We examined a range of cubic ${\mathrm{Bi}}_2{B}_2{\mathrm{O}}_6{\mathrm{O}}^{\prime }$ ($B=\mathrm{Ti}$, Ru, Rh, Ir, Os, and Pt) pyrochlores with density functional theory (DFT) calculations and report the structural parameters along with the electronic structure of the bismuth pyrochlores in their ideal cubic, defect-free structure. We also examined the role of cation displacements within the cubic structure and find that only ${\mathrm{Bi}}_2{\mathrm{Ti}}_2{\mathrm{O}}_7$ shows a substantial increase in favorability with Bi cation displacements. For ${\mathrm{Bi}}_2{\mathrm{Ti}}_2{\mathrm{O}}_7$, we find an average displacement of $0.38\pm 0.02\mathrm{\AA }$ for the Bi cation and an energy change of $0.146\pm 0.001\mathrm{eV}∕\mathrm{Bi}$ atom. The cation displacement in ${\mathrm{Bi}}_2{\mathrm{Ti}}_2{\mathrm{O}}_7$ follows the spin-ice rules reported in complex Bi-based pyrochlores, where two-long and two-short bonds are found in each tetrahedron of ${\mathrm{Bi}}_4{\mathrm{O}}^{\prime }$. Examination of the electronic structure shows the main driving force in the displacement is the extent of $\mathrm{Bi}\text{−}{\mathrm{O}}^{\prime }$ interactions in ${\mathrm{Bi}}_2{\mathrm{Ti}}_2{\mathrm{O}}_7$ and metallic bismuth pyrochlores. In ${\mathrm{Bi}}_2{\mathrm{Ti}}_2{\mathrm{O}}_7$, we observe more overlap of $\mathrm{Bi}s$ and $p$ states with $\mathrm{O}2p$ states, similar to the reported electronic structure of ${\mathrm{Bi}}_2{\mathrm{Sn}}_2{\mathrm{O}}_7$, PbO, and SnO, which leads to the asymmetric electronic structure around the Bi cation. This asymmetric electron structure is associated with the displacement of cations in ${\mathrm{Bi}}_2{\mathrm{Ti}}_2{\mathrm{O}}_7$. Our DFT results match the general understanding from experimental studies but underestimate the displacement in ${\mathrm{Bi}}_2{\mathrm{Ru}}_2{\mathrm{O}}_7$.

• Received 6 November 2007

DOI:https://doi.org/10.1103/PhysRevB.77.104123