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The d-vector in possibile spin triplet superconductor Na_{x}CoO_{2}yH_{2}O ismicroscopically investigated on the basis of the multi-orbital Hubbard modelincluding the atomic spin-orbit coupling. As a result of the perturbationtheory, we obtain the stable spin triplet superconductivity where the p-waveand f-wave states can be stabilized. If we neglect the spin-orbit coupling,superconducting state has 6-fold (3-fold) degeneracy in the p-wave (f-wave)state. This degeneracy is lifted by the spin-orbit coupling. We determine thed-vector within the linearlized Dyson-Gorkov equation. It is shown that thed-vector is always along the plane when the pairing symmetry is p-wave, whileit depends on the parameters in case of the f-wave state. The lifting ofdegeneracy is significant in the p-wave state while it is very small in thef-wave state. This is because the first order term with respect to thespin-orbit coupling is effective in the former case, while it is ineffective inthe latter case. The consistency of these results with NMR and \muSRmeasurements are discussed.Comment: To appear in J. Phys. Soc. Jpn. 74 (2005) No.

journal of the physical society of japan

Role of Spin–Orbit Coupling on the Spin Triplet Pairing in NaxCoO2·yH2O: I.d-Vector under Zero Magnetic Field