On standardization of the spin Hamiltonian and the ligand field Hamiltonian for orthorhombic symmetry

Abstract

The idea that the ratio E/D ≡ λ can be confined by a proper choice of the axis system to the range (0,±1/3) serves as a basis for the standardization of the spin Hamiltonian and the ligand field Hamiltonian for orthorhombic symmetry. Due to recent results on the transformation of the Stevens operators Oqk, relations are given which allow for extension of the standardization to the spin Hamiltonian for paramagnetic centers with spin S≥2. Several EPR studies of 3dn and 4 f n ions in crystals are reconsidered. The results prove the usefulness of the clear choice of the parameters Bqk suggested by the standardization idea. Application of the standardization in the area of the ligand field theory, which seems rather novel, is also considered. Crystal-field parameters for several rare earth ions in garnets are recalculated. An arbitrary choice from among the equivalent sets of the crystal-field parameters used in the review by Morrison and Leavitt (1982) should be replaced by a transformation to the ‘‘standard’’ set.