Generalized spin-Hamiltonian for paramagnetic ions in crystals. I. General formalism and its application to cubic crystalline symmetry

Abstract

In view of the limitations of the usual spin-Hamiltonian for characterizing exactly the low-lying levels of the paramagnetic ions in crystals, as evident from some recent electron paramagnetic resonance (EPR) and electron-nuclear double resonance (ENDOR) experiments on iron-transition group and rare-earth ions, a method is described here for deducing a general spin-Hamiltonian determined exclusively by the crystal-field symmetry. The Hamiltonian thus derived obviously includes all possible independent spin-operators, and, in general, has more terms than those considered in the usual spin-Hamiltonian. The method has been applied to the case of cubic crystalline symmetry, and the spin-Hamiltonian is written out correctly for the Zeeman field (H) independent part and the linearly field-dependent part, for all ions with both electron spin S and nuclear spin I up to 2. Terms which are quadratic in H are considered for spin values S and I up to 1 only. Relative importance of the independent operators are discussed with particular reference to two cases: Co²⁺ in eight co-ordinated cubic compounds and Yb³⁺ in CaF₂, which are expected to be two extreme examples of the effect of the excited levels on the ground state. Some of the terms which are usually neglected in the usual spin-Hamiltonian are shown to make significant contributions to the spin-levels. The importance of the terms quadratic in Zeeman field is emphasized for precise ENDOR experiments.