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 deformations¹. Lattices of Jahn-Teller ions can induce a cooperative distortion, as exemplified by LaMnO₃ (refs. ^2,3). Although many examples occur in octahedrally⁴ or tetrahedrally⁵ 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^6,7, nickel^8,9, iron^10,11 and manganese oxides¹². Here we synthesize single-crystal CaCoO₂ thin films by topotactic reduction of the brownmillerite CaCoO_2.5 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_xz and d_yz orbitals in the d⁷ 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 CoO₂ 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 CaCoO₂ structure forms an extended two-in-two-out type of Co distortion following 'ice rules'¹³.