Electronic band structures of the scheelite materialsCaMoO4,CaWO4,PbMoO4,andPbWO4

Abstract

Density-functional calculations using the linearized-augmented-plane-wave method were carried out for the scheelite materials ${\mathrm{CaMoO}}_{4},$ ${\mathrm{CaWO}}_{4},$ ${\mathrm{PbMoO}}_{4},$ and ${\mathrm{PbWO}}_{4}$ in order to determine their ground-state electronic properties. The results indicate that ${\mathrm{CaMoO}}_{4}$ and ${\mathrm{CaWO}}_{4}$ have direct band gaps at the center of the Brillouin zone, while ${\mathrm{PbMoO}}_{4}$ and ${\mathrm{PbWO}}_{4}$ have band extrema at wave vectors away from the zone center with possibly indirect band gaps. The magnitudes of the band gaps increase in the order ${\mathrm{PbMoO}}_{4}{<\mathrm{PbWO}}_{4}{<\mathrm{CaMoO}}_{4}{<\mathrm{CaWO}}_{4}.$ The valence and conduction bands near the band gap are dominated by molecular orbitals associated with the ${\mathrm{MoO}}_{4}^{\mathrm{\ensuremath{-}}\mathrm{\ensuremath{\alpha}}}$ and ${\mathrm{WO}}_{4}^{\mathrm{\ensuremath{-}}\mathrm{\ensuremath{\alpha}}}$ ions, where $\ensuremath{\alpha}\ensuremath{\approx}2.$ The valence-band widths are 5 and 5.5 eV for the Ca and Pb materials, respectively. In the Pb materials, the Pb $6s$ states form narrow bands 1 eV below the bottom of the valence bands, and also hybridize with states throughout the valence bands, while the Pb $6p$ states hybridize with states throughout the conduction bands. In the Ca materials, the Ca $3d$ states contribute to a high density of states 3--4 eV above the bottom of the conduction bands.