Electron Spin Resonance of Paramagnetic Crystals

The authors of this contribution to the literature of resonance spectroscopy in paramagnetic systems are primarily concerned with the properties of the rare earth ions and, as such, the formal derivation of crystal field theory is set out in a manner which reflects this dominant interest. The ions of the 3d transition group are perhaps given too cursory a treatment in Chapter Two for those students of RF spectroscopy who have a somewhat less rare-earth oriented interest in the subject. Since the exam­ ples cited in the text do include some 3d transition ions, it is perhaps worthwhile in a preface of this sort to extend the broad theoretical concepts and group characteriza­ tion of Chapter Two to cover, in a somewhat more detailed manner, the derivation of the spin-Hamiltonian for this case. In Chapter Two, mention is made of the fact that for the 4f rare earth ions the spin­ orbit coupling energy is in general large compared to the crystal field influence of the surrounding ligand matrix. In such a case, the quantum number J is a good quantum number for the rare earth ion in question and the crystal field effects are taken into account within 1M, states. In this formulation, which is pursued in detail in this book, the effects of spin-orbit coupling have been taken care of at the very outset by the d~"ining of the 1M, states.

Table of Contents:
One. Paramagnetic Ions of Transition Elements.- 1. Paramagnetism of incomplete electronic shells.- 2. Level splitting of free paramagnetic ions. The Zeeman effect.- 3. Level splitting of free atoms in an external electric field. The Stark effect.- Two. Levels of Paramagnetic Ions in Crystal Lattices and Magnetic Fields.- 1. Macroscopic description of crystal systems. Symmetry of crystals.- 2. Symmetry point groups.- 3. Representations of groups.- 4. Group-theoretical classification of levels in fields of various symmetries.- 5. Application of the interaction Hamiltonian to the calculation of initial splitting.- 6. Paramagnetic ions in crystal fields. Splitting of energy levels.- 7. Qualitative picture of level splitting in a static magnetic field.- 8. Application of spin Hamiltonians. Angular dependence of EPR spectra.- Three. Electron Paramagnetic Resonance.- 1. Phenomenological treatment of EPR.- 2. Dynamic theory of paramagnetic resonance.- Four. EPR Line Shapes and line Widths.- 1. Dipole-dipole interactions.- 2. Exchange interactions.- 3. Application of the method of moments to analysis of EPR line shapes.- Five. Relaxation Processes in Paramagnetic Crystals.- 1. Spin-lattice relaxation.- 2. Relaxation associated with spin-spin interactions.- 3. Multiple cross-relaxation transitions and harmonic cross-relaxation.- 4. Level population changes due to cross-relaxation processes.- 5. Spin-lattice relaxation of ions of the 4f-and 3d-transition groups.- Six. Paramagnetic Single Crystals as Active Elements in Quantum Paramagnetic Amplifiers (QPA).- 1. Operating principles of QPA.- 2. Requirements from paramagnetic crystals in QPA.- 3. Formation of local symmetry centers in the synthesis of paramagnetic single crystals.