Electronic theory for itinerant in-plane magnetic fluctuations in Na$_x$CoO$_2$

TL;DR

This paper develops an electronic theory for in-plane magnetic fluctuations in Na$_x$CoO$_2$, revealing how doping influences magnetic states and susceptibility peaks through detailed band structure analysis.

Contribution

It introduces a tight-binding model derived from ab-initio data that explains magnetic fluctuation behavior and the emergence of electron pockets at high doping levels.

Findings

Identification of a local minimum in the electronic dispersion near the $b3$ point.

Prediction of a critical doping concentration for ferromagnetic order.

Agreement with neutron scattering data on magnetic susceptibility trends.

Abstract

Starting from {\it ab-initio} band structure for Na$_x$CoO$_2$, we derive the single-electron energies and the effective tight-binding description for the $t_{2g}$ bands using a projection procedure. We find that due to the presence of the next-nearest-neighbor hoppings a local minimum in the electronic dispersion close to the $\Gamma$ point of the first Brillouin zone forms. Therefore, in addition to a large Fermi surface an electron pocket close to the $\Gamma$ point emerges at high doping concentrations. The latter yields the new scattering channel resulting in a peak structure of the itinerant magnetic susceptibility at small momenta. This indicates itinerant in-plane ferromagnetic state above certain critical concentration $x_m$, in agreement with neutron scattering data. Below $x_m$ the magnetic susceptibility shows a tendency towards the antiferromagnetic fluctuations. We estimate the value of $0.58 < x_m < 0.7$ within the rigid band model and within the Hubbard model with infinite on-site Coulomb repulsion consistent with the experimental phase diagram.