“Hexagonal” Perovskites: From Stacking Sequence to Space Group Symmetry and New Opportunities

The term “hexagonal perovskite” has been widely used in literature to discuss the structure of perovskite-type compounds with composition ABX3–y with partial h-type stacking of AX3 layers. Though the local surrounding of these AX3 layers resembles a hexagonal close packing, the space group symmetries reported for some of these materials are not belonging to the hexagonal crystal system but are trigonal or orthorhombic instead. Though reports and books with lists of hexagonal perovskites exist which assign stacking sequences and list a corresponding space group, a concise guideline on how the maximum symmetry of the perovskite type material is related to the stacking sequence has not been reported. Clearly, such a systematization of space group symmetry and stacking notations would be desirable; for distortion or ordering variants of the cubic perovskite, the whole research community benefits from concepts of group-subgroup relations or classification of tilting via the Glazer notation. In this article, we derive a fully consistent guideline on how the aristotype space group symmetry can be determined for any stacking sequence (e.g., cchhchcch, ...) in the Jagodzinski notation and provide a computer program which can do this analysis. By this, one can narrow down the possible aristotype space group symmetries for any perovskite stacking sequence with h-type layers to seven space groups in total (R3̅m, P3̅m, P63/mmc, P6̅m2, R3m, P3m, and P63mc). The space groups can be directly derived from the Jagodzinski sequence. Remarkably, the possibility to obtain polar perovskites with h-type layers by stacking has not been recognized in literature so far and provides the opportunity to develop new multiferroic materials by design of stacking.