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Starting from {\it ab-initio} band structure for Na$_x$CoO$_2$, we derive thesingle-electron energies and the effective tight-binding description for the$t_{2g}$ bands using a projection procedure. We find that due to the presenceof the next-nearest-neighbor hoppings a local minimum in the electronicdispersion close to the $\Gamma$ point of the first Brillouin zone forms.Therefore, in addition to a large Fermi surface an electron pocket close to the$\Gamma$ point emerges at high doping concentrations. The latter yields the newscattering channel resulting in a peak structure of the itinerant magneticsusceptibility at small momenta. This indicates itinerant in-planeferromagnetic state above certain critical concentration $x_m$, in agreementwith neutron scattering data. Below $x_m$ the magnetic susceptibility shows atendency towards the antiferromagnetic fluctuations. We estimate the value of$0.58 < x_m < 0.7$ within the rigid band model and within the Hubbard modelwith infinite on-site Coulomb repulsion consistent with the experimental phasediagram.Comment: 4 pages, 4 figures; LDA calculations were done with Na in the  symmetric 2d position contrary to the 6h position in a previous version of  this pape

Electronic theory for itinerant in-plane magnetic fluctuations in Na x CoO2