  A full phonon intensity cancellation is reported in a longitudinal polarized
inelastic neutron scattering experiment performed on the magnetocaloric
compound MnFe$_{4}$Si$_{3}$, a ferromagnet with $T_{Curie}$ $\approx$ 305 K.
The TA[100] phonon polarized along the $c$-axis measured from the Brillouin
zone center $\textbf{G}$=(0, 0, 2) is observed only in one ($\sigma_{z}^{++}$)
of the two non-spin-flip polarization channels and is absent in the other one
($\sigma_{z}^{--}$) at low temperatures. This effect disappears at higher
temperatures, in the vicinity of $T_{Curie}$, where the phonon is measured in
both channels with nonetheless marked different intensities. The effect is
understood as originating from nuclear-magnetic interference between the
nuclear one-phonon and the magnetovibrational one-phonon scattering
cross-sections. The total cancellation reported is accidental, i.e. does not
correspond to a systematic effect, as established by measurements in different
Brillouin zones.
