Electronic structure of Chevrel-phase high-critical-field superconductors

Using muffin-tin orbitals and the atomic-sphere approximation, we have studied the band structures of Chevrel-phase molybdenum chalcogenides, MₘMo₆X_8-x. Generally, these compounds exist for a broad variety of elements, M=Pb,Sn,Ag,Cu and X=S,Se,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 Mo₆X₁₄ clusters appropriate for the crystal structures of Mo₆{S}₈$, ${Mo}₆Se₈, and PbMo₆{S}7.5$, respectively. Self-consistent Mo and $X$ potentials have been estimated. The cluster levels give the positions of the $Mo 4d$-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 $Mo d$ bands are grouped into narrow subbands derived from the levels for an isolated ${Mo}₆$ octahedron. The Fermi level falls in a doubly degenerate ${E}g$ band with Mo wave functions of ${x}²{-}{y}²$ 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 $3{z}²{-}{r}²$ 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${Mo}₅S₆ and PbMo₅{S}₆$ are in good agreement with our estimates, $N(0)=11$ states/(spin Mo-atom Ry) and ${I}MoStoner=40$ mRy, of the band density of states and the effective exchange-interaction parameter. From the measured electronic-specific-heat coefficients we deduce the value ${λ}=2.5$ for the electron-phonon enhancement. In accord with experimental phonon spectra we estimate frequencies of 10 and 15 meV for a rocking mode of ${Mo}₆Se₈ and Mo₆{S}₈$ units, respectively. For the average electron-phonon matrix element in the Gaspari-Gyorffy and atomic-sphere approximations we find $〈{I}²〉=3×{}{10}^{{-}3}$ (Ry/bohr ${(Ry/bohr{{0ex}{0ex}}radius)}²$. 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.