The Effective Crystal Field Potential

J. Mulak, Z. Gajek

• Publisher: Elsevier Science
• Year: 2000
• Print ISBN: 9780080436081
• eBook ISBN: 9780080530710
• Topic: Physical Sciences
• Subtopic: Condensed Matter

As it results from the very nature of things, the spherical symmetry of the surrounding of a site in a crystal lattice or an atom in a molecule can never occur. Therefore, the eigenfunctions and eigenvalues of any bound ion or atom have to differ from those of spherically symmetric respective free ions. In this way, the most simplified concept of the crystal field effect or ligand field effect in the case of individual molecules can be introduced.The conventional notion of the crystal field potential is narrowed to its non-spherical part only through ignoring the dominating spherical part which produces only a uniform energy shift of gravity centres of the free ion terms. It is well understood that the non-spherical part of the effective potential "seen" by open-shell electrons localized on a metal ion plays an essential role in most observed properties. Light adsorption, electron paramagnetic resonance, inelastic neutron scattering and basic characteristics derived from magnetic and thermal measurements, are only examples of a much wider class of experimental results dependent on it. The influence is discerned in all kinds of materials containing unpaired localized electrons: ionic crystals, semiconductors and metallic compounds including materials as intriguing as high-Tc superconductors, or heavy fermion systems. It is evident from the above that we deal with a widespread effect relative to all free ion terms except those which can stand the lowered symmetry, e.g. S-terms.Despite the universality of the phenomenon, the available handbooks on solid state physics pay only marginal attention to it, merely making mention of its occurrence. Present understanding of the origins of the crystal field potential differs essentially from the pioneering electrostatic picture postulated in the twenties. The considerable development of the theory that has been put forward since then can be traced in many regular articles scattered throughout the literature. The last two decades have left their impression as well but, to the authors' best knowledge, this period has not been closed with a more extended review. This has also motivated us to compile the main achievements in the field in the form of a book.

Table of contents

• Front Cover
• The Effective Crystal Field Potential
• Copyright Page
• Contents
• Chapter 1. Introduction
• Chapter 2. Parameterization of crystal field Hamiltonian
• Chapter 3. The effective crystal field potential. Chronological development of crystal field models
• Chapter 4. Ionic complex or quasi-molecular cluster. Generalized product function
• Chapter 5. Point charge model (PCM)
• Chapter 6. One-configurational model with neglecting the non-orthogonality. The charge penetration and exchange effects
• Chapter 7. The exclusion model. One-configurational approach with regard to non-orthogonality of the wave functions
• Chapter 8. Covalency contribution, i.e. the charge transfer effect
• Chapter 9. Schielding and antishielding effect: contributions from closed electron shells
• Chapter 10. Electrostatic crystal field contributions with consistent multipolar effects. Polarization
• Chapter 11. Crystal field effect in the Stevens perturbation approach
• Chapter 12. Specific mechanisms of metallic states contributing to the crystal field potential
• Chapter 13. Screening the crystal field in metallic materials
• Chapter 14. Virtual bound state contribution to the crystal field potential
• Chapter 15. Hybridization or covalent mixing between localized states and conduction band states in metallic crystals
• Chapter 16. Density functional theory approach
• Chapter 17. Analysis of the experimental data . Interpretation of crystal field parameters with additive models
• Chapter 18. Lattice dynamics contribution
• Chapter 19. Extension of the crystal field potential beyond the one-electron model
• Chapter 20. Appendices
• References
• Author Index
• Subject Index