Jahn-Teller mediated ordering in layeredLixMO2compounds

Lithium ordering in layered ${\mathrm{Li}}_{x}M{\mathrm{O}}_{2}$ compounds $(M=\mathrm{N}\mathrm{i},\mathrm{}\mathrm{C}\mathrm{o},\mathrm{}\mathrm{Mn})$ is investigated with first-principles calculations. We found that apart from the in-plane Li-Li interactions, the stability of ordered ${\mathrm{Li}}_{x}M{\mathrm{O}}_{2}$ structures strongly depends on the interlayer Li-Li interactions through the M cations. When several stacking sequences are possible, the selection of stacking is shown to be driven by the electronic structure of the transition-metal cations (metallic for ${\mathrm{Co}}^{+3/+4},$ localized for ${\mathrm{Ni}}^{+3/+4}$ and ${\mathrm{Mn}}^{+3/+4}).$ In ${\mathrm{Li}}_{x}{\mathrm{CoO}}_{2}$ the stacking is chosen so as to minimize the variations in coordination of the symmetrically different Co sites, thus enhancing electronic charge delocalization. In ${\mathrm{Li}}_{x}{\mathrm{NiO}}_{2},$ lithium ordering couples to orbital and Jahn-Teller ordering so as to form 180\ifmmode^\circ\else\textdegree\fi{} ${\mathrm{L}\mathrm{i}\ensuremath{-}\mathrm{O}\ensuremath{-}\mathrm{N}\mathrm{i}}^{+3}\ensuremath{-}\mathrm{O}\ensuremath{-}\mathrm{L}\mathrm{i}$ complexes. The presence of these 180\ifmmode^\circ\else\textdegree\fi{} ${\mathrm{Li}}_{A}\ensuremath{-}\mathrm{O}\ensuremath{-}M\ensuremath{-}{\mathrm{O}\ensuremath{-}\mathrm{L}\mathrm{i}}_{B}$ interactions ensures distinct M environments and charge localization. We indicate how the coupling between the ${e}_{g}^{*}$ and $\mathrm{Li}\ensuremath{-}2s$ orbital hybridization and the Jahn-Teller distortion produces a long-range attractive interaction between Li ions.