  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.
