Electron correlation in the two-dimensional triangle lattice ofNaxCoO2

Abstract

Magnetism of layered cobaltites ${\text{Na}}_{x}{\text{CoO}}_{2}$ with $x=0.6$ and 0.9 has been investigated by a positive muon spin rotation and relaxation $({\ensuremath{\mu}}^{+}\text{SR})$ spectroscopy together with magnetic susceptibility and specific-heat measurements, using single-crystal samples in the temperature range between 250 and $1.8\phantom{\rule{0.3em}{0ex}}\mathrm{K}$. Zero-field-(ZF-) ${\ensuremath{\mu}}^{+}\text{SR}$ measurements on ${\text{Na}}_{0.9}{\text{CoO}}_{2}$ indicate a transition from a paramagnetic to an incommensurate spin-density wave state (IC-SDW) at $19\phantom{\rule{0.3em}{0ex}}\mathrm{K}(={T}_{\text{SDW}})$. The anisotropic ZF-${\ensuremath{\mu}}^{+}\text{SR}$ spectra suggest that the oscillating moments of the IC-SDW direct along the $c$ axis. Since ${\text{Na}}_{0.6}{\text{CoO}}_{2}$ is paramagnetic down to $1.8\phantom{\rule{0.3em}{0ex}}\mathrm{K}$, the magnitude of ${T}_{\text{SDW}}$ is found to strongly depend on $x$. This behavior is well explained using the Hubbard model within a mean-field approximation on two-dimensional triangular lattice in the ${\text{CoO}}_{2}$ plane. Also, both the appearance of the IC-SDW state by the change in $x$ and the magnitude of the electronic specific-heat parameter of ${\text{Na}}_{0.6}{\text{CoO}}_{2}$ indicate that ${\text{Na}}_{x}{\text{CoO}}_{2}$ is unlikely to be a typical strongly correlated electron system.