Van Hove singularities at the $L$-face of the lutetium nitride phonon dispersion

We report the structural and vibrational properties of the prototypical 4$f$-filled nonmagnetic member LuN of the lanthanide nitrides, $\mathit{\text{Ln}}$N, with elastic and inelastic neutron scattering data at $4$~K. We find a peak in the generalized density of states which, through input from a DFT+$U$ computation, we ascribe to a van Hove singularity on the fourfold-degenerate $L$-face of the Brillouin zone. This work advances the understanding of phonon dynamics in $\mathit{\text{Ln}}$N beyond the $\mathrm{\Gamma }$-point.