We calculated the nuclear spin-lattice relaxation rate $1/T_1$ for the D+iD superconducting state with impurities. We found that small amount of unitary impurities quickly produces the residual density of states inside the gap. As a result, the T-linear behavior in 1/T$_1$ is observed at low temperatures. Our results show that the D+iD pairing symmetry of the superconducting state of Na$_{ 0.35}$CoO$_{ 2} \cdot y$H$_2$ O is compatible with recent $^{ 59}$Co 1/T$_1$ experiments of several groups.
Categories: cond-mat.str-el