Electron correlation in the two-dimensional triangle lattice of Na${}_x$CoO${}_2$

Abstract

Magnetism of layered cobaltites Na${}_x$CoO${}_2$ with $x$ = 0.6 and 0.9 has been investigated by a positive muon spin rotation and relaxation (${\mu }^{+}$SR) spectroscopy together with magnetic susceptibility and specific heat measurements, using single crystal samples in the temperature range between 250 and 1.8 K. Zero-field (ZF-) ${\mu }^{+}$SR measurements on Na${}_{0.9}$CoO${}_2$ indicates a transition from a paramagnetic to an incommensurate spin density wave state at 19 K(=$T_{\mathsf{SDW}}$). The anisotropic ZF-${\mu }^{+}$SR spectra suggest that the oscillating moments of the {\sf IC-SDW} directs along the c-axis. Since Na${}_{0.6}$CoO${}_2$ is paramagnetic down to 1.8 K, the magnitude of $T_{\mathsf{SDW}}$ is found to strongly depend on $x$.This behavior is well explained using the Hubbard model within a mean field approximation on two-dimensional triangle lattice in the CoO${}_2$ plane. Also, both the appearance of the {\sf IC-SDW} state by the change in $x$ and the magnitude of the electronic specific heat parameter of Na${}_{0.6}$CoO${}_2$ indicate that Na${}_x$CoO${}_2$ is unlikely to be a typical strongly correlated electron system.

8 pages, 6 figures