Unconventional Superconductivity and Nearly Ferromagnetic Spin Fluctuations in Na$_x$CoO$_2$$\cdot y$H$_2$O

Co NQR studies were performed in recently discovered superconductor Na$_x$CoO$_2$$\cdot y$H$_2$O to investigate physical properties in the superconducting (SC) and normal states. Two samples from the same Na$_x$CoO$_2$ were examined, SC bilayer-hydrate sample with $T_c \sim 4.7$ K and non-SC monolayer-hydrate sample. From the measurement of nuclear-spin lattice relaxation rate $1/T_1$ in the SC sample, it was found that the coherence peak is absent just below $T_c$ and that $1/T_1$ is proportional to temperature far below $T_c$. These results, which are in qualitatively agreement with the previous result by Fujimoto {\it et al.}, suggest strongly that unconventional superconductivity is realized in this compound. In the normal state, $1/T_1T$ of the SC sample shows gradual increase below 100K down to $T_c$, whereas $1/T_1T$ of the non-SC sample shows the Korringa behavior in this temperature range. From the comparison between $1/T_1T$ and $\chi_{\rm bulk}$ in the SC sample, the increase of $1/T_1T$ is attributed to nearly ferromagnetic fluctuations. These remarkable findings suggest that the SC sample possesses nearly ferromagnetic fluctuations, which are possibly related with the unconventional superconductivity in this compound. The implication of this finding is discussed.