We have studied the magnetization and magnetoresistance of CeRu2Al10 in the applied magnetic field H along the c-axis up to ~ 55 T. The magnetization M at low temperatures shows an H-linear increase with a small slope of M/H than that for H // a-axis up to ~ 55 T after showing a small anomaly at H ~ 4 T, which indicates that the critical field to the paramagnetic phase H_c^p is higher than 55 T for H // c-axis. The magnetization curves for H // a- and c-axes below the antiferro magnetic (AFM) transition temperature T0 behave as if the magnetic anisotropy in the AFM-ordered phase is small, although there exists a large magnetic anisotropy in the paramagnetic phase, which favors the easy magnetization axis along the a-axis. On the other hand, very recently, Khalyavin et al. have reported that the AFM order where the magnetic moment is parallel to the c-axis takes place below T0. These results indicate that the AFM order in this compound is not a simple one. The longitudinal magnetoresistance for H // c-axis at low temperatures shows no anomaly originating from the phase transition, but shows oscillations below 4.2 K. This oscillatory behavior below 4.2 K originates from the Shubnikov-de Haas oscillations, from which the cross section of the Fermi surface normal to the c-axis is estimated to be 1.0*10^14 cm-2, with no large effective mass. This is the first direct evidence of the existence of the Fermi surface below T0.
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