ENERGY LEVELS OF CAF2 - GD3+ IN A CUBIC CRYSTAL FIELD

The energy levels of Gd3+ in the cubic crystal field of CaF2 are calculated using free-ion vectors computed with spin-other-orbit and spin-spin interactions included. The B04 and B06 coefficients are fitted to the experimental P726 and P526 splittings. Using only the 18 MJ components of the P6 free-ion levels as a basis, values of B04=-2270.79 cm-1 and B06=730.65 cm-1 are obtained. This calculation gives a mean error of 8 cm-1 between calculated and experimental levels. To improve the quality of the fit, the basis was extended to the 134 MJ components of the S8 and (P,I,D)6 free-ion levels. For this calculation, B04=-2160.0 cm-1 and B06=792.85 cm-1, and the mean error is reduced to about 0.5 cm-1. This calculation predicts the correct order of the ground-state levels and gives an over-all ground-state splitting of about one-half the experimental splitting. The calculated ground-state splitting does not change when the basis is further extended to include all higher free-ion levels containing G6 character. We conclude that a good crystal-field calculation for Gd3+ is possible and depends strongly on the quality of the free-ion states. © 1969 The American Physical Society.