Competing crystal structures in ${\mathrm{La}}_{0.5}{\mathrm{Ca}}_{0.5}\mathrm{Mn}{\mathrm{O}}_3$: Conventional charge order versus Zener polarons

Equilibrium crystal structures for ${\mathrm{La}}_{0.5}{\mathrm{Ca}}_{0.5}\mathrm{Mn}{\mathrm{O}}_3$ have been calculated using hybrid Hartree-Fock and density functional methods. Two distinct ground states with either conventional checkerboard charge ordering, in which Mn ions have formal valence 3 or 4, or Zener polaron formation, in which each Mn ion has valence 3.5, are found depending on the proportion of Hartree-Fock exchange used. These structures correspond to those identified by various experiments and they differ by small displacements of key oxygen ions.

Figure 1

$\mathbf{a}\mathbf{b}$ plane atomic positions for ${\mathrm{La}}_{0.5}{\mathrm{Ca}}_{0.5}\mathrm{Mn}{\mathrm{O}}_3$ shown to scale. (a) $Pn{2}_{1}m$ structure. Mn ion positions in the ZP state (Table ) are indicated by small circles, ${\mathrm{O}}^{2-}$ ions by shaded circles and ${\mathrm{O}}^{-}$ ions in the ZP state by a filled circle. Mn and O ion positions in the checkerboard state (Table ) are indicated by small and large dashed circles. (b) $P{2}_{1}nm$ ZP structure (Table ). Directions of transverse displacements of Mn ions from their ideal perovskite positions are indicated by arrows. Labels on ions refer to Tables .

Figure 2

Spin density and charge density difference for ${\mathrm{La}}_{0.5}{\mathrm{Ca}}_{0.5}\mathrm{Mn}{\mathrm{O}}_3$ in the ZP state with $A$-type magnetic order and $Pn{2}_{1}m$ symmetry obtained using a UHF wave function. (Left-hand side) Spin density. The unit cell shown in Fig. 1a is outlined. (Right-hand side) Charge density difference.

Figure 3

Spin density and charge density difference for ${\mathrm{La}}_{0.5}{\mathrm{Ca}}_{0.5}\mathrm{Mn}{\mathrm{O}}_3$ in the checkerboard state with CE-type magnetic order and $Pn{2}_{1}m$ symmetry obtained using 60% HF exchange. (Left-hand side) Spin density. (Right-hand side) Charge density difference.