Charge and Spin Ordering in Insulating Na$_{0.5}$CoO$_2$: Effects of Correlation and Symmetry

TL;DR

This study uses ab initio calculations to explore charge and spin ordering in insulating Na$_{0.5}$CoO$_2$, revealing complex patterns influenced by correlations and symmetry, with notable similarities and differences to cuprate materials.

Contribution

It provides a detailed analysis of charge and spin ordering patterns in Na$_{0.5}$CoO$_2$, highlighting the effects of correlations and symmetry, and introduces a new charge transfer variant within the Co 3d system.

Findings

Identification of the 'out-of-phase stripe' magnetic pattern.

Analysis of various charge and spin ordering patterns.

Discovery of a tiny gap associated with a new charge transfer variant.

Abstract

Ab initio band theory including correlations due to intra-atomic repulsion is applied to study charge disproportionation and charge- and spin-ordering in insulating Na$_{0.5}$CoO$_2$. Various ordering patterns (zigzag and two striped) for four-Co supercells are analyzed before focusing on the observed "out-of-phase stripe" pattern of antiferromagnetic Co$^{4+}$ spins along charge-ordered stripes. This pattern relieves frustration and shows distinct analogies with the cuprate layers: a bipartite lattice of antialigned spins, with axes at 90 degree angles. Substantial distinctions with cuprates are also discussed, including the tiny gap of a new variant of "charge transfer" type within the Co 3d system.