Universal Phase Diagram and Reentrant Superconductivity of $Bi$layer Hydrated Na${}_x$CoO${}_2\cdot y$H${}_2$O

We report duration dependence of superconductivity in a 43 % humidity atmosphere and ${}^{59}$Co nuclear quadrupole resonance (NQR) of polycrystalline samples of $bi$layer hydrated Na${}_x$CoO${}_2\cdot y$H${}_2$O. We found a reentrant behavior of superconductivity with respect to the time duration. We obtained the universal phase diagram where two superconducting phases and an in-between magnetic phase are classified by ${}^{59}$Co NQR frequency. Zero field ${}^{59}$Co nuclear spin-lattice relaxation rates $1\mathrm{/}{T}_1$ indicated a magnetic critical slowing down at 5 K in the magnetic phase, excluding a charge density wave ordering, and an enhancement at and just above $T_{\mathrm{c}}$ in a new superconducting phase, suggesting a coexistence of magnetic ordering.