Charge and spin ordering in insulating Na0.5CoO2:: Effects of correlation and symmetry

Ab initio band theory including correlations due to intra-atomic repulsion is applied to study charge disproportionation and charge and spin ordering in insulating Na0.5CoO2. Various ordering patterns (zigzag and two striped) for four-Co supercells are analyzed before focusing on the observed out-of-phase stripe pattern of antiferromagnetic Co4+ spins along charge-ordered stripes. This pattern relieves frustration and shows distinct analogies with the cuprate layers: a bipartite lattice of antialigned spins, with axes at 90 degrees angles. Substantial distinctions with cuprates are also discussed, including the tiny gap of a new variant of charge-transfer type within the Co 3d system.