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The isothermal magnetoresistance (MR) with magnetic field (H) parallel to andperpendicular to ab plane is systematically studied on the single crystalNa$_{0.52}$CoO$_2$ with charge ordering at $\sim 50$ K and an in-planeferromagnetism below 25 K. The isothermal MR behavior with H $\parallel$ abplane and H $\perp$ ab plane is quite different. When H $\parallel$ ab plane,the MR is always negative and the in-plane ferromagnetic behavior is enhanced.While the MR with H $\perp$ ab plane changes from negative to positive withdecreasing temperature or increasing H, and the in-plane ferromagnetic behavioris suppressed. A striking feature is that the MR with H $\perp$ ab plane showsa hysteresis behavior below 25 K, which is absent for the case of H $\parallel$ab plane. These results provide strong evidence for a spin-flop transition ofsmall moments of Co$^{3.5-\delta}$ sites induced by H $\perp$ ab plane, leadingto a metamagnetic transition for small moments of Co$^{3.5-\delta}$ sites.These complex magnetism suggests an unconventional superconductivity inNa$_x$CoO$_2$ system because the Na$_x$CoO$_2$ around x=0.5 is considered to bethe parent compound of superconductivity.Comment: 6 pages, 6 figure

physical review. b, condensed matter and materials physics

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Magnetic-field-induced spin-flop transition inNaxCoO2(0.5<