Figure 1. Superlattice geometry, major structural distortions, and resulting ferroelectric, charge and orbital ordering.

The A²⁺TiO₃-R³⁺TiO₃ digital superlattice 10-atom high-symmetry tetragonal P4/mmm reference structure undergoes two major structural distortions: AFD motions and a breathing oxygen cage distortion. The rocksalt arrangement of large (blue) and small (grey) octahedral cages of the breathing distortion are shown in the 20-atom cell. The AFD motions induce ferroelectricity through a unique anharmonic coupling to an in-plane polar mode. The combination of the AFD motions and breathing oxygen cage allows for an unusual charge and orbital ordering. Blue, grey, red and green spheres represent R³⁺, A²⁺, O and Ti, respectively. Distortions are exaggerated for illustrative purposes.