Crystal-Field Energy Levels of Trivalent Erbium Ion in Cubic Symmetry

This paper describes a scheme for the numerical calculation of crystal field (CF) energy levels and at the same time wave functions of the trivalent erbium ion in cubic symmetry. The 16-fold degenerate term 4I of the trivalent erbium ion splits into three Stark quartets Γ and two different doublets Γ and Γ (irreducible representations). The CF energy matrix of the Er ion has been constructed and calculated from the complete diagonalization method, and the corresponding wave functions were used to calculate the ground state g-values. This method is outlined and illustrated by the examples of the Si:Er for comparison. The calculated g-factors are = 6:8 and = 6:0 for Γ and Γ , respectively