The possibility of multiple phase diagram in the novel superconductor NaxCoO2·yH2O is analyzed on the basis of the multi-orbital Hubbard model including the atomic spin-orbit coupling. We have shown that the spin triplet pairing state is stable in this model. The p-wave (f-wave) state is stabilized when the Hund's rule coupling is large (small). In the precedent paper, we have determined the direction of d-vector at T = Tc and H = 0 within the linearized Dyson-Gorkov equation. In this paper, the pairing state below Tc and under the magnetic field is determined within the weak coupling approximation including the paramagnetic effect. We find that the p + f coexistent state is stabilized at low temperatures in a part of parameter range. We point out that the phase diagram in the H-T plane is quite different between the p-wave, f-wave and p + f -wave superconductivities. The characteristics of each phase are clarified by showing the magnetic susceptibility and specific heat. We discuss the comparison with experimental results and suggest some future experiments to detect the multiple phase transition.
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