Unconventional superconductivity and electron correlations in the cobalt oxyhydrate Na0.35CoO2.yH2O from nuclear quadrupole resonance.

We report a careful 59Co nuclear quadrupolar resonance measurement on the recently discovered cobalt oxyhydrate Na0.35CoO2.yH(2)O superconductor from T=40 K down to 0.2 K. We find that in the normal state the spin-lattice relaxation rate 1/T(1) follows a Curie-Weiss type temperature (T) variation, 1/T(1)T=C/(T-theta), with theta=-42 K, suggesting two-dimensional antiferromagnetic spin correlations. Below T(c)=3.9 K, 1/T(1) decreases with no coherence peak and follows a T(n) dependence with n approximately 2.2 down to approximately 2.0 K but crosses over to a 1/T(1) proportional to T variation below T=1.4 K, which suggests non-s-wave superconductivity. The data in the superconducting state are most consistent with the existence of line nodes in the gap function.