The quantum theory of magnetism:
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| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
New Jersey [u.a.]
World Scientific
2007
|
| Edition: | 2. ed. |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XIII, 377 S. |
| ISBN: | 9812567925 9789812567925 |
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MARC
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| 020 | |a 9789812567925 |9 978-981-256-792-5 | ||
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| 084 | |a PHY 721f |2 stub | ||
| 100 | 1 | |a Majlis, Norberto |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a The quantum theory of magnetism |c Norberto Majlis |
| 250 | |a 2. ed. | ||
| 264 | 1 | |a New Jersey [u.a.] |b World Scientific |c 2007 | |
| 300 | |a XIII, 377 S. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 650 | 4 | |a Quantentheorie | |
| 650 | 4 | |a Magnetism | |
| 650 | 4 | |a Quantum theory | |
| 650 | 0 | 7 | |a Quantentheorie |0 (DE-588)4047992-4 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Magnetismus |0 (DE-588)4037021-5 |2 gnd |9 rswk-swf |
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| 689 | 0 | 1 | |a Quantentheorie |0 (DE-588)4047992-4 |D s |
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| 856 | 4 | 2 | |m Digitalisierung UB Regensburg |q application/pdf |u http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016361431&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |3 Inhaltsverzeichnis |
| 999 | |a oai:aleph.bib-bvb.de:BVB01-016361431 | ||
| 344 | |h graph. Darst. | ||
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| adam_text | Contents
1
Paramagnetism
1
1.1
Introduction
.............................. 1
1.2
Quantum mechanics of atoms
.................... 4
1.2.1
L-S (Russel-Saunders) coupling
............... 4
1.2.2
Hunďs
rales
......................... 6
1.2.3
Spin-orbit splitting
...................... 7
1.3
The quantum theory of paramagnetism
.............. 8
1.4
Crystal-field corrections
....................... 11
1.4.1
Effects of crystal-field symmetry
.............. 12
1.4.2
Stevens operator equivalents
................ 14
1.5
Quenching of
L
............................ 18
1.6
Time reversal and spin
........................ 20
1.6.1
Kramers degeneracy
..................... 21
1.7
Effective spin Hamiltonian
...................... 22
1.7.1
Effective gyromagnetic ratio
................. 23
1.7.2
Single-ion anisotropy energy
................. 23
2
Interacting Spins
27
2.1
Weiss model of ferromagnetism
................... 27
2.1.1
Critical behaviour of Weiss model
............. 28
2.2
Microscopic basis of magnetism
................... 29
2.2.1
The direct exchange interaction
............... 30
2.2.2
The superexchange mechanism
............... 36
2.2.3
The RKKY interaction
................... 40
3
Mean Field Approximation
43
3.1
Helmholtz free energy
........................ 43
3.2
Mean field susceptibility
....................... 50
3.3
Specific heat of ferromagnet
..................... 52
3.4
The Oguchi method
......................... 55
3.5
Modulated phases
.......................... 58
3.6
MFA for antiferromagnetism
..................... 61
3.6.1
Longitudinal susceptibility
.................. 63
3.6.2
Transverse susceptibility
................... 65
ix
CONTENTS
3.6.3
Spin-flop and other transitions
............... 68
3.7
Helimagnetism
............................ 72
3.8
Goldstone s theorem
......................... 76
Spin Waves
79
4.1
Introduction
.............................. 79
4.2
Holstein-Primakoff transformation
................. 82
4.3
Linear spin-wave theory
....................... 84
4.4
Semiclassical picture
......................... 85
4.5
Macroscopic
magnon
theory
..................... 88
4.6
Thermal properties
.......................... 89
4.6.1
Total spin deviation
..................... 89
4.6.2
Non-linear corrections
.................... 91
4.7
The
Heisenberg antiferromagnet .................. 92
4.7.1
Introduction
......................... 92
4.7.2
Antiferromagnetic spin-waves
................ 93
4.7.3
Sublattice
magnetization
.................. 97
4.7.4
Ground state energy of AFM
................ 99
Magnetic Anisotropy
101
5.1
Introduction
.............................. 101
5.2
Microscopic origin of anisotropy
................... 104
5.3
Magneto-elastic coupling
....................... 108
5.4
Magnetostriction
...........................
Ill
5.5
Inverse magnetostriction
....................... 113
5.6
Induced magneto-crystalline anisotropy
.............. 115
Green s Functions Methods
117
6.1
Definitions
...............................117
6.2
Spectral representation
........................119
6.3
RPA
for spin
1/2
ferromagnet
....................122
6.4
Comparison of
RPA
and MFA
....................126
6.5
RPA
for arbitrary spin
........................127
6.6
RPA
for ferromagnets
........................129
6.6.1
Paramagnetic phase
.....................129
6.6.2
Linear
FM
chain
.......................132
6.6.3
Square
FM
lattice
......................133
6.7 FM
with a finite applied field
....................135
6.8
RPA
for antiferromagnet
.......................136
6.8.1
Spin
1/2
AFM
........................137
6.8.2
Arbitrary spin AFM
.....................138
6.8.3
Zero-point spin deviation
..................139
6.8.4
Correlation length
......................140
6.9
RPA
susceptibility of AFM
.....................143
6.10
Spin-flop transition
.........................146
6.11
ХЦ
at low
Τ
..............................148
CONTENTS xi
6.12
Transverse susceptibility
....................... 149
6.13
Single-site anisotropy
......................... 150
6.14
Dynamic linear response
....................... 153
6.15
Energy absorbed from external field
................ 156
6.16
Susceptibility of
FM......................... 158
6.17
Corrections to
RPA
......................... 158
7 Dipole-Dipole
Interactions
161
7.1
Dipolar Hamiltonian
......................... 161
7.2
Dipole-exchange spin-waves
..................... 166
7.3
Uniform precession (k
= 0)
mode
.................. 170
7.4
Eigenmodes for
к
φ
0........................ 174
7.4.1
Demagnetization factors
................... 176
7.5
Ellipticity of spin precession
..................... 176
7.6
Effect of
magnons on
total spin
................... 177
7.7
Magnetostatic modes
......................... 179
8
Coherent States of
Magnons
183
8.1
Introduction
.............................. 183
8.2
Coherent states of bosons
...................... 183
8.2.1
Overcompleteness of coherent states basis
......... 185
8.3
Magnon
number distribution function
............... 186
8.4
Uncertainty relations
......................... 187
8.5
Phase states
.............................. 188
8.6
Magnon
states of well defined phase
................ 190
8.7
Properties of the single-mode number states
............ 191
8.8
Properties of a single-mode phase state
............... 192
8.9
Expectation value of local spin operators in a coherent state
. . . 192
9
Itinerant Magnetism
195
9.1
Introduction
..............................195
9.2 Pauli
paramagnetic susceptibility
..................195
9.3
Stoner
model of ferromagnetic metals
...............196
9.4
Hubbard Hamiltonian
........................198
9.5
Instability of paramagnetic phase
..................199
9.6
Magnons
in the
Stoner
model
....................200
9.6.1
The
RPA
susceptibility
...................200
9.6.2
Singularities of the susceptibility
..............204
9.7
Tc in
Stoner
model
..........................208
9.8
Metals with degenerate bands
....................210
9.9
Spin-density wave
...........................213
9.10
Hartree-Fock description of SDW
..................215
9.11
Effects of correlations
........................222
9.11.1
Kinetic exchange interaction
................224
9.12
Paramagnetic instability and paramagnons
............228
9.12.1
Paramagnon contribution to the specific heat
.......232
xii CONTENTS
9.13
Beyond
Stoner
theory and
RPA
...................234
9.14
Magnetism and superconductivity
.................234
10
Indirect Exchange
239
10.1
Introduction
..............................239
10.2
Effective s-d exchange interaction
..................240
10.3
Indirect exchange Hamiltonian
...................247
10.4
Range function and band structure
.................248
10.5
Semiconductors
............................256
10.5.1
Intrinsic semiconductors, high
Τ
..............256
10.5.2
Intrinsic semiconductors, low
Τ
...............257
10.5.3
Degenerate semiconductors
.................259
10.6
Magnetic multilayer systems
.....................259
11
Local Moments
263
11.1
The s-d and Anderson Hamiltonians
................ 263
11.2
Anderson model
........................... 263
11.3
Hartree-Fock solution of Anderson Hamiltonian
.......... 264
11.4
Kondo effect
.............................. 267
11.4.1
Calculation of resistivity
................... 268
11.4.2
Calculation of the collision time
............... 269
11.4.3
Higher order contributions
..................275
12
Low Dimensions
277
12.1
Introduction
..............................277
12.2
Proof of Mermin-Wagner theorem
.................278
12.2.1
Bogoliubov inequality
....................278
12.2.2
Application to the
Heisenberg
model
............279
12.3
Dipolar interactions in low dimensions
...............282
12.3.1
Dipole-exchange cross-over
.................286
12.4
One dimensional instabilities
....................287
12.5
Antiferromagnetic chain
.......................289
12.6
RPA
for the AFM chain
.......................291
12.6.1
Exchange dominated regime
.................291
12.6.2
Dipolar dominated regime
..................294
12.7
Dipolar interaction in layers
.....................295
12.7.1
Monolayer
...........................297
12.7.2
Bilayer
.............................298
13
Surface Magnetism
305
13.1
Introduction
.............................. 305
13.2
MFA treatment of surfaces
...................... 306
13.3
Surface excitations
.......................... 309
13.4
LRPA method
............................ 310
13.5
Wave functions for bulk and surface
................ 316
13.6
Surface density of
magnon
states
.................. 317
CONTENTS xiii
13.7
Surface
phase-transitions
.......................319
13.8
Dipolar surface effects
........................323
13.9
Surface magnetism in metals
....................324
14
Two-Magnon Eigenstates
329
14.1
Introduction
..............................329
14.2
Green s function formalism
.....................331
14.3
One dimension
............................337
14.4
Two dimensions
............................339
14.5
Summary of results
..........................340
14.6
Anisotropy effects
...........................341
15
Other Interactions
345
15.1
Introduction
..............................345
15.2
Two-magnon interaction
.......................347
15.3
Three-magnon processes
.......................349
15.4
Magnon-phonon interaction
.....................353
15.5
Bilinear magnon-phonon interaction
................355
Appendix A Group Theory
359
A.I Definition of group
..........................359
A.
2
Group representations
........................360
A.2.1 Reducibility
..........................361
A.3 Orthogonality relations
........................362
A.4 Projection operators
.........................362
A.
5
Coordinate transformations
.....................363
A.6 Wigner-Eckart theorem
.......................364
A.
7
Space groups
.............................365
A.8 Bloch s theorem
............................366
Appendix
В
Time Reversal
369
B.I Antilinear operators
.........................369
B.2 Anti-unitary operators
........................371
B.3 Time reversal
.............................371
Index
375
|
| adam_txt |
Contents
1
Paramagnetism
1
1.1
Introduction
. 1
1.2
Quantum mechanics of atoms
. 4
1.2.1
L-S (Russel-Saunders) coupling
. 4
1.2.2
Hunďs
rales
. 6
1.2.3
Spin-orbit splitting
. 7
1.3
The quantum theory of paramagnetism
. 8
1.4
Crystal-field corrections
. 11
1.4.1
Effects of crystal-field symmetry
. 12
1.4.2
Stevens operator equivalents
. 14
1.5
Quenching of
L
. 18
1.6
Time reversal and spin
. 20
1.6.1
Kramers degeneracy
. 21
1.7
Effective spin Hamiltonian
. 22
1.7.1
Effective gyromagnetic ratio
. 23
1.7.2
Single-ion anisotropy energy
. 23
2
Interacting Spins
27
2.1
Weiss model of ferromagnetism
. 27
2.1.1
Critical behaviour of Weiss model
. 28
2.2
Microscopic basis of magnetism
. 29
2.2.1
The direct exchange interaction
. 30
2.2.2
The superexchange mechanism
. 36
2.2.3
The RKKY interaction
. 40
3
Mean Field Approximation
43
3.1
Helmholtz free energy
. 43
3.2
Mean field susceptibility
. 50
3.3
Specific heat of ferromagnet
. 52
3.4
The Oguchi method
. 55
3.5
Modulated phases
. 58
3.6
MFA for antiferromagnetism
. 61
3.6.1
Longitudinal susceptibility
. 63
3.6.2
Transverse susceptibility
. 65
ix
CONTENTS
3.6.3
Spin-flop and other transitions
. 68
3.7
Helimagnetism
. 72
3.8
Goldstone's theorem
. 76
Spin Waves
79
4.1
Introduction
. 79
4.2
Holstein-Primakoff transformation
. 82
4.3
Linear spin-wave theory
. 84
4.4
Semiclassical picture
. 85
4.5
Macroscopic
magnon
theory
. 88
4.6
Thermal properties
. 89
4.6.1
Total spin deviation
. 89
4.6.2
Non-linear corrections
. 91
4.7
The
Heisenberg antiferromagnet . 92
4.7.1
Introduction
. 92
4.7.2
Antiferromagnetic spin-waves
. 93
4.7.3
Sublattice
magnetization
. 97
4.7.4
Ground state energy of AFM
. 99
Magnetic Anisotropy
101
5.1
Introduction
. 101
5.2
Microscopic origin of anisotropy
. 104
5.3
Magneto-elastic coupling
. 108
5.4
Magnetostriction
.
Ill
5.5
Inverse magnetostriction
. 113
5.6
Induced magneto-crystalline anisotropy
. 115
Green's Functions Methods
117
6.1
Definitions
.117
6.2
Spectral representation
.119
6.3
RPA
for spin
1/2
ferromagnet
.122
6.4
Comparison of
RPA
and MFA
.126
6.5
RPA
for arbitrary spin
.127
6.6
RPA
for ferromagnets
.129
6.6.1
Paramagnetic phase
.129
6.6.2
Linear
FM
chain
.132
6.6.3
Square
FM
lattice
.133
6.7 FM
with a finite applied field
.135
6.8
RPA
for antiferromagnet
.136
6.8.1
Spin
1/2
AFM
.137
6.8.2
Arbitrary spin AFM
.138
6.8.3
Zero-point spin deviation
.139
6.8.4
Correlation length
.140
6.9
RPA
susceptibility of AFM
.143
6.10
Spin-flop transition
.146
6.11
ХЦ
at low
Τ
.148
CONTENTS xi
6.12
Transverse susceptibility
. 149
6.13
Single-site anisotropy
. 150
6.14
Dynamic linear response
. 153
6.15
Energy absorbed from external field
. 156
6.16
Susceptibility of
FM. 158
6.17
Corrections to
RPA
. 158
7 Dipole-Dipole
Interactions
161
7.1
Dipolar Hamiltonian
. 161
7.2
Dipole-exchange spin-waves
. 166
7.3
Uniform precession (k
= 0)
mode
. 170
7.4
Eigenmodes for
к
φ
0. 174
7.4.1
Demagnetization factors
. 176
7.5
Ellipticity of spin precession
. 176
7.6
Effect of
magnons on
total spin
. 177
7.7
Magnetostatic modes
. 179
8
Coherent States of
Magnons
183
8.1
Introduction
. 183
8.2
Coherent states of bosons
. 183
8.2.1
Overcompleteness of coherent states basis
. 185
8.3
Magnon
number distribution function
. 186
8.4
Uncertainty relations
. 187
8.5
Phase states
. 188
8.6
Magnon
states of well defined phase
. 190
8.7
Properties of the single-mode number states
. 191
8.8
Properties of a single-mode phase state
. 192
8.9
Expectation value of local spin operators in a coherent state
. . . 192
9
Itinerant Magnetism
195
9.1
Introduction
.195
9.2 Pauli
paramagnetic susceptibility
.195
9.3
Stoner
model of ferromagnetic metals
.196
9.4
Hubbard Hamiltonian
.198
9.5
Instability of paramagnetic phase
.199
9.6
Magnons
in the
Stoner
model
.200
9.6.1
The
RPA
susceptibility
.200
9.6.2
Singularities of the susceptibility
.204
9.7
Tc in
Stoner
model
.208
9.8
Metals with degenerate bands
.210
9.9
Spin-density wave
.213
9.10
Hartree-Fock description of SDW
.215
9.11
Effects of correlations
.222
9.11.1
Kinetic exchange interaction
.224
9.12
Paramagnetic instability and paramagnons
.228
9.12.1
Paramagnon contribution to the specific heat
.232
xii CONTENTS
9.13
Beyond
Stoner
theory and
RPA
.234
9.14
Magnetism and superconductivity
.234
10
Indirect Exchange
239
10.1
Introduction
.239
10.2
Effective s-d exchange interaction
.240
10.3
Indirect exchange Hamiltonian
.247
10.4
Range function and band structure
.248
10.5
Semiconductors
.256
10.5.1
Intrinsic semiconductors, high
Τ
.256
10.5.2
Intrinsic semiconductors, low
Τ
.257
10.5.3
Degenerate semiconductors
.259
10.6
Magnetic multilayer systems
.259
11
Local Moments
263
11.1
The s-d and Anderson Hamiltonians
. 263
11.2
Anderson model
. 263
11.3
Hartree-Fock solution of Anderson Hamiltonian
. 264
11.4
Kondo effect
. 267
11.4.1
Calculation of resistivity
. 268
11.4.2
Calculation of the collision time
. 269
11.4.3
Higher order contributions
.275
12
Low Dimensions
277
12.1
Introduction
.277
12.2
Proof of Mermin-Wagner theorem
.278
12.2.1
Bogoliubov inequality
.278
12.2.2
Application to the
Heisenberg
model
.279
12.3
Dipolar interactions in low dimensions
.282
12.3.1
Dipole-exchange cross-over
.286
12.4
One dimensional instabilities
.287
12.5
Antiferromagnetic chain
.289
12.6
RPA
for the AFM chain
.291
12.6.1
Exchange dominated regime
.291
12.6.2
Dipolar dominated regime
.294
12.7
Dipolar interaction in layers
.295
12.7.1
Monolayer
.297
12.7.2
Bilayer
.298
13
Surface Magnetism
305
13.1
Introduction
. 305
13.2
MFA treatment of surfaces
. 306
13.3
Surface excitations
. 309
13.4
LRPA method
. 310
13.5
Wave functions for bulk and surface
. 316
13.6
Surface density of
magnon
states
. 317
CONTENTS xiii
13.7
Surface
phase-transitions
.319
13.8
Dipolar surface effects
.323
13.9
Surface magnetism in metals
.324
14
Two-Magnon Eigenstates
329
14.1
Introduction
.329
14.2
Green's function formalism
.331
14.3
One dimension
.337
14.4
Two dimensions
.339
14.5
Summary of results
.340
14.6
Anisotropy effects
.341
15
Other Interactions
345
15.1
Introduction
.345
15.2
Two-magnon interaction
.347
15.3
Three-magnon processes
.349
15.4
Magnon-phonon interaction
.353
15.5
Bilinear magnon-phonon interaction
.355
Appendix A Group Theory
359
A.I Definition of group
.359
A.
2
Group representations
.360
A.2.1 Reducibility
.361
A.3 Orthogonality relations
.362
A.4 Projection operators
.362
A.
5
Coordinate transformations
.363
A.6 Wigner-Eckart theorem
.364
A.
7
Space groups
.365
A.8 Bloch's theorem
.366
Appendix
В
Time Reversal
369
B.I Antilinear operators
.369
B.2 Anti-unitary operators
.371
B.3 Time reversal
.371
Index
375 |
| any_adam_object | 1 |
| any_adam_object_boolean | 1 |
| author | Majlis, Norberto |
| author_facet | Majlis, Norberto |
| author_role | aut |
| author_sort | Majlis, Norberto |
| author_variant | n m nm |
| building | Verbundindex |
| bvnumber | BV023174816 |
| callnumber-first | Q - Science |
| callnumber-label | QC754 |
| callnumber-raw | QC754.2.Q34 |
| callnumber-search | QC754.2.Q34 |
| callnumber-sort | QC 3754.2 Q34 |
| callnumber-subject | QC - Physics |
| classification_rvk | UP 6000 |
| classification_tum | PHY 721f |
| ctrlnum | (OCoLC)558678651 (DE-599)BVBBV023174816 |
| discipline | Physik |
| discipline_str_mv | Physik |
| edition | 2. ed. |
| format | Book |
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| id | DE-604.BV023174816 |
| illustrated | Not Illustrated |
| index_date | 2024-07-02T19:59:21Z |
| indexdate | 2024-07-09T21:12:18Z |
| institution | BVB |
| isbn | 9812567925 9789812567925 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-016361431 |
| oclc_num | 558678651 |
| open_access_boolean | |
| owner | DE-703 DE-20 DE-355 DE-BY-UBR DE-384 DE-91G DE-BY-TUM |
| owner_facet | DE-703 DE-20 DE-355 DE-BY-UBR DE-384 DE-91G DE-BY-TUM |
| physical | XIII, 377 S. |
| publishDate | 2007 |
| publishDateSearch | 2007 |
| publishDateSort | 2007 |
| publisher | World Scientific |
| record_format | marc |
| spelling | Majlis, Norberto Verfasser aut The quantum theory of magnetism Norberto Majlis 2. ed. New Jersey [u.a.] World Scientific 2007 XIII, 377 S. 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 Digitalisierung UB Regensburg application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016361431&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis graph. Darst. |
| spellingShingle | Majlis, Norberto The 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 | The quantum theory of magnetism |
| title_auth | The quantum theory of magnetism |
| title_exact_search | The quantum theory of magnetism |
| title_exact_search_txtP | The quantum theory of magnetism |
| title_full | The quantum theory of magnetism Norberto Majlis |
| title_fullStr | The quantum theory of magnetism Norberto Majlis |
| title_full_unstemmed | The quantum theory of magnetism Norberto Majlis |
| title_short | The quantum theory of magnetism |
| title_sort | the 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=016361431&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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