Electron correlation in the two-dimensional triangle lattice of Na_xCoO₂

Magnetism of layered cobaltites Na_xCoO₂ with x=0.6 and 0.9 has been investigated by a positive muon spin rotation and relaxation (μ⁺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-) μ⁺SR measurements on Na_0.9CoO₂ indicate a transition from a paramagnetic to an incommensurate spin-density wave state (IC-SDW) at 19 K(=T_SDW). The anisotropic ZF-μ⁺SR spectra suggest that the oscillating moments of the IC-SDW direct along the c axis. Since Na_0.6CoO₂ is paramagnetic down to 1.8 K, the magnitude of T_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 CoO₂ 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 Na_0.6CoO₂ indicate that Na_xCoO₂ is unlikely to be a typical strongly correlated electron system.