Soft Elastic Constants From Phonon Spectroscopy In Hole-Doped Ba(1-X)(K, Na)(X)Fe2as2 And Sr1-Xnaxfe2as2

We report inelastic x-ray scattering measurements of the in-plane polarized transverse acoustic phonon mode propagating along q parallel to [100] in various hole-doped compounds belonging to the 122 family of iron-based superconductors. The slope of the dispersion of this phonon mode is proportional to the square root of the shear modulus C-66 in the q -> 0 limit and, hence, sensitive to the tetragonal to orthorhombic structural phase transition occurring in these compounds. In contrast to a recent report for Ba(Fe0.94Co0.06)(2)As-2 [Weber et al., Phys. Rev. B 98, 014516 (2018)], we find qualitative agreement between values of C-66 deduced from our experiments and those derived from measurements of the Young modulus in Ba1-x(K, Na)(x)Fe2As2 at optimal doping. These results provide an upper limit of about 50 angstrom for the nematic correlation length for the investigated optimally hole-doped compounds. Furthermore, we also studied compounds at lower doping levels exhibiting the orthorhombic magnetic phase, where C-66 is not accessible by volume probes, as well as the C-4 tetragonal magnetic phase.