Unconventional Upper- and Lower-Critical Fields and Normal-State Magnetic Susceptibility of the Novel Superconducting Compound $Na_{0.35} Co O_2 cdot 1.3 H_2O$

Magnetic properties of the novel layered superconductor, Na$_{0.35}$CoO$_{2}$$cdot$1.3H$_{2}$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 $T_{C}=4.6$ K, $H_{C2}(0)=61.0$ T and $H_{C1}(0)=28.1$ Oe. These values give quite unusual phenomenological parameters, textit{i.e.}, coherent length, penetration depth and Ginzburg-Landau parameter of $xi=2.32$ nm, $lambda=5.68times 10^{3}$ AA and $kappaequivlambda/xi=244$, suggesting an unconventional nature of superconductivity. Normal-state magnetic susceptibility shows an upturn below 130 K, which is confirmed to be inherent by high-field magnetization data. The upturn may have relevance to the mechanism of the superconductivity.