Powder Na$_{x}$CoO$_{2}$ ($0.70leq xleq 0.84$) samples were synthesized and characterized carefully by X-ray diffraction analysis, inductive-coupled plasma atomic emission spectroscopy, and redox titration. It was proved that $gamma$-Na$_{x}$CoO$_{2}$ is formed only in the narrow range of $0.70leq xleq 0.78$. Nevertheless, the magnetic properties depend strongly on $x$. We found, for the first time, two characteristic features in the magnetic susceptibility of Na$_{0.78}$CoO$_{2}$, a sharp peak at $T_{p}=16$ K and an anomaly at $T_{k}=9$ K, as well as the transition at $T_{c}=22$ K and the broad maximum at $T_{m}=50$ K which had already been reported. A type of weak ferromagnetic transition seems to occur at $T_{k}$. The transition at $T_{c}$, which is believed to be caused by spin density wave formation, was observed clearly for $xgeq 0.74$ with constant $T_{c}$ and $T_{p}$ independent of $x$. On the other hand, ferromagnetic moment varies systematically depending on $x$. These facts suggest the occurrence of a phase separation at the microscopic level, such as the separation into Na-rich and Na-poor domains due to the segregation of Na ions. The magnetic phase diagram and transition mechanism proposed previously should be reconsidered.
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