Observation of acoustic-phonon-like mode driven by magnetic imbalance between neighboring Fe atoms in Fe$_{1+y}$Te ($y < 0.12$)*

We have studied the evolution with temperature of the low-energy inelastic spectra of Fe$_{1+y}$Te ($y < 0.12$), a parent compound of the iron-chalcogenide superconductor family, revealing an acoustic mode at an unexpected position. Recently, we found evidence for the formation of a bond-order wave leading to ferro-orbital order in the monoclinic phase, in part due to the observation of an elastic structural peak at (100) in the low-temperature monoclinic phase [D. Fobes, \textit{et al.}, arXiv:1307.7162]. In the inelastic spectra we observe a sharp acoustic-phonon-like mode dispersing out of the (100) position in the monoclinic phase. Surprisingly, the mode survives in the tetragonal phase, despite the absence of a Bragg peak at (100); such a peak is forbidden by symmetry. LDA calculations suggest this mode could involve significant magnetic scattering. By assuming in-phase virtual displacement of the Fe atoms from their equilibrium position in a frozen phonon calculation, we have found a small but significant imbalance in the magnetic moments between the two Fe atoms within the unit cell, suggesting magnetic contribution to the mode.