Crystal-Field Splitting of Electronic Configuration d(N): d(3) (d7) Configuration in C3 Symmetry,
HARRY DIAMOND LABS ADELPHI MD
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In the transition-metal ions, at least in the first series, the spin- orbit interaction is usually assumed to be negligible when compared to the Coulomb interaction of the N electrons in the d superscript N configuration. When the transition metal ion enters a solid, the interaction of the electrons with the crystal field is very large. Thus the two largest interactions for a transition metal ion in a solid are the Coulomb interaction and the crystal- field interaction. In this report and those to follow in this series, the matrix elements of the crystal field and Coulomb interaction will be calculated for various point symmetries. The matrix elements of the crystal field and Coulomb interaction are calculated for the d3 d7 electronic configuration. The crystal field matrix elements for C3i symmetry are given in tabular form. The Coulomb plus crystal field matrix was diagonalized using aproximate values of the Slater parameters and approximate crystal field parameters for CR3 in Gd3Sc2Ga3O12 GSGG. A similar result is given assuming a cubic approximation for the crystal field in GSGG.
- Atomic and Molecular Physics and Spectroscopy