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We report inelastic neutron scattering measurements of phonon spectra in theparent superconductor iron-tuned chalcogenide Fe$_{1+x}$Te, for two different xcontents (x $\leq$ 0.11), using neutron time-of-flight technique. Thermalneutron spectroscopy allowed to collect the low-temperature Stokes spectra overan extended Q-range, at 2, 40 and 120K - hence covering both the magneticmonoclinic and the paramagnetic tetragonal phases. Whereas cold-neutronsallowed to measure high-resolution anti-Stokes spectra at 140, 220 and 300K,thus covering the tetragonal phase. Our results evidence a spin-phonon couplingbehaviour towards the observed noticeable temperature-dependent change of theStokes spectra across the transition temperatures. On the other hand, theanti-Stokes spectra reveal a pronounced hardening of the low-energy, acousticregion, of the phonon spectrum, upon heating, indicating a strong anharmonicityand a subtle dependence of phonons on structural evolution within thetetragonal phase. Experimental results are accompanied by ab initiocalculations of phonon spectra of the tetragonal stoichiometric phase for acomparison with the high-resolution anti-Stokes spectra. Calculations includeddifferent density functional methods. Spin polarization and van der Waalsinteraction, were either considered or neglected, individually orconcomitantly, in order to study their respective effect on lattice dynamicsdescription. Our results suggest that including van der Waals interaction hasonly a slight effect on phonon dynamics, however, phonon spectra are betterdescribed when spin polarization is included, in a cooperative way with van derWaals interactions.

Phonon Spectra in the Parent Superconducting Iron-tuned Telluride Fe$_{1+x}$Te from Inelastic Neutron Scattering and Ab Initio Calculations