Data obtained from neutron scattering are presented for the generalized perpendicular magnetic susceptibility Imχ⊥(q,ω) at room temperature along the <001>-axis of a single crystal of face-centred-cubic Mn73Ni27 whose elastic, magnetic and crystallographic characteristics have also been closely examined. Here q stands for the wavevector and ω for the frequency of an excitation in the crystal. Plotted against q and ω, the measured function shows a broad ridge that sweeps up from ℏω = 4 meV at q = 0 to ca. 140 meV at the zone boundary qmax. We take this to be the track of an exceptionally diffuse spin-wave mode. The broadening of this excitation, however, is so great that beyond energies of ca. 40 meV it would have to be said that the whole Brillouin zone is involved in the setting-up of an excited state at any specified energy. To investigate that feature, attempts were made to analyse the measured Imχ as a well-defined spin-wave ‘dispersion law’ of elementary form, broadened either in q or in ω by some simply-expressed interaction. A successful outcome would indicate, in these two extreme cases, that the broadening arose from the excitation being limited by considerations respectively of space or of time. Our efforts to fit χ with broadening in ω ran into problems, making it difficult to argue for a picture of well-defined spin waves interacting strongly with phonons, electrons or other quanta. By contrast, the entire set of 15 spectral surveys could be fitted to a smooth theoretical function with a statistical chi-squared per degree of freedom of 1.57 if we took a sharp antiferromagnetic spin-wave dispersion law subject to a generalized Ornstein–Zernike broadening-in-q function based on a spatial correlation function between spin magnitudes varying as e−κr/rα, where r is an interatomic distance in Å and α = 0.59 was the best-fitting exponent. The dispersion law thus obtained was linear between∼0.15qmax and∼0.65qmax, over which range the fit indicated a propagation velocity of 34 km s−1. Up to a rather higher limit of wavevector, κ was also quite accurately linear in q, specifically κ = (0.25 ±0.01)q. Correspondingly, linewidths were accurately linear in q out to about 0.8qmax. Thus the tremendous broadening of the spin-wave line in the 27% nickel alloy is preponderantly due to the spin correlation function suffering severe decoherence as a function of distance in all spatial directions—an effect we attribute to the magnetic structural irregularities induced by the alloying. A ‘spin wave’ in these materials is therefore a rather localized oscillation confined to a restricted region of mean dimension just a few angstroms.