Geometric frustration of Jahn-Teller order in the infinite-layer lattice.

The Jahn-Teller effect, in which electronic configurations with energetically degenerate orbitals induce lattice distortions to lift this degeneracy, has a key role in many symmetry-lowering crystal deformations. Lattices of Jahn-Teller ions can induce a cooperative distortion, as exemplified by LaMnO (refs. ). Although many examples occur in octahedrally or tetrahedrally coordinated transition metal oxides due to their high orbital degeneracy, this effect has yet to be manifested for square-planar anion coordination, as found in infinite-layer copper, nickel, iron and manganese oxides. Here we synthesize single-crystal CaCoO thin films by topotactic reduction of the brownmillerite CaCoO phase. We observe a markedly distorted infinite-layer structure, with ångström-scale displacements of the cations from their high-symmetry positions. This can be understood to originate from the Jahn-Teller degeneracy of the d and d orbitals in the d electronic configuration along with substantial ligand-transition metal mixing. A complex pattern of distortions arises in a [Formula: see text] tetragonal supercell, reflecting the competition between an ordered Jahn-Teller effect on the CoO sublattice and the geometric frustration of the associated displacements of the Ca sublattice, which are strongly coupled in the absence of apical oxygen. As a result of this competition, the CaCoO structure forms an extended two-in-two-out type of Co distortion following 'ice rules'.