Spontaneous polarization as a Berry phase of the Hartree-Fock wave function: The case of KNbO 3

We have investigated the ferroelectric polarization of the perovskite oxide KNbO{sub 3} within the self-consistent Hartree-Fock (HF) method, where the crystalline orbitals are expanded over a set of localized functions. According to the modern theory, macroscopic polarization is a geometric quantum phase: here we show that{emdash}within the HF framework{emdash}polarization can be cast as a Berry phase of Slater determinants. We calculate this observable for KNbO{sub 3} in its tetragonal phase. Besides polarization, we investigate several other properties of the electronic ground state, including the broken-symmetry instability of the tetragonal structure. We therefore assess the reliability and the predictive power of the HF approach when dealing with this material, which is a paradigmatic case of intermediate ionic/covalent crystal. {copyright} {ital 1997} {ital The American Physical Society}