Unconventional upper- and lower-critical fields and normal-state magnetic susceptibility of the superconducting compound ${\mathrm{Na}}_{0.35}{\mathrm{CoO}}_2\cdot 1.3{\mathrm{H}}_2\mathrm{O}$

Magnetic properties of the layered superconductor, ${\mathrm{Na}}_{0.35}{\mathrm{CoO}}_2\cdot 1.3{\mathrm{H}}_2\mathrm{O}$ have been investigated. From the temperature dependence and field dependence of the magnetization, the superconducting transition temperature, as well as upper- and lower-critical fields have been estimated to be $T_C=4.6\mathrm{}\mathrm{K},$ $H_{C2\mathrm{}}\mathrm{}\left(0\right)=61.0\mathrm{}\mathrm{T}$ and $H_{C1\mathrm{}}\mathrm{}\left(0\right)=28.1\mathrm{}\mathrm{Oe},$ respectively. These values give quite unusual phenomenological parameters, i.e., coherent length, penetration depth and Ginzburg-Landau parameter of $\xi =2.32\mathrm{}\mathrm{nm},$ $\lambda =5.68\mathrm{}\times {10}^2\mathrm{nm},$ and $\kappa \equiv \lambda /\xi =244,$ respectively, suggesting an unconventional nature of superconductivity. Additionally, the magnetic susceptibility above $T_C$ and the magnetization curve up to 54 T are also reported.