Magnetic Ions in Crystals

This text demonstrates that it is possible to replace crystal field theory as a basis for the spin-Hamiltonians of single magnetic ions and pairs of lattices of magnetic ions, even when the nuclei have vibrational motion.

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The theory developed in this text begins with a generic Hamiltonian, one that is common to most molecular and solid state problems and that does not violate the symmetry requirements imposed on electrons and nuclei. Using a version of degenerate perturbation theory due to Bloch and the introduction of Wannier functions, projection operators and unitary transformations, the author shows that it is possible to replace crystal field theory as a basis for the spin-Hamiltonians of single magnetic ions and pairs of lattices of magnetic ions, even when the nuclei have vibrational motion. The power of the method is further demonstrated by showing that it can be extended to include lattice vibration and conduction by electron hopping such as probably occurs in high-Tc superconductors. The book should be of interest to all physicists and chemists concerned with understanding the special properties of molecules and solids that are imposed by the presence of magnetic ions.