Electronic structure studies of the differences in ferroelectric behavior of batio₃ and PbTiO₃

Abstract

We have performed extensive self-consistent total energy calculations for PbTiO₃ and BaTiO₃ in order to better understand the origin of the ferroelectric instability in perovskites and the reasons for different ferroelectric behavior in the two materials. Physically reasonable ferroelectric instabilities are found for both materials at the experimental volume. However, the results are quite sensitive to volume and typical local density approximation (LDA) errors in volume can lead to significant errors in the potential surface for ferroelectric distortions. The sensitivity of the perovskite ferroelectrics to defects and chemistry, as well as the sensitivity to approximations in first principles calculations, stems from the delicate near-cancellation of long-range ionic forces which favor the instability with short-range repulsions that inhibit the ferroelectric state. The spontaneous strain is also an important feature of ferroelectrics, and we find that the large tetragonal strain stabilizes the tetragonal structure in PbTiO₃. The differences in behavior between BaTiO₃ and PbTiO₃ stem from their different electronic structures: The Pb 6s and O 2p states are strongly hybridized in PbTiO₃, whereas Ba is essentially a fully ionic Ba²⁺ ion in BaTiO₃. In both materials the Ti 3d states hybridize with O 2p, and it is the Ti-O interaction that is responsible for the ferroelectric instability. We also discuss the nature of the ferroelectric phase transition, including effects of electrical boundary conditions.

Keywords:

• electronic structure
• total energies
• lattice dynamics
• frozen phonons