .506 A.4.1 Bloch Electrons .506 A.4.2 Wannier Electrons .508 A.4.3 Density Operator .509 A.4.4 Coulomb Interaction .510 A.5 Problems .511 В The Method of Green's Functions .515 B. 1 Linear Response Theory .515 B.I.I Kubo Formula .515 B.1.2 Magnetic Susceptibility .518 B. 1.3 Dielectric Function .520 B.2 Spectroscopies and Spectral Densities .523 B.3 Double-Time Green's Functions .528 B.3. 1 Definitions and Equations of Motion .528 B.3.2 Spectral Representations .531 B.3.3 Spectral Theorem .534 B.3.4 Spectral Moments .536 B.3.5 Kramer's-Kronig Relations .537 B.3.6 Simple Applications .539 B.4 The Quasiparticle Concept .545 B.4. 1 Interacting Electrons .545 B.4.2 Electronic Self-energy .548 B.4.3 Quasiparticles .551 B.4.4 Quasiparticle Density of States .555 B.4.5 Thermodynamics .558 B.5 Problems .559 С Solutions to Problems .563 Index .743
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illustrated	Illustrated
index_date	2024-07-02T22:21:39Z
indexdate	2024-07-09T21:22:49Z
institution	BVB
isbn	9783540854159 9783540854166
language	English
oai_aleph_id	oai:aleph.bib-bvb.de:BVB01-016789931
oclc_num	243822187
open_access_boolean
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physical	XIII, 752 S. graph. Darst.
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publisher	Springer
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spelling	Nolting, Wolfgang 1944- Verfasser (DE-588)115505261 aut Quantum theory of magnetism Wolfgang Nolting and Anupuru Ramakanth Heidelberg [u.a.] Springer 2009 XIII, 752 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Quantentheorie Magnetism Quantum theory Quantentheorie (DE-588)4047992-4 gnd rswk-swf Magnetismus (DE-588)4037021-5 gnd rswk-swf Magnetismus (DE-588)4037021-5 s Quantentheorie (DE-588)4047992-4 s DE-604 Ramakanth, Anupuru Verfasser aut Digitalisierung UB Bayreuth application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016789931&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis
spellingShingle	Nolting, Wolfgang 1944- Ramakanth, Anupuru Quantum theory of magnetism Quantentheorie Magnetism Quantum theory Quantentheorie (DE-588)4047992-4 gnd Magnetismus (DE-588)4037021-5 gnd
subject_GND	(DE-588)4047992-4 (DE-588)4037021-5
title	Quantum theory of magnetism
title_auth	Quantum theory of magnetism
title_exact_search	Quantum theory of magnetism
title_exact_search_txtP	Quantum theory of magnetism
title_full	Quantum theory of magnetism Wolfgang Nolting and Anupuru Ramakanth
title_fullStr	Quantum theory of magnetism Wolfgang Nolting and Anupuru Ramakanth
title_full_unstemmed	Quantum theory of magnetism Wolfgang Nolting and Anupuru Ramakanth
title_short	Quantum theory of magnetism
title_sort	quantum theory of magnetism
topic	Quantentheorie Magnetism Quantum theory Quantentheorie (DE-588)4047992-4 gnd Magnetismus (DE-588)4037021-5 gnd
topic_facet	Quantentheorie Magnetism Quantum theory Magnetismus
url	http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016789931&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA
work_keys_str_mv	AT noltingwolfgang quantumtheoryofmagnetism AT ramakanthanupuru quantumtheoryofmagnetism

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