Surface Reconstruction with a Fractional Hole: $(\sqrt{5}\times \sqrt{5})R26.6°$ ${\mathrm{LaAlO}}_3$ (001)

The structure of the $(\sqrt{5}\times \sqrt{5})R26.6°$ reconstruction of ${\mathrm{LaAlO}}_3$ (001) has been determined using transmission electron diffraction combined with direct methods. It has a lanthanum oxide termination with one lanthanum vacancy per surface unit cell. Density functional calculations indicate that charge compensation occurs by a fractional number of highly delocalized holes, and that the surface contains no oxygen vacancies and the holes are not filled with hydrogen. The reconstruction can be understood in terms of expulsion of the more electropositive cation from the surface and increased covalency.

Figure 1

Dark field image showing extended $⟨100⟩$ faceting with step bunches and reconstructed terraces. A small probe off-zone diffraction pattern (inset) is shown with the rhombohedral ($1\times 1$) bulk unit cell (right) and the surface unit cell for both domains of the reconstruction (left).

Figure 2

Top view of the Rt5 surface reconstruction (left) with the surface unit cell outlined in black ($a=8.537\AA$). Contour map of the valence density in the surface plane (right) at $0.1\mathrm{e}/{\AA }^3$ showing the increased electron density between the surface oxygen (O1 and O2) and lanthanum atoms (La1) corresponding to increased covalent bonding. The La vacancy is at the corner of the unit cell; atoms O1, O2, and La1 are in the surface layer, while Al1, O3, O4, and O5 are in the second layer.

Figure 3

Integrated hole density plot along the [100] direction at $0.01\mathrm{e}/{\AA }^2$ shown next to the crystal structure.