Ab initio calculations of the atomic and electronic structure of ${\text{CaTiO}}_3$ (001) and (011) surfaces

We present the results of calculations of surface relaxations, energetics, and bonding properties for ${\text{CaTiO}}_3$ (001) and (011) surfaces using a hybrid description of exchange and correlation. We consider both CaO and ${\text{TiO}}_2$ terminations of the nonpolar (001) surface and Ca, TiO, and O terminations of the polar (011) surface. On the (001) surfaces, we find that all upper-layer atoms relax inward on the CaO-terminated surface, while outward relaxations of all atoms in the second layer are found for both terminations. For the ${\text{TiO}}_2$-terminated (001) surface, the largest relaxations are on the second-layer atoms. The surface rumpling is much larger for the CaO terminated than for the ${\text{TiO}}_2$-terminated (001) surface, but their surface energies are quite similar at 0.94 and 1.13 eV/cell, respectively. In contrast, different terminations of the (011) ${\text{CaTiO}}_3$ surface lead to very different surface energies of 1.86, 1.91, and 3.13 eV/cell for the O-terminated, Ca-terminated, and TiO-terminated (011) surface, respectively. Our results for surface energies contrast sharply with those of Zhang et al. [Phys. Rev. B 76, 115426 (2007)], where the authors found a rather different pattern of surface energies. We predict a considerable increase in the Ti-O chemical bond covalency near the (011) surface as compared both to the bulk and to the (001) surface.

Figure 1

(Color online) Side view of ${\text{CaTiO}}_3$ (001) surfaces. (a) CaO-terminated surface. (b) ${\text{TiO}}_2$-terminated surface with definitions of surface rumpling $s$ and the near-surface interplanar separations $\Delta d_{12}$ and $\Delta d_{23}$.

Figure 2

(Color online) Sketch of the cubic ${\text{CaTiO}}_3$ perovskite structure showing two (011) cleavage planes that give rise to charged CaTiO and ${\text{O}}_2$ (011) surfaces.

Figure 3

(Color online) Possible (011) surface slab models considered in the text. [(a)–(c)] Slabs obtained by simple cleavage yielding mixed O-terminated and CaTiO-terminated polar surfaces, respectively. [(d)–(f)] Slabs with nonpolar TiO-terminated, Ca-terminated, and O-terminated surfaces, respectively.