Charge and spin order on the triangular lattice -- Na$_x$CoO$_2$ at $x=0.5$

TL;DR

This paper investigates the complex charge and spin ordering phenomena in Na$_x$CoO$_2$ at $x=0.5$, revealing how Na dopant order influences electronic states and induces multiple phase transitions in a frustrated triangular lattice.

Contribution

It introduces a novel extended Hubbard model analysis showing how Na dopant order causes specific charge and spin orderings, alleviating frustration and leading to observable phase transitions.

Findings

Weak charge inhomogeneity alleviates AF frustration.

Na dopant order induces charge order in Co layer.

Fermi surface is reconstructed into small pockets.

Abstract

The nature of electronic states due to strong correlation and geometric frustration on the triangular lattice is investigated in connection to the unconventional insulating state of Na$_x$CoO$_2$ at $x=0.5$. We study an extended Hubbard model using a spatially unrestricted Gutzwiller approximation. We find a new class of charge and spin ordered states at $x=1/3$ and $x=0.5$ where antiferromagnetic (AF) frustration is alleviated via weak charge inhomogeneity. At $x=0.5$, we show that the $\sqrt{3}a\times2a$ off-plane Na dopant order induces weak $\sqrt{3}a\times1a$ charge order in the Co layer. The symmetry breaking enables successive $\sqrt{3}a\times1a$ AF and $2a\times2a$ charge/spin ordering transitions at low temperatures. The Fermi surface is truncated by the $2a\times2a$ hexagonal zone boundary into small electron and hole pockets. We study the phase structure and compare to recent experiments.