Spin and charge fluctuations and superconductivity in Na xCoO2·yH2O are studied based on a multiorbital Hubbard model. Tight-binding parameters are determined to reproduce the results of band calculations. By applying the fluctuation-exchange approximation, we show that the Hund's-rule coupling between the Co t 2g orbitals causes ferromagnetic (FM) spin fluctuation. Triplet fy(y2-3x2)-wave and p-wave pairings are favored by this FM fluctuation on the hole-pocket band. We propose that, in NaxCoO 2·yH2O, the Co t2g orbitals and interorbital Hund's-rule coupling play important roles on the triplet pairing, and this compound can be a first example of the triplet superconductor in which the orbital degrees of freedom play substantial roles.
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