Perturbation methods in the calculation of zeeman interactions and magnetic dipole line strengths for d3 trigonal-crystal spectra

Abstract

Using a perturbation expansion based on a strong cubic-field zeroth-order approximation, we have obtained analytical expressions for the g values of the t23, A24, and F2 terms for d3 impurity ions in trigonal crystal fields. We have compared these expressions whth the results of a numerical calculation in which the magnetic dipole operator was transformed to the basis of eigenvectors of the zero-field Hamiltonian computed within the complete d3 configuration, and we find them to be a very good approximation. This is not true of the published g-value expressions which are currently available. Absolute magnetic dipole absorption cross sections and nonlinear g values are also calculated. This the first time such a detailed calculation of these quantities has been made for transition-ion impurity systems. For levels derived from cubic terms other than t23, A24, and E2, the analytical-perturbation techniques are not satisfactory and numerical methods must be used. We present an analysis of the g values of the nominally t23 terms, A24, E2, T12, and T22, for emerald, ruby, ZnAl2O4: Cr3+, MgO: Cr3+, and ZnO: Co2+, and of magnetic dipole absorption cross sections for centrosymmetric ZnAl2O4: Cr3+ and MgO: Cr3+. These systems were chosen because there are quite extensive experimental data available on them. The model parameters were determined from the zero-field energy levels, and very good agreement with experiment was obtained in our calculation of the g values and absorption strengths. This provides confidence in the validity of the crystal-field model to predict the magnetic properties of at least the t23 levels, which couple weakly to phonons. © 1970 The American Physical Society.