Influence of Covalency upon Rare-Earth Ligand Field Splittings

摘要: Experimental results for the shift with uniaxial stress of $(^{2}F_{\frac{5}{2}},{\ensuremath{\Gamma}}_{7})\ensuremath{\rightarrow}(^{2}F_{\frac{7}{2}},{\ensuremath{\Gamma}}_{7})$ laser transition in ${\mathrm{Tm}}^{2+}$:Ca${\mathrm{F}}_{2}$ and ${\mathrm{Tm}}^{2+}$:Sr${\mathrm{F}}_{2}$ are presented. The results, 1.75 ${\mathrm{cm}}^{\ensuremath{-}1}$${(\mathrm{d}\mathrm{y}\mathrm{n}/{\mathrm{cm}}^{2})}^{\ensuremath{-}1}$ 1.78 ${\mathrm{cm}}^{\ensuremath{-}1}$${(\mathrm{d}\mathrm{y}\mathrm{n}/{\mathrm{cm}}^{2})}^{\ensuremath{-}1}$, used to calculate radial dependence cubic ligand field splitting. resulting is somewhat larger than that predicted by familiar electrostatic model Partially determine its influence on above result, we have considered effect covalency means a semiempirical molecular-orbital model. overlap $4f$ orbitals neighboring fluoride ions was calculated using Hartree-Fock wave functions known internuclear distances. off-diagonal elements interaction Hamiltonian were obtained from Wolfsberg-Helmholz approximation ${H}_{\mathrm{ij}}=\frac{2{S}_{\mathrm{ij}}({H}_{\mathrm{ii}}+{H}_{\mathrm{jj}})}{2}$. A range reasonable values diagonal analogy those necessary explain iron-series splittings. largest group function ${\mathrm{F}}^{1\ensuremath{-}}$ ligands found be 3.6% leads sizable (our best estimate Ca${\mathrm{F}}_{2}$ 50%) covalent contribution We also investigated some consequences this magnitude. part energy greater part. thus better agreement experiment. Transferred hyperfine effects compared experiment, but extent hard ascertain because uncertainty sign experimental quantity polarization effects. orbital reduction factor much smaller observed. expected variation ${(\mathrm{rare}\mathrm{earth})}^{3+}\ensuremath{-}{F}^{1\ensuremath{-}}$ as atomic number.