First-order localized-electron collective-electron transition in LaCoO3

Precision x-ray measurements of the motions of the atoms in LaCo${\mathrm{O}}_{3}$ every 50\ifmmode^\circ\else\textdegree\fi{}C from room temperature to 1000\ifmmode^\circ\else\textdegree\fi{}C indicate that the crystal space group is $R\overline{3}c$ below 375\ifmmode^\circ\else\textdegree\fi{}C and $R\overline{3}$ above 375\ifmmode^\circ\else\textdegree\fi{}C. In the symmetry $R\overline{3}$ there are two distinguishable octahedral cobalt positions, ${\mathrm{Co}}_{\mathrm{I}}$ having larger crystalline fields than ${\mathrm{Co}}_{\mathrm{II}}$. Since high- and low-spin cobalt ions are simultaneously present, this indicates preferential long-range ordering of low-spin cobalt at ${\mathrm{Co}}_{\mathrm{I}}$ sites, and of high-spin cobalt at ${\mathrm{Co}}_{\mathrm{II}}$ sites for $Tg375$\ifmmode^\circ\else\textdegree\fi{}C. Calorimetric data show a first-order transition at ${T}_{t}=937$\ifmmode^\circ\else\textdegree\fi{}C and a higher order transition in the temperature interval $125lTl375$\ifmmode^\circ\else\textdegree\fi{}C, which is also manifest in a large Debye-Waller factor in this interval and in a plateau in the curve of reciprocal susceptibility versus temperature. At about 650\ifmmode^\circ\else\textdegree\fi{}C there is some evidence, from differential thermal-analysis data, of another higher order transition. The electrical conductivity increases with increasing temperature below 650\ifmmode^\circ\else\textdegree\fi{}C, but much more rapidly in the interval $125lTl650$\ifmmode^\circ\else\textdegree\fi{}C than below 125\ifmmode^\circ\else\textdegree\fi{}C. It is nearly temperature-independent in the interval $650lTl937$\ifmmode^\circ\else\textdegree\fi{}C and is continuous through the first-order transition. However, above 937\ifmmode^\circ\else\textdegree\fi{}C the resistivity increases with temperature as in a metal. The space group remains $R\overline{3}$ and the pseudocubic cell edge is continuous through the first-order phase change, but the rhombohedral angle drops abruptly from 60.4\ifmmode^\circ\else\textdegree\fi{} to 60\ifmmode^\circ\else\textdegree\fi{} and the ${\mathrm{La}}^{3+}$ ions are shifted discontinously along the $c$ axis toward a ${\mathrm{Co}}_{\mathrm{I}}$ ion. Similar ${\mathrm{La}}^{3+}$-ion displacements occur in the temperature interval $400lTl650$\ifmmode^\circ\else\textdegree\fi{}C. The Debye-Waller factor decreases by an order of magnitude on going to the high-temperature phase. It is pointed out that crystal-field and band theory should describe two different thermodynamic states of electrons: localized and collective. The data are interpreted to indicate (1) that the first-order phase change at ${T}_{t}=937$\ifmmode^\circ\else\textdegree\fi{}C is a localized-electron $\ensuremath{\leftrightarrows}$ collective-electron phase change for electrons in orbitals of ${e}_{g}$ symmetry, higher temperatures introducing a Fermi surface and partial disproportionation between high- and low-spin cations at ${\mathrm{Co}}_{\mathrm{II}}$ and ${\mathrm{Co}}_{\mathrm{I}}$ positions; (2) that the number of charge carriers is constant through the transition, because the number of localized charge carriers is saturated below ${T}_{t}$ and just above ${T}_{t}$ the bandwidth of the collective-electron states is $\ensuremath{\Delta}\ensuremath{\epsilon}lk{T}_{t}$; (3) that the mobilities of the charge carriers are also continuous through the transition, the activation energy for a localized-electron hop becoming $\ensuremath{\ll}\mathrm{kT}$ at $T\ensuremath{\le}937$\ifmmode^\circ\else\textdegree\fi{}C; (4) that the higher-order transition in the interval $125lTl375$\ifmmode^\circ\else\textdegree\fi{}C represents a region of short-range order, the ordered phase occurring at higher temperatures where the populations of high- and low-spin cobalt ions approach one another; and (5) that exciton transfer is an important mechanism in LaCo${\mathrm{O}}_{3}$.