We report a first-principles projector augmented wave (PAW) study on ${\mathrm{Na}}_{0.5}{\mathrm{CoO}}_2$. With the sodium ion ordered insulating phase being identified in experiments, pure density functional calculations fail to predict an insulating ground state, which indicates that $\mathrm{Na}$ ordering alone cannot produce accompanying $\mathrm{Co}$ charge ordering if additional correlation is not properly considered. At this level of theory, the most stable phase presents ferromagnetic ordering within the ${\mathrm{CoO}}_2$ layer and antiferromagnetic coupling between these layers. When the on-site Coulomb interaction for $\mathrm{Co}$ $3d$ orbitals is included by an additional Hubbard parameter $U$, a charge ordered insulating ground state can be obtained. The effect of on-site interaction magnitude on electronic structure is studied. At a moderate value of $U$ ($4.0\mathrm{eV}$, for example), the ground state is antiferromagnetic, with a ${\mathrm{Co}}^{4+}$ magnetic moment about $1.0{\mu }_B$ and a magnetic energy of $0.12\mathrm{eV}∕\mathrm{Co}$. The rehybridization process is also studied in the $\mathrm{DFT}+U$ point of view (where DFT represents density functional theory).

• Received 1 April 2004

DOI:https://doi.org/10.1103/PhysRevB.71.024502