Atomistic mechanism leading to complex antiferroelectric and incommensurate perovskites

An atomic interaction is identified in all perovskite compounds, such as $AB{\mathrm{O}}_{3}$ oxides, that can potentially result in unconventional structures. The term is harmonic in nature and couples the motions of the $A$ cations with the rotations of the oxygen octahedra in the perovskite lattice. When strong enough, this coupling leads to hybrid normal modes that present both (anti)polar and rotational characters, which are keys to understand a variety of exotic phases. For example, we show that not only does this new coupling explain the long-period soft phonons characterizing prototype antiferroelectric ${\mathrm{PbZrO}}_{3}$, but it also provides us with an unified description of the complex antipolar structures of a variety of perovskites, including the possible occurrence of incommensurate phases. This coupling is further demonstrated to result, in the continuum limit, in an energy invariant adopting an analytical form that has been previously overlooked, to the best of our knowledge.