Crystal Field for Yb3+ in Garnets

Abstract

An attempt has been made to determine the nine parameters required to define the crystal field acting on an Yb3+ ion in yttrium gallium garnet. Even for this most favorable case, there are at present insufficient data to determine the parameters from experiment alone, and we have therefore carried out an analysis combining seven independent and reliable experimental measurements with theoretical estimates based on an accurate point-charge calculation. The results of the point-charge calculations, made also for several other garnet lattices, indicate that distortions from a cubic potential are generally large, and that the second-degree terms are poorly determined by the model. In fitting to the experimental data, the parameters V20, V22, V40, and V60 (Vnm = Anm〈rn〉) were treated as adjustable, and the remaining parameters given the values expected from the point-charge ratios. The set of parameters thus obtained fit the six experimental g values to within 0.2 and the two fitted energy splittings to within 2 cm—1, and they also predict further energy levels in agreement with less definite experimental evidence. The remaining discrepancies reflect the inadequacies of the point-charge model. The apparent success of previous analyses of data for Yb garnets in terms of a near-cubic approximation is discussed, and it is shown how an insufficient number of parameters may incorrectly account for a limited set of experimental data.