Oxygen Octahedral Rotations in BaTiO$_{3}$/CaTiO$_{3}$ Superlattices

Complex oxide superlattices have a wide range of electronic and magnetic properties, which are affected by the structure of the interfaces between different components of the superlattice. The magnitude, coherence, and electric field response of oxygen displacements in three different BaTiO$_{3}$/CaTiO$_{3}$ superlattice compositions are measured using x-ray diffraction. The displacements are greater in compositions with more consecutive CaTiO$_{3}$ layers. The pattern of layer-by-layer alternating displacements is coherent over less than two superlattice unit cells. The net in-phase rotation of the oxygen octahedra gives rise to an x-ray reflection at (3/2 1/2 1). Density functional theory calculations for a 2(BaTiO$_{3})$/4(CaTiO$_{3})$ composition predict a decrease in displacements of oxygen octahedra between barium and calcium layers when an electric field is applied, causing an intensity increase in this reflection. We found the intensity of this reflection for this composition increases by 1.6{\%} when a 12.5 V pulse is applied, a weaker response than the 11{\%} increase predicted. When a 20 V pulse is applied, the reflection intensity actually decreases by 3{\%}, indicating a more complicated response.