Band Structure and Fermi Surface of ReO3

The nonrelativistic augmented-plane-wave (APW) method has been applied to calculate the band structure of Re${\mathrm{O}}_3$. An important feature of this calculation is that it includes corrections to the usual "muffintin" approximation. Because of convergence difficulties, the APW calculation has been carried out only at symmetry points in the Brillouin zone. These results have been used in conjunction with the Slater-Koster linear-combination-of-atomic-orbitals interpolation scheme to determine the band structure and Fermi surface throughout the Brillouin zone. The Fermi energy occurs in the $t_{2g}$ manifold of the rhenium $5d$ bands. The calculation predicts a Fermi surface consisting of two closed electron sheets centered about $\Gamma$, plus a third electron sheet which is open along $〈100〉$. The tight-binding parameters, which affect both the oxygen-rhenium ($2p-5d$) energy separation and the corresponding bandwidths, have been adjusted to fit the optical and Fermi-surface data for Re${\mathrm{O}}_3$. Spin-orbit effects for the rhenium $5d$ bands have been included by means of a spin-orbit parameter ${\xi }_{5d}$. The optimum value for this parameter has been determined by detailed comparisons between the theoretical and experimental Fermi-surface areas. The final results agree to within 10%.