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

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.