Influence of the interconfigurational interaction on the crystal field of Ln3+ ions

A theory of the crystal field for Ln³⁺ ions is proposed which takes account of the difference in the effect of excited configurations on high-lying and low-lying multiplets. The effective-operator method in third-order perturbation theory is used to obtain the Hamiltonian of the crystal field, which in addition to the usual terms contains energy-dependent operators. Their role is discussed in detail. For the new operators we have obtained convenient expressions which make it possible for the first time to determine the parameters of an odd crystal field on the basis of an analysis of the structure of the energy spectrum. Theory is compared with experiment for the laser crystals Y₃Al₅O₁₂:Tm³⁺ and LiYF₄:Pr³⁺. Taking the new terms of the crystal-field Hamiltonian into account produces an additional shift of individual levels within the limits from −40 cm⁻¹ to 40 cm⁻¹ and makes it possible in a number of cases not only to substantially reduce the value of the standard deviation, but also to obtain the correct arrangement of levels. Zh. éksp. Teor. Fiz. 116, 2087–2102 (December 1999)