  Polarized neutron scattering experiments on the slightly overdoped
superconductor Ba$_{0.5}$K$_{0.5}$Fe$_2$As$_2$ reveal broad magnetic resonance
scattering peaking at approximately 15 meV. In spite of doping far beyond the
suppression of magnetic order, this compound exhibits dispersive and
anisotropic magnetic excitations. At energies below the resonance maximum,
magnetic correlations polarized parallel to the layers but perpendicular to the
propagation vector are reduced by a factor two compared to those in the two
orthogonal directions; in contrast correlations at the peak maximum are
isotropic.
