Why the magnetic interactions in Na$_{x}$CoO$_{2}$ are 3D

TL;DR

This paper explains the 3D magnetic interactions in Na$_{x}$CoO$_{2}$, a layered oxide, using first principles calculations that reveal multiple interplanar exchange paths leading to effective three-dimensional magnetism.

Contribution

It demonstrates that multiple exchange pathways cause the magnetic interactions to be effectively 3D despite the 2D layered structure.

Findings

Calculations agree with neutron scattering results.

Superexchange occurs via O-O hopping and Na $sp^2$ hybrids.

Multiple exchange paths lead to 3D magnetic behavior.

Abstract

The puzzle of 3D magnetic interactions in the structurally 2D layered oxide Na$_{x}$CoO$_2$ is addressed using first principles calculations and analysis of the exchange mechanisms. The calculations agree with recent neutron results, favoring AFM stacking of FM planes. Superexchange via direct O-O hopping and through intermediate Na $sp^2$ hybrids couples each Co to its nearest and six \textit{next}-nearest interplanar neighbors equally. The individual exchange constants are rather 2D, like the lattice itself, but due to multiple c-axis exchange paths, the magnetism becomes effectively 3D.