Considerable non-local electronic correlations in strongly doped Na$_x$CoO$_2$

TL;DR

This study combines advanced theoretical methods to reveal significant non-local electronic correlations in heavily doped Na$_x$CoO$_2$, elucidating complex magnetic and charge-ordering phenomena in this strongly correlated material.

Contribution

It introduces a novel combination of density functional theory and RISB in a cluster approach to accurately model non-local correlations in sodium cobaltate.

Findings

Local Hubbard U captures in-plane magnetic behavior.

Charge-ordering physics explained by inter-site Coulomb V.

Identification of a fluctuating charge-density-wave state at x~3/4.

Abstract

The puzzling electronic correlation effects in the sodium cobaltate system are studied by means of the combination of density functional theory and the rotationally invariant slave boson (RISB) method in a cellular-cluster approach. Realistic non-local correlations are hence described in the short-range regime for finite Coulomb interactions on the underlying frustrated triangular lattice. A local Hubbard U is sufficient to model the gross in-plane magnetic behavior with doping x, namely antiferromagnetic correlations at intermediate doping and the onset of ferromagnetic order above x>3/4 with a mixed phase for 0.62<x<3/4. Important insight is thereby provided by the occupations of local cluster multiplets retrieved from the RISB framework. The extended modeling of the x$\ge$2/3 doping regime with an additional inter-site Coulomb repulsion V on an experimentally verified effective kagom\'e lattice allows to account for relevant charge-ordering physics. Therewith a fluctuating charge-density-wave state with small quasiparticle weight and a maximum in-plane magnetic susceptibility may be identified at x$\sim$3/4, just where the magnetic ordering sets in.