  We use inelastic neutron scattering (INS) to investigate the effect of
electron correlations on spin dynamics in the iron-based superconductor
Ba$_{0.75}$K$_{0.25}$Fe$_{2}$As$_{2}$. Our INS data show a spin-wave-like
dispersive feature, with a zone boundary energy of 200 meV. A first principles
analysis of dynamical spin susceptibility, incorporating the mass
renormalization factor of 3, as determined by angle-resolved photoemission
spectroscopy, provides a reasonable description of the observed spin
excitations. This analysis shows that electron correlations in the Fe-3$d$
bands yield enhanced effective electron masses, and consequently, induce
substantial narrowing of the spin excitation bandwidth. Our results highlight
the importance of electron correlations in an itinerant description of the spin
excitations in iron-based superconductors.
