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Fe$_{1.057(7)}$Te undergoes a first-order tetragonal to monoclinc structuraltransition at T$_{S} \sim 70$ K, breaking the C$_{4}$ lattice symmetry andsimultaneously breaking time reversal symmetry with bicollinear magnetic order.We investigate the soft acoustic lattice dynamics near this combinedmagneto-structural transition. We apply spherically neutron polarimetry tostudy the static magnetism near this transition, characterized with x-raypowder diffraction, and find no evidence of static incommensurate magneticcorrelations near the onset of monoclinic and bicollinear antiferromagneticorder. This fixes the position of our single crystal sample in the Fe$_{1+x}$Tephase diagram in the magnetic bicollinear region and illustrates that oursample statically undergoes a transition from a paramagnetic phase to alow-temperature bicollinear phase. We then apply neutron spectroscopy to studythe acoustic phonons, related to elastic deformations of the lattice. We find atemperature dependent soft acoustic branch for phonons propagating along [010]and polarized along [100]. The slope of this acoustic phonon branch issensitive to the elastic constant $C_{66}$ and the shear modulus. Thetemperature dependence of this branch displays a softening with a minimum nearthe magneto-structural transition of T$_{S}$ $\sim$ 70 K and a recovery withinthe magnetically ordered low temperature phase. Soft acoustic instabilities arepresent in the collinear phases of the chalcogenides Fe$_{1+x}$Te where nematicorder found in Fe$_{1+\delta}$Se is absent. We speculate, based on localizedsingle-ion magnetism, that the relative energy scale of magnetic spin-orbitalcoupling on the Fe$^{2+}$ transition metal ion is important for the presence ofa nematicity in the chalcogenides.

Acoustic lattice instabilities at the magneto-structural transition in Fe$_{1.057(7)}$Te