Surface Effects in Ferroelectrics: Periodic Slab Computations for BaTiO$_3$

Total energies, electronic structure, surface energies, polarization, potentials and charge densities were studied for slabs of BaTiO$_3$ using the Linearized Augmented Plane Wave (LAPW) method. The depolarization field inhibits ferroelectricity in the slabs, and the macroscopic field set up across a ferroelectric slab is sufficient to cause electronic states to span the gap and give a metallic band structure, but the band shifts are not rigid and O $p$ states tend to pile up at the Fermi level. There are electronic surface states, especially evident on TiO$_2$ surfaces. The dangling bonds bond back to the surface Ti's and make the surface stable and reactive. The BaO surfaces are more ionic than the bulk.