  Topological quantum magnets FeSn and Fe$_{3}$Sn$_{2}$ were studied using
neutron scattering and first-principles calculations. Both materials are
metallic but host dispersionless flat bands with Dirac nodes at the $K$ point
in reciprocal space. The local structure determined from the pair density
function analysis of the neutron diffraction data provided no evidence for
electron localization in both compounds, consistent with their metallic nature.
At the same time, in FeSn, an anomalous suppression in the $c$-axis lattice
constant coupled with changes in the phonon spectra were observed across
T$_{N}$ indicating the presence of magneto-elastic coupling and spin-phonon
interactions. In addition, it was observed that spin waves persisted well above
T$_{N}$, suggesting that the in-plane ferromagnetic spin correlations survive
at high temperatures. In contrast, no lattice anomaly was observed in
Fe$_{3}$Sn$_{2}$. The inelastic signal could be mostly accounted for by
phonons, determined from density functional theory, showing typical softening
on warming.
