In order to investigate the relationship between superconductivity and magnetism in bilayer-hydrate cobaltate Na_x(H_3O)_zCoO_2 cdot yH_2O, Co nuclear magnetic resonance (NMR) and nuclear quadrupole resonance (NQR) measurements were performed on three different samples, which demonstrate various ground states at low temperatures. The appearance of small internal fields is observed in the NQR spectra below approximately 6 K on one of the samples that possesses the largest c-axis length and the highest NQR frequency. The other two samples exhibit superconducting transition in zero magnetic field, while these two samples show different ground states in the magnetic fields greater than 5 T. The comparison of the NMR spectra of these two samples obtained in high magnetic fields reveals the appearance of static internal magnetic fields at the Co site below 4 K in the sample that possesses the intermediate c-axis length and the NQR frequency.
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