Zeeman Splittings of Paramagnetic Atoms in Crystalline Fields

Abstract

The paper deals with the energy levels as a function of magnetic field of paramagnetic ions in crystalline surroundings. The necessary information is given to write down the Hamiltonian matrix for ions in common crystalline fields. The method has been previously developed and it consists of determining the Hamiltonian matrix of $\ensuremath{\beta}\mathrm{H}\ifmmode\cdot\else\textperiodcentered\fi{}(\mathrm{L}+2\mathrm{S})$ for the lowest states of an ion by the methods of group theory and time inversion considerations. The Hamiltonian matrix contains a certain number of undetermined constants which may be evaluated if the wave functions of the ions are known or the constants may be determined from experiment. In general, the number of available constants is larger than found in the conventional spin Hamiltonian formalism. The present method may be applied in cases where the conventional spin Hamiltonian formalism is inadequate to describe experimental results or where greater accuracy is required.