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

Abstract

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 4I15=2 of the trivalent erbium ion splits into three Stark quartets Γ8 and two different doublets Γ6 and Γ7 (irreducible representations). The CF energy matrix of the Er3+ 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 g = 6:8 and g = 6:0 for Γ6 and Γ7, respectively