Understanding the overall features of magnetic excitation is essential for clarifying the mechanism of Cooper pair formation in iron-based superconductors. In particular, clarifying the relationship between magnetism and superconductivity is a central challenge because magnetism may play a key role in their exotic superconductivity. BaFe2As2 is one of ideal systems for such investigation because its superconductivity can be induced in several ways, allowing a comparative examination. Here we report a study on the spin fluctuations of the hole-overdoped iron-based superconductors Ba1-xKxFe2As2 (x = 0.5 and 1.0
Tc = 36 K and 3.4 K, respectively) over the entire Brillouin zone using inelastic neutron scattering. We find that their spin spectra consist of spin wave and chimney-like dispersions. The chimney-like dispersion can be attributed to the itinerant character of magnetism. The band width of the spin wave-like dispersion is almost constant from the non-doped to optimum-doped region, which is followed by a large reduction in the overdoped region. This suggests that the superconductivity is suppressed by the reduction of magnetic exchange couplings, indicating a strong relationship between magnetism and superconductivity in iron-based superconductors.