Comprehensive low-temperature specific-heat data $C(T,H)$ of ${\mathrm{Na}}_{0.35}{\mathrm{CoO}}_2·1.3{\mathrm{H}}_2\mathrm{O}$ with temperature $T$ down to $0.6\mathrm{K}$ and the magnetic field $H$ up to $8\mathrm{T}$ are presented. In the normal state, the values of ${\gamma }_{\mathrm{n}}=13.94\mathrm{mJ}∕\mathrm{mol}{\mathrm{K}}^2$ and Debye temperature ${\Theta }_{\mathrm{D}}=362\mathrm{K}$ are reported. At zero field, a very sharp superconducting anomaly was observed at $T_c=4.5\mathrm{K}$ with $\Delta C∕{\gamma }_{\mathrm{ns}}{T}_c=1.45$ if the specific-heat jump is normalized to the superconducting volume fraction, which is estimated to be 47.4% based on the consideration of entropy balance at $T_c$ for the second-order superconducting phase transition. In the superconducting state, the electronic contribution $C_{es}$ at $H=0$ can be well described by the model of the line nodal order parameter. In low $H$, $\delta \gamma \left(H\right)\propto H^{1∕2}$, which is also a manifestation of the line nodes. The behaviors of both $T_c\left(H\right)$ and $\gamma \left(H\right)$ suggest the anisotropy of $H_{c2}$, or possible crossovers or transitions occurring in the mixed state.

• Received 24 November 2004

DOI:https://doi.org/10.1103/PhysRevB.71.020504