Origin of the electron disproportionation in the metallic sodium cobaltates

TL;DR

This study investigates the origin of electron disproportionation in metallic sodium cobaltates, revealing how sodium ordering and electron correlations induce non-uniform charge and magnetic densities, with competing magnetic states contributing to the phenomenon.

Contribution

It introduces a detailed analysis of the magnetic states and charge distribution in sodium cobaltates using GGA+U calculations, highlighting the role of sodium ordering and electron correlations in disproportionation.

Findings

Disproportionation driven by sodium cation ordering and correlations

Identification of competing magnetic states: low spin hexagons and high spin kagome lattice

Coexistence of magnetic states explains observed charge and spin inhomogeneity

Abstract

Recently the unusual metallic state with a substantially non-uniform distribution of a charge and mag\-ne\-tic density in CoO$_2$ planes was found experimentally in the Na$_x$CoO$_2$ compound with $x>0.6$. We have investigated an origin of such electron disproportionation in the lamellar sodium cobaltates by calculating the ion states as a function of a strength of the electron correlations in the $d$(Co)-shells within the GGA+U approximation for the system with a realistic crystal structure. It was found that the nonuniformity of spin and charge densities are induced by an ordering of the sodium cations and enhanced correlations. Two important magnetic states of cobalt lattice competing with each other at realistic values of the correlation parameter were found~---~low spin hexagons (LS) and higher spin kagom\'e lattice (HS-KSL). In the heterogeneous metallic HS-KSL phase magnetic Co ions form a kagom\'e structure. In LS phase the kagom\'e pattern is decomposed into hexagons and Co ions possess minimal values of their spin. Coexistence of these states could explain the emergence of the disproportionation with the peculiar kagom\'e structure experimentally revealed in previous studies of the cobaltates.