Geometrical, electronic and magnetic properties of Na$_{0.5}$CoO$_2$ from first principles

TL;DR

This study uses first-principles calculations to explore the structural, electronic, and magnetic properties of Na$_{0.5}$CoO$_2$, highlighting the importance of electron correlation effects in predicting its insulating state.

Contribution

It demonstrates that including on-site Coulomb interactions (U) in DFT calculations is essential to accurately model the charge ordering and insulating behavior of Na$_{0.5}$CoO$_2$.

Findings

Pure DFT fails to predict insulating state without correlation effects.

Including Hubbard U leads to charge-ordered insulating ground state.

At U=4.0 eV, the system is antiferromagnetic with Co$^{4+}$ moments.

Abstract

We report a first-principles projector augmented wave (PAW) study on Na$_{0.5}$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 Na ordering alone can not produce accompanying Co charge ordering, if additional correlation is not properly considered. At this level of theory, the most stable phase presents ferromagnetic ordering within the CoO$_2$ layer and antiferromagnetic coupling between these layers. When the on-site Coulomb interaction for Co 3d orbitals is included by an additional Hubbard parameter $U$, 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 eV for example), the ground state is antiferromagnetic, with a Co$^{4+}$ magnetic moment about 1.0 $\mu_B$ and a magnetic energy of 0.12 eV/Co. The rehybridization process is also studied in the DFT+U point of view.