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 1 . Lattices of Jahn-Teller ions can induce a cooperative distortion, as exemplified by LaMnO 3 (refs. 2,3 ). Although many examples occur in octahedrally 4 or tetrahedrally 5 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 oxides 12 . Here we synthesize single-crystal CaCoO 2 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 d 7 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 2 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 2 structure forms an extended two-in-two-out type of Co distortion following 'ice rules' 13 .