Corner- versus face-sharing octahedra in $A\mathrm{Mn}{\mathrm{O}}_3$ perovskites ($A=\mathrm{Ca}$, Sr, and Ba)

The electronic structure of the series of perovskites $A\mathrm{Mn}{\mathrm{O}}_3$ $(A=\mathrm{Ca},\mathrm{Sr},\mathrm{Ba})$ is examined with the aid of density-functional calculations. A range of possible crystal structures is examined for each compound, and in each case the calculated lowest-energy structure is that observed at low temperature. The factors that control the variation in structure with the alkaline-earth ion $A^{2+}$ are discussed. $\mathrm{Ca}\mathrm{Mn}{\mathrm{O}}_3$ consists of corner-sharing octahedra but is orthorhombically distorted consistent with ${\mathrm{Ca}}^{2+}$ being too small for the 12-fold site within a perfect cubic $\mathrm{Mn}{\mathrm{O}}_6$ polyhedral framework. When the size of the alkaline-earth cation increases, a transformation from corner-sharing to face-sharing octahedra is induced since the alkaline-earth cation now becomes too large for the 12-fold site. While $\mathrm{Sr}\mathrm{Mn}{\mathrm{O}}_3$ at $0\mathrm{K}$ has the four-layered hexagonal ($4H$) structure with corner-sharing ${\mathrm{Mn}}_2{\mathrm{O}}_9$ dimers, $\mathrm{Ba}\mathrm{Mn}{\mathrm{O}}_3$ at $0\mathrm{K}$ adopts the two-layered hexagonal $\left(2H\right)$ structure with infinite chains of face-sharing octahedra. The Mn charge is much lower than the conventional ionic model charge due to Mn-O covalence, and this reduces the Mn-Mn repulsion and favors sharing of the octahedral faces. We see no evidence for direct Mn-Mn metal bonding which has often been invoked to rationalize the adoption of this type of structure. We also discuss the atomistic origins of acid-base stabilization of ternary oxides from their binary constituents. A link between cation size and acid-base properties is suggested for $A\mathrm{Mn}{\mathrm{O}}_3$.

Figure 1

Polyhedral representations of (a) the ideal cubic perovskite (b) the four-layered hexagonal perovskite and (c) the two-layered hexagonal perovskite structures.

Figure 2

The enthalpy of formation of ternary oxides from their binary constituents. Squares represent the cubic polymorph, circles the $4H$ polymorph, and triangles the $2H$ polymorph. The filled symbol denotes orthorhombic $\mathrm{Ca}\mathrm{Mn}{\mathrm{O}}_3$.

Figure 3

(Color online) The electronic density of states for (a) $\mathrm{Ca}\mathrm{Mn}{\mathrm{O}}_3$, (b) $\mathrm{Sr}\mathrm{Mn}{\mathrm{O}}_3$, and (c) $\mathrm{Ba}\mathrm{Mn}{\mathrm{O}}_3$. The total densities of states are given on the left-hand side of the figures. The Mn and O contributions to the densities of state are given on the right-hand side of the figure. The Mn contributions are represented by thick black lines, while the oxygen contributions are given by thin red (solid) and (for $4H$ polymorphs) blue (dashed) lines. For $4H$ polymorphs, the red curves are for corner-sharing oxygens, and blue curves for face-sharing oxygens.

Figure 4

(Color online) The $t_{2g}\text{−}{e}_g$ decomposed electronic density of state ($d$-orbitals only) of manganese in G-type AF cubic $A\mathrm{Mn}{\mathrm{O}}_3$. The $t_{2g}$ contribution is given in black (thick line), and the $e_g$ in red (thin line).

Figure 5

The sum of the enthalpy of formation (from the elements) of the binary alkaline-earth oxides and $\mathrm{Mn}{\mathrm{O}}_2$ (Ref. 28). The enthalpy of formation of ternary $2H$ $A\mathrm{Mn}{\mathrm{O}}_3$ from the elements are also included to visualize the physical meaning of ${\Delta }_{f,\text{oxides}}{H}_m^{\mathrm{o}}$. The enthalpy of formation of the ternary oxides from the elements is obtained by adding the presently calculated ${\Delta }_{f,\text{oxides}}{H}_m^{\mathrm{o}}$ to the enthalpy of formation for the binary oxides (Ref. 28).

Figure 6

The total electronic density of states (spin up and spin down) for $2H$ $A\mathrm{Mn}{\mathrm{O}}_3$.

Figure 7

(Color online) The site-decomposed electronic density of states for the $2H$ ternary oxides and the corresponding binary oxides: (a) CaO, $\mathrm{Mn}{\mathrm{O}}_2$, and $\mathrm{Ca}\mathrm{Mn}{\mathrm{O}}_3$; (b) SrO, $\mathrm{Mn}{\mathrm{O}}_2$, and $\mathrm{Sr}\mathrm{Mn}{\mathrm{O}}_3$; and (c) BaO, $\mathrm{Mn}{\mathrm{O}}_2$, and $\mathrm{Ba}\mathrm{Mn}{\mathrm{O}}_3$. Thick black lines represent the ternary oxide, thin red lines the $A\mathrm{O}$ oxides, and dotted lines $\mathrm{Mn}{\mathrm{O}}_2$.

Figure 8

The lattice energy decomposed into contributions (see insert to figure) for the different polymorphs considered for (a) $\mathrm{Ca}\mathrm{Mn}{\mathrm{O}}_3$ and (b) $\mathrm{Ba}\mathrm{Mn}{\mathrm{O}}_3$.

Figure 9

The changes in Coulomb energy due to relaxation of the oxygen and manganese ions from the “ideal” positions of the $4H$ $A\mathrm{Mn}{\mathrm{O}}_3$ structure. Details are given in the text.