  Co and Na NMR are used to probe the local susceptibility and charge state of
the two Co sites of the Na-ordered orthorhombic Na0.5CoO2. Above T_N=86K, both
sites display a similar T-dependence of the spin shift, suggesting that there
is no charge segregation into Co3+ and Co4+ sites. Below T_N, the magnetic long
range commensurate order found is only slightly affected by the metal-insulator
transition (MIT) at T_MIT=51K. Furthermore, the electric field gradient at the
Co site does not change at these transitions, indicating the absence of charge
ordering. All these observations can be explained by successive SDW induced by
two nestings of the Fermi Surface specific to the x=0.5 Na-ordering.
