Lattice screening of the polar catastrophe and hidden in-plane polarization in KNbO$_{3}$/BaTiO$_{3}$ interfaces

Abstract

We have carried out first-principles simulations, based on density functional theory, to obtain the atomic and electronic structure of (001) BaTiO$_{3}$/KNbO$_{3}$ interfaces in an isolated slab geometry. We tried different types of structures including symmetric and asymmetric configurations, and variations in the thickness of the constituent materials. The spontaneous polarization of the layer-by-layer non neutral material (KNbO$_{3}$) in these interfaces cancels out almost exactly the "built-in" polarization responsible for the electronic reconstruction. As a consequence, the so-called polar catastrophe is quenched and all the simulated interfaces are insulating. A model, based on the modern theory of polarization and basic electrostatics, allows an estimation of the critical thickness for the formation of the two-dimensional electron gas between 42 and 44 KNbO$_{3}$ unit cells. We also demonstrate the presence of an unexpected in-plane polarization in BaTiO$_{3}$ localized at the $p$-type TiO$_2$/KO interface, even under in-plane compressive strains. We expect this in-plane polarization to remain hidden due to angular averaging during quantum fluctuations unless the symmetry is broken with small electric fields.