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

TL;DR

This study models the electronic states of Na0.5CoO2 using a 11-band d-p model on a triangular lattice, revealing how Na order and Coulomb interactions induce antiferromagnetism, charge, and orbital orderings, and lead to insulating states.

Contribution

It introduces a detailed 11-band d-p model incorporating Na order and Coulomb interactions to explain magnetic and charge ordering in Na0.5CoO2.

Findings

Na order enhances Fermi surface nesting and antiferromagnetism.

Coulomb interactions induce coexistence of magnetic, charge, and orbital orderings.

System becomes insulating when nearest-neighbor Coulomb interaction exceeds critical value.

Abstract

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.