Electron Paramagnetic Resonance of Transition Ions

by Abragam, A.; Bleaney, B.

• ISBN13: 9780199651528
• ISBN10: 0199651523
• Edition: Reprint
• Format: Paperback
• Copyright: 2012-07-26
• Publisher: Oxford University Press

Summary

This book is a reissue of a classic Oxford text, and provides a comprehensive treatment of electron paramagnetic resonance of ions of the transition groups. The emphasis is on basic principles, with numerous references to publications containing further experimental results and more detailed developments of the theory. An introductory survey gives a general understanding, and a general survey presents such topics as the classical and quantum resonance equations, thespin-Hamiltonian, Endor, spin-spin and spin-lattice interactions, together with an outline of the known behaviour of ions of each of the five transition groups, at the experimentalist's level. Finally a theoretical survey, using group theory and symmetry properties, discusses the fundamentals of the theory ofparamagnetism.

Table of Contents

Preliminary Survey
Introduction to Electron Paramagnetic Resonance
Electronic and nuclear magnetic dipole moments	p. 1
Hyperfine structure in a free atom or ion	p. 5
Magnetic resonance	p. 9
Effective spin and anisotropy	p. 10
'Initial splittings' or 'fine structure'	p. 16
Magnetic hyperfine structure	p. 25
Hyperfine structure including nuclear electric quadrupole interaction	p. 31
A simple example	p. 33
Transition group ions and ligand fields	p. 39
Spin-spin interaction	p. 52
Spin-lattice interaction	p. 60
Dynamic nuclear orientation	p. 74
Endor	p. 87
Experimental aspects	p. 92
General Survey
The Resonance Phenomenon
Use of rotating coordinates	p. 95
Magnetic resonance	p. 96
Quantum-mechanical analysis	p. 98
Magnetic resonance in aggregated systems	p. 102
Adiabatic rapid passage	p. 104
Relaxation effects	p. 108
Radio-frequency pulses and spin-echoes	p. 113
Solution of the macroscopic equations for slow passage	p. 115
Intensity and line width	p. 119
Spectrometer sensitivity	p. 125
The Spin Hamiltonian and the Spectrum
The spin Hamiltonian	p. 133
The effect of anisotropy in the g-factor	p. 135
Multipole fine structure	p. 139
Fine structure in cubic fields (S = &frac52;, &frac72;)	p. 142
Electronic 'quadrupole' fine structure (S = 1, &frac32;)	p. 151
Electronic 'quadrupole' fine structure in a strong magnetic field	p. 156
Hyperfine structure I-introductory remarks	p. 163
Hyperfine structure II-strong external field	p. 167
Hyperfine structure III-nuclear electric quadrupole interaction	p. 178
'Forbidden' hyperfine transitions	p. 186
Ligand hyperfine structure	p. 192
The spectrum of a powder	p. 200
Effects of crystal imperfections	p. 205
Weak-field Zeeman interaction for non-Kramers ions	p. 209
Electron-Nuclear Double Resonance (Endor)
Introduction	p. 217
The Endor spectrum	p. 223
Enhancement of the nuclear transition probability	p. 228
Endor on donors in silicon	p. 234
Endor on donors in silicon-relaxation effects	p. 239
Relaxation effects in Endor-general	p. 243
The hyperfine structure of europium	p. 251
The Endor spectrum of Nd3+ in LaCl3	p. 255
Endor measurements of ligand hyperfine structure	p. 259
Endor line widths	p. 264
'Indirect' observation of Endor transitions	p. 272
Summary	p. 274
The Lanthanide (4f) Group
Lanthanide compounds	p. 271
The free ions	p. 282
Crystalline field theory-C3h symmetry	p. 285
Magnetic hyperfine structure	p. 296
Nuclear electric quadrupole interaction	p. 301
Experimental results for ethylsulphates and anhydrous chlorides	p. 303
Experimental results for the double nitrates, Ln2Mg3(NO3)12 24H2O	p. 320
Lanthanide ions in cubic symmetry	p. 325
Ions with a half-filled 4f-shell, 4f7, 8S7\2, Eu2, Gd3+ Tb4+	p. 335
Higher-order terms in the spin Hamiltonian	p. 341
The Actinide (5f) Group
Ions and compounds of the actinide group	p. 346
Tripositive actinide ions	p. 348
Actinide ions in CaF2	p. 350
Actinide ions in octahedral symmetry	p. 354
Neptunyl and plutonyl ions	p. 359
Ions of the 3d Group in Intermediate Ligand Fields
Introduction	p. 365
The intermediate crystal field approach	p. 372
The strong crystal field approach	p. 377
The effects of bonding	p. 392
The electronic spin Hamiltonian	p. 398
Magnetic hyperfine interaction	p. 406
Nuclear electric quadrupole and nuclear Zeeman interaction	p. 414
3d1. Ti3+ in an octahedral field. 2D, L = 2, S = ½	p. 417
3d2. V3+, Cr4+ in an octahedral field. 43F, L = 3, S = 1	p. 426
3d3. V2+, Cr3+ Mn4+ in an octahedral field. 4F, L = 3, S = &frac32;	p. 430
3d4. Cr2+ in an octahedral field. 5D, L = 2, S = 2	p. 434
3d5. Cr+, Mn2+ Fe3+ in an octahedral field. 6S, L = 0, S = &frac52;	p. 436
3d6. Fe2+ in an octahedral field. 5D, L = 2, S = 2	p. 443
3d7. Fe+ Co2+, Ni3+ in an octahedral field. 4F, L = 3, S = &frac32;	p. 446
3d8. Co+, Ni2+, Cu3+ in an octahedral field. 3F, L = 3, S = 1	p. 449
3d9. Ni+, Cu2+ in an octahedral field. 2D, L = 2, S = ½	p. 455
3d ions in tetrahedral symmetry	p. 467
Ions of the d-Groups in Strong Ligand Fields
The ions and their compounds	p. 472
The strong ligand field octahedral complex	p. 476
Hyperfine interaction	p. 478
d1 in strong octahedral field; (d¿)1, (t2), S = ½	p. 478
d2 in strong octahedral field; (d¿) 2, (t2)2 S = 1	p. 479
d3 in strong octahedral field; (d¿)3, (t2)3, S = &frac32;	p. 479
d4 in strong octahedral field; (d¿)4, (t2)4, S = 1	p. 480
d5 in strong octahedral field; (d¿)5, (t2)5, S = ½	p. 481
d6 in strong octahedral field; (d¿) 6, (t2)6, S = 0	p. 486
d7 in strong octahedral field; (d¿)6 (d¿), (t2)6e, S = ½	p. 486
d8 in strong octahedral field; (d¿)6 (d¿)2, (t2)2e2, S = 1	p. 487
d9 in strong octahedral field; (d¿)6 (d¿)3, (t2)6e3, S = ½	p. 487
d1 in cubic (eightfold) coordination	p. 490
Spin-Spin Interaction
Introduction	p. 491
Magnetic dipole-dipole interaction	p. 492
Exchange interaction	p. 495
Multipole interactions	p. 499
Interaction between a pair of similar ions	p. 502
Interaction between a pair of dissimilar ions	p. 509
Line broadening by spin-spin interaction	p. 514
Line shape due to dipolar spin-spin interaction	p. 521
Effect of exchange interaction on line shape	p. 527
Magnetic dilution, and the spectra of pairs	p. 529
Temperature-dependent effects	p. 535
Spin-Phonon Interaction
The attainment of thermal equilibrium	p. 541
The phonon radiation bath	p. 547
Spin-lattice relaxation by phonons-Waller processes	p. 551
Spin-lattice relaxation by modulation of the ligand field	p. 557
Summary and comparison with experiment	p. 565
The phonon 'bottle-neck' and phonon 'avalanche'	p. 574
Theoretical Survey
The Electronic Zeeman Interaction
The interaction between electrons and a magnetic field	p. 585
The Zeeman effect in a free atom (or ion)	p. 586
LS-coupling and the Landé formula	p. 587
Self-consistent field configurations	p. 589
Spin-orbit coupling	p. 592
Matrix elements between Slater determinants	p. 593
Introduction of the crystal field	p. 595
Gboup Theory-An Outline
In variance and degeneracy	p. 601
Linear representations, equivalence, and irreducibility	p. 602
Orthogonality relations, characters, and classes	p. 603
Reduction of a representation and calculation of the characters	p. 605
Splitting of a degenerate level by a perturbation of lower symmetry	p. 607
The direct product of two representations	p. 611
Group Theory-The Rotation Group
Angular momentum	p. 615
The irreducible representations	p. 617
The coupling of angular momenta	p. 620
Multiple vector coupling and Racah symbols	p. 622
Irreducible tensor operators, the Wigner-Eckart theorem, and equivalent operators	p. 624
The Cubic Group and Some Other Groups
The cubic group	p. 629
The fictitious angular momentum	p. 632
The multiplets ¿4 and ¿5 in trigonal axes	p. 633
The double cubic group	p. 634
Groups of lower symmetry	p. 638
Improper rotations	p. 640
Time Reversal and Kramers Degeneracy
Operations involving the time	p. 643
Complex conjugation	p. 644
Determination of the time reversal operator	p. 646
Kramers degeneracy	p. 647
Time-reversal operator in the J, M> representation	p. 649
The 'Spin Hamiltonian' for a Kramers doublet	p. 650
The rhombic group	p. 654
Threefold symmetry	p. 654
Selection rules related to time-reversal	p. 656
The effect of an applied electric field on a paramagnetic ion	p. 659
Elementary Theory of the Crystal Field
The crystal field (or crystal potential)	p. 665
Equivalent operators	p. 670
Off-diagonal matrix elements of the crystal field	p. 676
The electronic Zeeman interaction	p. 677
Electron spin-spin interactions	p. 678
Hyperfine Structure
Electrostatic hyperfine interactions	p. 680
Magnetic hyperfine interactions	p. 687
Alternative derivation of the magnetic hyperfine interaction	p. 690
Equivalent operators for the magnetic hyperfine interaction	p. 692
The effect of s-electrons: configuration interaction	p. 695
The effect of s-electrons: core polarization	p. 702
Finer effects in the theory of hyperfine structure	p. 706
Ions in a Weak Crystal Field (f Electrons)
Kramers ions in a weak crystal field	p. 713
Rare-earth ions in cubic symmetry	p. 719
The quadruplet ¿8	p. 721
Representation of an irreducible tensor within the quadruplet ¿8-quadrupole coupling	p. 731
Non-Kramers ions in the rare-earth group	p. 732
Non-Kramers rare-earth ions in cubic surroundings	p. 739
Intermediate Crystal Fields (The Iron Group)
Effect of the cubic crystal potential	p. 742
'Singlet' orbital ground state (ions of type A)	p. 745
Triplet orbital ground state (ions of type B)	p. 751
Departures from cubic symmetry	p. 755
The influence of excited terms	p. 758
The Effects Of Covalent Bonding
Summary of the foregoing theory	p. 761
The molecular orbitals model for covalent bonding	p. 762
Bonding and anti-bonding orbitals, overlap, and covalency	p. 764
The ground states in weakly covalent compounds	p. 767
Orbital momentum and spin-orbit coupling in the presence of covalent bonding	p. 773
Ligand hyperfine structure for ions of type A	p. 777
Orbital singlets: correction terms for the ligand hyperfine structure	p. 781
Ligand hyperfine structure for ions of type B	p. 784
Ligand quadrupole hyperfine structure	p. 788
The Jahn-Teller Effect in Paramagnetic Resonance
Introduction	p. 79$
The Born-Oppenheimer approximation and the Jahn-Teller theorem	p. 79$
The magnetic properties of a 2E level	p. 79$
The static Jahn-Teller effect in a 2E state	p. 80$
Dynamic features of the static Jahn-Teller effect	p. 80$
The dynamic Jahn-Teller effect in a 2E state	p. 80$
Motional narrowing of the Jahn-Teller spectrum	p. 82$
Comparison with experiment	p. 832
The Jahn-Teller effect in a triplet state	p. 835
The Jahn-Teller effect in an orbital triplet with ¿3 coupling	p. 835
The Jahn-Teller effect in an orbital triplet with ¿5 coupling	p. 841
Comparison with experiment	p. 846
Thermal and magnetic properties of a paramagnetic substance	p. 848
Tables 1 to 26	p. 856
Bibliography	p. 879
Author Index	p. 893
Subject Index	p. 898
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