Theory of prospective tetrahedral perovskite ferroelectrics

Using first-principles methods, we predict the energy landscape and ferroelectric states of double perovskites of the form AA$'$BB$'$O$_6$ in which the atoms on both the A and B sites are arranged in rock-salt order. While we are not aware of compounds that occur naturally in this structure, we argue that they might be realizable by directed synthesis. The high-symmetry structure formed by this arrangement belongs to the tetrahedral $F\bar{4}3m$ space group. If a ferroelectric instability occurs, the energy landscape will tend to have minima with the polarization along tetrahedral directions, leading to a rhombohedral phase, or along Cartesian directions, leading to an orthorhombic phase. We find that the latter scenario applies to CaBaTiZrO$_6$ and KCaZrNbO$_6$, which are weakly ferroelectric, and the former one applies to PbSnTiZrO$_6$, which is strongly ferroelectric. The results are modeled with a fourth- or fifth-order Landau-Devonshire expansion, providing good agreement with the first-principles calculations. Computations of zone-center soft modes are also carried out in order to characterize the polar and octahedral-rotation instabilities in more detail. Prospects for synthesis of ferroelectric materials belonging to this class are discussed.