Close correlation between magnetic properties and the soft phonon mode of the structural transition in BaFe$_{2}$As$_{2}$ and SrFe$_{2}$As$_{2}$

Parent compounds of Fe-based superconductors undergo a structural phase transition from a tetragonal to an orthorhombic structure. We investigated the temperature dependence of the frequencies of transverse acoustic (TA) phonons that extrapolate to the shear vibrational mode at the zone center, which corresponds to the orthorhombic deformation of the crystal structure at low temperatures in BaFe 2 As 2 and SrFe 2 As 2 . We found that acoustic phonons at small wavevectors soften gradually towards the transition from high temperatures, tracking the increase of the size of slowly fluctuating magnetic domains. On cooling below the transition to base temperature the phonons harden, following the square of the magnetic moment. Our results provide evidence for close correlation between magnetic and phonon properties in Fe-based superconductors.