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The phonon renormalization across the semiconductor-to-metal crossover inFeSi is investigated by inelastic neutron scattering combined with\textit{ab-initio} lattice dynamical calculations. A significant part ofreciprocal space with a particular focus on the 110$-$001 scattering plane ismapped by the time-of-flight inelastic neutron scattering data taken below andabove the crossover. Individual momentum values are investigated in more detailas a function of temperature. The data reveal that the anomalous phononsoftening upon metallization is not exclusive to the high symmetry $R$ and$\Gamma$ points. Several other phonon modes around the $R$-point as well as thephonon modes at the $M$ and $X$ points of the Brillouin zone exhibit anomalousphonon softening with magnitudes comparable to that observed at the $R$-point.The momentum dependence of the phonon softening is reproduced by the latticedynamical calculation based on the density functional perturbation theory. Wediscuss our findings with respect to the nature of the semiconductor-to-metalcrossover in FeSi, for which different microscopic origins have been proposed,i.e., lattice thermal disorder and electronic correlation effects.

A combined inelastic neutron scattering and \textit{ab initio} lattice dynamics study of FeSi