Dynamical magnetic susceptibility in the lamellar cobaltate superconductor NaxCoO2ṡyH2O

We systematically analyze the influence of the superconducting gap symmetry and the electronic structure on the dynamical spin susceptibility in superconducting Na_xCoO₂ṡyH₂O within three different models: The single a_1g -band model with nearest-neighbor hoppings, the realistic three-band t_2g model with, and without e_g^' pockets present at the Fermi surface. We show that the magnetic response in the normal state is dominated by the incommensurate antiferromagnetic spin density wave fluctuations at large momenta in agreement with experimental temperature dependence of the spin-lattice relaxation rate. Also, we demonstrate that the presence or the absence of the e_g^' pockets at the Fermi surface does not significantly affect this conclusion. In the superconducting state our results for d_x²-y² - or d_xy -wave symmetries of the superconducting order parameter are consistent with experimental data and exclude nodeless d_x²-y²+id_xy -wave symmetry. We further point out that the spin-resonance peak proposed earlier is improbable for the realistic band structure of Na_xCoO₂ṡyH₂O . Moreover, even if present the resonance peak is confined to the antiferromagnetic wave vector and disappears away from it.