Anisotropic Magnetoresistance in Charge-Ordering $Na_{0.34}(H_3O)_{0.15}CoO_2$:Strong Spin-Charge Coupling and Spin Ordering

Angular-dependent in-plane magnetoresistance (AMR) for single crystal $Na_{0.34}(H_3O)_{0.15}CoO_2$ with charge ordering is studied systematically. The anisotropic magnetoresistance shows a twofold symmetry at high temperature with rotating H in the Co-O plane, while a sixfold symmetry below a certain temperature ($T_\rho$). At $T_\rho$, the symmetry of AMR changes from twofold to fourfold with rotating magnetic field (H) in the plane consisting of the current and c-axis. The variation of AMR symmetry with temperature arises from the subtle changes of the spin structure. These results give a direct evidence for the itinerant electrons directly coupled to the localized spins.