Theory of prospective perovskite ferroelectrics with double rocksalt order

Using first-principles methods, we predict the energy landscape and ferroelectric states of double perovskites of the form AA${}^{\prime }$BB${}^{\prime }$O${}_6$ in which the atoms on both the A and B sites are arranged in rocksalt order. While we are not aware of compounds that occur naturally in this structure, they might be realizable by directed synthesis, as has recently been demonstrated experimentally. The high-symmetry structure formed by this arrangement belongs to the tetrahedral $F\overline{4}3m$ 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.

Figure 1

Structure of AA${}^{\prime }$BB${}^{\prime }$O${}_6$ double perovskites, with A (red circles) and ${\mathrm{A}}^{\prime }$ (magenta squares) atoms forming one rocksalt framework, and B (blue diamonds) and ${\mathrm{B}}^{\prime }$ (green triangles) atoms forming a second interpenetrating one. Oxygen atoms are not shown, although one oxygen octahedron is outlined to clarify that the local bonding environment is still roughly octahedral. Dashed lines illustrate the tetrahedral point symmetry.

Figure 2

Symmetry-determined possibilities for directions of energy minima in the space of polarization, represented by red dots. (a)–(c) Cubic composition leading to high-symmetry $\mathit{Pm}3m$ structure. (d)–(f) Tetrahedral composition leading to high-symmetry $F\overline{4}3m$ structure.

Figure 3

(a) Type-I and (b) type-II configuration of SCTM.