Antiferromagnetic, Charge and Orbital Ordered States of Na0.5CoO2 Based on the Two-Dimensional Triangular Lattice d-p Model

We investigate the electronic state of a CoO_2 plane in the layered cobalt oxides Na_xCoO_2 using the 11 band d-p model on a two-dimensional triangular lattice, where the tight-binding parameters are determined so as to fit the LDA band structure. Effects of the Coulomb interaction at a Co site: the intra- and inter-orbital direct terms U and U', the exchange coupling J and the pair-transfer J', are treated within the Hartree-Fock approximation. We also consider the effect of the Na order at x=0.5, where Na ions form one-dimensional chains, by taking into account of an effective one-dimensional potential Delta epsilon_{d}. It is found that the one-dimensional Na order enhances the Fermi surface nesting and antiferromagnetism is caused which is suppressed due to the frustration effect in the case without the Na order. %It is found that the Na order enhances the Fermi surface nesting resulting in a metallic antiferromagnetism which is suppressed due to the frustration effect in the case without the Na order. Furthermore, we consider the effect of the Coulomb interaction between the nearest-neighbor Co sites V and find that a coexistence of the magnetic, charge and orbital ordered state takes place for V>V_c where the system becomes insulator.