First-principles study of cubic Bi pyrochlores

摘要: We examined a range of cubic ${\mathrm{Bi}}_{2}{B}_{2}{\mathrm{O}}_{6}{\mathrm{O}}^{\ensuremath{'}}$ ($B=\mathrm{Ti}$, Ru, Rh, Ir, Os, and Pt) pyrochlores with density functional theory (DFT) calculations report the structural parameters along electronic structure bismuth in their ideal cubic, defect-free structure. also role cation displacements within find that only ${\mathrm{Bi}}_{2}{\mathrm{Ti}}_{2}{\mathrm{O}}_{7}$ shows substantial increase favorability Bi displacements. For ${\mathrm{Bi}}_{2}{\mathrm{Ti}}_{2}{\mathrm{O}}_{7}$, we an average displacement $0.38\ifmmode\pm\else\textpm\fi{}0.02\phantom{\rule{0.3em}{0ex}}\mathrm{\AA{}}$ for energy change $0.146\ifmmode\pm\else\textpm\fi{}0.001\phantom{\rule{0.3em}{0ex}}\mathrm{eV}∕\mathrm{Bi}$ atom. The follows spin-ice rules reported complex Bi-based pyrochlores, where two-long two-short bonds are found each tetrahedron ${\mathrm{Bi}}_{4}{\mathrm{O}}^{\ensuremath{'}}$. Examination main driving force is extent $\mathrm{Bi}\text{\ensuremath{-}}{\mathrm{O}}^{\ensuremath{'}}$ interactions metallic pyrochlores. In observe more overlap $\mathrm{Bi}\phantom{\rule{0.2em}{0ex}}s$ $p$ states $\mathrm{O}\phantom{\rule{0.2em}{0ex}}2p$ states, similar to ${\mathrm{Bi}}_{2}{\mathrm{Sn}}_{2}{\mathrm{O}}_{7}$, PbO, SnO, which leads asymmetric around cation. This electron associated cations ${\mathrm{Bi}}_{2}{\mathrm{Ti}}_{2}{\mathrm{O}}_{7}$. Our DFT results match general understanding from experimental studies but underestimate ${\mathrm{Bi}}_{2}{\mathrm{Ru}}_{2}{\mathrm{O}}_{7}$.