Theory of Sodium Ordering in NaxCoO2

TL;DR

This paper systematically investigates Na ion ordering in Na_xCoO_2 using DFT and model calculations, revealing the primary role of Coulomb interactions and explaining the absence or presence of charge order at specific compositions.

Contribution

It combines DFT and model calculations to identify ground state Na ordering patterns and explains their effects on electronic properties, advancing understanding of Na_xCoO_2.

Findings

Na ordering is driven by screened Coulomb interactions.

No charge order at x=2/3 due to lack of commensurate Na pattern.

Stable Na ordering at x=0.5 promotes charge ordering and insulating behavior.

Abstract

The ordering of Na ions in Na$_x$CoO$_2$ is investigated systematically by combining detailed density functional theory (DFT) studies with model calculations. Various ground state ordering patterns are identified, and they are in excellent agreement with avaliable experimental results. Our results suggest that the primary driving force for the Na ordering is the screened Coulomb interaction among Na ions. Possible effects of the Na ordering on the electronic structure of the CoO$_2$ layer are discussed. We propose that the nonexistence of a charge ordered insulating state at $x = 2/3$ is due to the lack of a commensurate Na ordering pattern, whereas an extremely stable Na ordering at $x = 0.5$ enhances the charge ordering tendency, resulting in an insulating state as observed experimentally.