Energy Levels of Trivalent Gadolinium and Ionic Contributions to the Ground-State Splitting

Abstract

This paper represents an attempt to estimate the ionic contributions to the ground-state splitting of the trivalent gadolinium ion in a lanthanum ethyl sulfate lattice. The energy levels of the $4{f}^{7}$ configuration are calculated and compared with those observed experimentally. The calculated ground-state $g$ factor is found to deviate significantly from its measured value. An attempt has been made to estimate the contributions to the ground-state splitting for eight different mechanisms: (1) a fourth-order mechanism that is linear in the crystal-field strength and cubic in the spin-orbit interaction; (2) fourth-order mechanisms that are quadratic in both the crystal-field strength and the spin-orbit interaction; (3) a third-order spin-spin mechanism acting within the $4{f}^{7}$ configuration; (4) Pryce's second-order spin-spin configuration mixing mechanism; (5) a second-order relativistic mechanism; (6) mechanisms involving configuration mixing by the crystal field; (7) mechanisms involving nonlinear electrostatically correlated crystal-field interactions; (8) fifth-order configuration interaction mechanisms. The total contribution due to these mechanisms is found to be twice the magnitude of the observed splitting and of opposite sign. It is suggested that no purely ionic model can account for the observed splitting and that the correct explanation must involve the detailed interaction of the gadolinium ion with its ligands. A semiqualitative explanation of some of the intensity features of the crystal and solution spectra of trivalent gadolinium is attempted.