Modeling the crystal-field splitting of energy levels of Er~(3+)(4f~(11)) in charge-compensated sites of KPb_2Cl_5

摘要

A point-charge lattice-sum model corrected for induced multipoles is used to investigate the crystal-field splitting of the ~(2S+1)L_J energy levels of Er~(3+)(4f~(11)) ions that occupy charge-compensated sites in the laser host crystal KPb_2Cl_5. Spectroscopic data are reported and analyzed for Er~(3+) between 1550 and 440 nm at cryogenic temperatures. The crystal-field (Stark) splitting of the ground-state manifold ~4I_(15/2) and the splitting of individual excited manifolds of Ei~(3+) are established from analyses of temperature-dependent (hot band) absorption spectra. The analyses confirm the Stark splitting of the ~4I_J and ~4F_(9/2) manifolds that are reported in the literature. From an analysis of the data, it appears that only one of the two possible Pb~(2+) sites serving as a charge-compensated site for Er~(3+) is involved in the optical activity of the Er~(3+) ions. From an examination of the crystallographic data of KPb_2Cl_5, we identify a possible site for the optically active Er~(3+) ion in the lattice and calculate the lattice-sum components for that site. These components are used to evaluate the crystal-field splitting of the energy levels of Er~(3+) at that site. The charge-compensation model assumes that Er~(3+) substitutes for Pb~(2+) in the Pb(2) site with a vacancy in a nearby K~+ site. To obtain the best overall agreement between calculated and experimental levels, the position of the Er~(3+) ion is treated as an adjustable parameter along the quantization axis. Individual manifold centroids of the Er~(3+) ion are also varied. From a least-squares fitting analysis, we obtain a rms deviation of 10 cm~(-1) between 48 calculated-to-observed Stark levels.