The Quantum Theory of Magnetism

by Majlis, Norberto

• ISBN13: 9789810240189
• ISBN10: 981024018X
• Format: Hardcover
• Copyright: 2001-03-01
• Publisher: WORLD SCIENTIFIC PUB CO INC

Summary

A textbook for a two-semester graduate-level course for physicists, engineers, and chemists with a background in quantum and statistical mechanics. Offers extensive use of Green's function techniques and detailed discussion of the application of the mean-field approximation and dipole-dipole interactions in one, two and three dimensions. Includes a total of 60 exercises.

Table of Contents

Paramagnetism	1	(34)
Introduction	1	(4)
Quantum mechanics of atoms	5	(5)
L-S (Russel-Saunders) coupling	5	(3)
Hund's rules	8	(1)
Spin-orbit splitting	9	(1)
The quantum theory of paramagnetism	10	(4)
Crystal-field corrections	14	(9)
Effects of crystal-field symmetry	15	(4)
Stevens operator equivalents	19	(4)
Quenching of L	23	(3)
Time reversal and spin	26	(2)
Kramers degeneracy	27	(1)
Effective Spin Hamiltonian	28	(7)
Effective gyromagnetic ratio	30	(1)
Single-ion anisotropy energy	30	(5)
Interacting Spins	35	(22)
Weiss model of ferromagnetism	35	(3)
Critical behaviour of Weiss model	37	(1)
Microscopic basis of magnetism	38	(19)
The direct exchange interaction	39	(9)
The superexchange mechanism	48	(5)
The RKKY interaction	53	(4)
Mean Field Approximation	57	(46)
Helmholtz Free Energy	57	(10)
Mean Field Susceptibility	67	(2)
Specific Heat of Ferromagnet	69	(3)
The Oguchi method	72	(5)
Modulated Phases	77	(4)
MFA for Antiferromagnetism	81	(12)
Longitudinal susceptibility	84	(2)
Transverse susceptibility	86	(3)
Spin-flop and other transitions	89	(4)
Helimagnetism	93	(6)
Goldstone's theorem	99	(4)
Spin waves	103	(30)
Introduction	103	(5)
Holstein-Primakoff transformation	108	(1)
Linear spin-wave theory	109	(2)
Semiclassical picture	111	(3)
Macroscopic magnon theory	114	(2)
Thermal properties	116	(5)
Total spin deviation	116	(3)
Non-linear corrections	119	(2)
The Heisenberg antiferromagnet	121	(1)
Introduction	121	(1)
AFM spin-waves	122	(5)
Sublattice magnetization	127	(2)
Ground state energy of AFM	129	(4)
Green's functions methods	133	(56)
Definitions	133	(3)
Spectral representation	136	(4)
RPA for spin 1/2 ferromagnet	140	(4)
Comparison of RPA and MFA	144	(1)
RPA for arbitrary spin	145	(3)
RPA for ferromagnets	148	(8)
Paramagnetic phase	148	(4)
Linear FM chain	152	(1)
Square FM lattice	153	(3)
FM with a finite applied field	156	(1)
RPA for antiferromagnet	157	(9)
Spin 1/2 AFM	157	(2)
Arbitrary spin AFM	159	(2)
Zero-point spin deviation	161	(1)
Correlation length	162	(4)
RPA susceptibility of AFM	166	(5)
Spin-flop transition	171	(1)
X‖ at low T	172	(2)
Transverse susceptibility	174	(2)
Single-site anisotropy	176	(3)
Dynamic linear response	179	(5)
Energy absorbed from external field	184	(1)
Susceptibility of FM	185	(1)
Corrections to RPA	186	(3)
Dipole-Dipole interactions	189	(28)
Dipolar Hamiltonian	189	(6)
Dipole-exchange spin-waves	195	(6)
Uniform precession (k = 0) mode	201	(3)
Eingenmodes for k ≠ 0	204	(3)
Demagnetization factors	206	(1)
Ellipticity of spin precession	207	(1)
Effect of magnons on total spin	208	(2)
Magnetostatic modes	210	(7)
Itinerant Magnetism	217	(46)
Introduction	217	(2)
Hubbard Hamiltonian	219	(3)
Instability of paramagnetic phase	222	(2)
Magnons in the Stoner model	224	(9)
The RPA susceptibility	224	(3)
Singularities of the susceptibility	227	(6)
Tc in Stoner model	233	(2)
Metals with degenerate bands	235	(4)
Spin-density waves	239	(3)
Hartree Fock description of SDW	242	(8)
Effects of correlations	250	(13)
Kinetic exchange interaction	252	(11)
Indirect Exchange	263	(30)
Introduction	263	(2)
Effective s-d exchange interaction	265	(9)
Indirect exchange Hamiltonian	274	(1)
Range function and band structure	275	(10)
Semiconductors	285	(4)
Intrinsic semiconductors, high T	285	(2)
Intrinsic semiconductors, low T	287	(1)
Degenerate semiconductors	288	(1)
Magnetic multilayer systems	289	(4)
Low dimensions	293	(36)
Introduction	293	(1)
Mermin-Wagner theorem	294	(6)
Bogoliubov inequality	295	(1)
Application to the Heisenberg model	296	(4)
Dipolar interactions in low dimensions	300	(5)
Dipole-exchange cross-over	305	(1)
One dimensional instabilities	305	(3)
Antiferromagnetic chain	308	(3)
RPA for the AFM chain	311	(5)
Exchange dominated regime	311	(4)
Dipolar dominated regime	315	(1)
Dipolar interaction in layers	316	(13)
Monolayer	318	(2)
Bilayer	320	(9)
Surface magnetism	329	(32)
Introduction	329	(1)
MFA treatment of surfaces	330	(4)
Surface excitations	334	(1)
LRPA method	335	(8)
Wave functions for bulk and surface	343	(1)
Surface density of magnon states	344	(3)
Surface phase-transitions	347	(4)
Dipolar surface effects	351	(3)
Surface magnetism in metals	354	(7)
Two-magnon eigenstates	361	(20)
Introduction	361	(3)
Green's function formalism	364	(7)
One dimension	371	(3)
Two dimensions	374	(1)
Summary of results	375	(2)
Anisotropy effects	377	(4)
Other interactions	381	(20)
Introduction	381	(4)
Two-magnon interaction	385	(2)
Three-magnon processes	387	(5)
Magnon-phonon interaction	392	(3)
Bilinear magnon-phonon interaction	395	(6)
A Group theory	401	(12)
A.1 Definition of group	401	(2)
A.2 Group representations	403	(2)
A.2.1 Reducibility	403	(2)
A.3 Orthogonality relations	405	(1)
A.4 Projection operators	406	(1)
A.5 Coordinate transformations	406	(1)
A.6 Wigner-Eckart theorem	407	(2)
A.7 Space groups	409	(2)
A.8 Bloch's theorem	411	(2)
B Appendix B Time Reversal	413	(6)
B.1 Antilinear operators	413	(2)
B.2 Anti-unitary operators	415	(1)
B.3 Time reversal	416	(3)
Index	419