Angular-dependent Magnetoresistance Oscillations in Na$_{0.48}$CoO$_{2}$ Single Crystal

We report measurements of the c-axis angular-dependent magnetoresistance (AMR) for a Na$_{0.48}$CoO$_{2}$ single crystal, with a magnetic field of 10 T rotating within Co-O planes. Below the metal-insulator transition temperature induced by the charge ordering, the oscillation of the AMR is dominated by a two-fold rotational symmetry. The amplitudes of the oscillation corresponding to the four- and six-fold rotational symmetries are distinctive in low temperatures, but they merge into the background simultaneously at about 25 K. The six-fold oscillation originates naturally from the lattice symmetry. The observation of the four-fold rotational symmetry is consistent with the picture proposed by Choy, et al., that the Co lattice in the charge ordered state will split into two orthorhombic sublattice with one occupied by Co$^{3+}$ ions and the other by Co$^{4+}$ ions. We have also measured the c-axis AMR for Na$_{0.35}$CoO$_{2}$ and Na$_{0.85}$CoO$_{2}$ single crystals, and found no evidence for the existence of two- and four-fold symmetries.