  Hexagonal oxide perovskites, in contrast to the more familiar perovskites,
allow for face-sharing of metal-oxygen octahedra or trigonal prisms within
their structural frameworks. This results in dimers, trimers, tetramers, or
longer fragments of chains of face-sharing octahedra in the crystal structures,
and consequently in much shorter metal-metal distances and lower
metal-oxygen-metal bond angles than are seen in the more familiar perovskites.
The presence of the face-sharing octahedra can have a dramatic impact on
magnetic properties of these compounds, and dimer-based materials, in
particular, have been the subjects of many quantum-materials-directed studies
in materials physics. Hexagonal oxide perovskites are of contemporary interest
due to their potential for geometrical frustration of the ordering of magnetic
moments or orbital occupancies at low temperatures, which is especially
relevant to their significance as quantum materials. As such, several hexagonal
oxide perovskites have been identified as potential candidates for hosting the
quantum spin liquid state at low temperatures. In our view, hexagonal oxide
perovskites are fertile ground for finding new quantum materials. This review
briefly describes the solid state chemistry of many of these materials.
