Electronic Structure of MgF2:Co++

Abstract

The ${\mathrm{F}}^{19}$ superhyperfine structure of the EPR spectra of ${\mathrm{Co}}^{++}$ in Mg${\mathrm{F}}_{2}$ is interpreted with simple molecular-orbital theory. A necessary preliminary analysis is made of the $g$ tensor and of the spacing of the six Kramers doublets derived from the $^{4}T_{1}$ ground manifold. The ligand-field parameters of the rhombic field, $\ensuremath{\Delta}\ensuremath{\cong}510$ ${\mathrm{cm}}^{\ensuremath{-}1}$ and $\ensuremath{\Gamma}\ensuremath{\cong}\ensuremath{-}390$ ${\mathrm{cm}}^{\ensuremath{-}1}$, and the spin-orbit coupling, $\ensuremath{\lambda}\ensuremath{\cong}\ensuremath{-}157$ ${\mathrm{cm}}^{\ensuremath{-}1}$, are significantly different from values derived from less complete data. The reported superhyperfine interactions provide sufficient data to determine, without recourse to much less certain orbital-reduction factors, the $s$-, sigma-, and pi-bonding fractions: ${f}_{s}=(0.61\ifmmode\pm\else\textpm\fi{}0.02)%$, ${f}_{\ensuremath{\sigma}}=(3.9\ifmmode\pm\else\textpm\fi{}0.3)%$, and ${f}_{\ensuremath{\pi}}=(0.9\ifmmode\pm\else\textpm\fi{}0.3)%$ for the two equivalent fluorine ions along [110]. For the other four fluorine ions similar estimates are obtained. These results are at variance with the suggestion, made for octahedral ${\mathrm{Co}}^{++}$, that sigma and pi bonding are of comparable magnitude.