Using muffin-tin orbitals and the atomic-sphere approximation, we have studied the band structures of Chevrel-phase molybdenum chalcogenides, ${M}_{m}{\mathrm{Mo}}_{6}{X}_{8\ensuremath{-}x}$. Generally, these compounds exist for a broad variety of elements, $M=\mathrm{Pb},\mathrm{Sn},\mathrm{Ag},\mathrm{Cu}$ and $X=\mathrm{S},\mathrm{Se},\mathrm{Te}$. $m$ may be between 0 and 2, depending on the element $M$. We present level schemes, computed for a range of Mo and $X$ potentials, for three ${\mathrm{Mo}}_{6}{X}_{14}$ clusters appropriate for the crystal structures of ${\mathrm{Mo}}_{6}$${\mathrm{S}}_{8}$, ${\mathrm{Mo}}_{6}$${\mathrm{Se}}_{8}$, and Pb${\mathrm{Mo}}_{6}$${\mathrm{S}}_{7.5}$, respectively. Self-consistent Mo and $X$ potentials have been estimated. The cluster levels give the positions of the $\mathrm{Mo} 4d$-like bands, while the widths and dispersions are estimated analytically in the tight-binding approximation taking the covalent mixing with the $X p$ states into account. The 30 $\mathrm{Mo} d$ bands are grouped into narrow subbands derived from the levels for an isolated ${\mathrm{Mo}}_{6}$ octahedron. The Fermi level falls in a doubly degenerate ${E}_{g}$ band with Mo wave functions of ${x}^{2}\ensuremath{-}{y}^{2}$ character and the ${E}_{g}$ bandwidths vary between 65 and 35 mRy in the compounds considered. The ${E}_{g}$ band is probably crossed by a five times wider, singly degenerate ${A}_{1g}$ band of predominantly $3{z}^{2}\ensuremath{-}{r}^{2}$ character. The ${E}_{g}$ and ${A}_{1g}$ bands are the only ones crossing the Fermi level in the ternaries but, in the binaries, the octahedra are elongated and a 50-35 mRy wide ${A}_{u}$ band, split off from a triply degenerate ${T}_{2u}$ band, furthermore overlaps the ${E}_{g}$ band. The susceptibilities measured for Sn${\mathrm{Mo}}_{5}$${\mathrm{S}}_{6}$ and Pb${\mathrm{Mo}}_{5}$${\mathrm{S}}_{6}$ are in good agreement with our estimates, $N(0)=11$ states/(spin Mo-atom Ry) and ${I}_{\mathrm{Mo}}^{\mathrm{Stoner}}=40$ mRy, of the band density of states and the effective exchange-interaction parameter. From the measured electronic-specific-heat coefficients we deduce the value $\ensuremath{\lambda}=2.5$ for the electron-phonon enhancement. In accord with experimental phonon spectra we estimate frequencies of 10 and 15 meV for a rocking mode of ${\mathrm{Mo}}_{6}$${\mathrm{Se}}_{8}$ and ${\mathrm{Mo}}_{6}$${\mathrm{S}}_{8}$ units, respectively. For the average electron-phonon matrix element in the Gaspari-Gyorffy and atomic-sphere approximations we find $〈{I}^{2}〉=3\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}3}$ (Ry/bohr ${(\mathrm{R}\mathrm{y}/\mathrm{b}\mathrm{o}\mathrm{h}\mathrm{r}\phantom{\rule{0ex}{0ex}}\mathrm{r}\mathrm{a}\mathrm{d}\mathrm{i}\mathrm{u}\mathrm{s})}^{2}$. The magnitude and extreme sensitivity to local environment effects of the spin-orbit coupling in the ${E}_{g}$ band offer an explanation for the high critical magnetic fields measured in the ternaries.
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Sep 1, 1983
J.M Tarascon + 4
Open Access