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We systematically analyze the influence of the superconducting gap symmetryand the electronic structure on the dynamical spin susceptibility insuperconducting Na_xCoO_2$\cdot y$H_2O within a three different models: thesingle a_{1g}-band model with nearest-neighbor hoppings, the realisticthree-band t_{2g}-model with, and without e'_g pockets present at the Fermisurface. We show that the magnetic response in the normal state is dominated bythe incommensurate antiferromagnetic spin density wave fluctuations at largemomenta in agreement with experimental temperature dependence of thespin-lattice relaxation rate. Also, we demonstrate that the presence or theabsence of the e'_g-pockets at the Fermi surface does not affect significantlythis conclusion. In the superconducting state our results for d_{x^2-y^2}- ord_{xy}-wave symmetries of the superconducting order parameter are consistentwith experimental data and exclude nodeless $d_{x^2-y^2} + id_{xy}$-wavesymmetry. We further point out that the spin-resonance peak proposed earlier isimprobable for the realistic band structure of Na_xCoO_2$\cdot y$H_2O.Moreover, even if present the resonance peak is confined to theantiferromagnetic wave vector and disappears away from it.

Dynamical magnetic susceptibility in the lamellar cobaltate superconductor Na_xCoO_2$\cdot y$H_2O