Soft elastic constants from phonon spectroscopy in hole-doped Ba${}_{1-x}$(K,Na)${}_x$Fe${}_2$As${}_2$ and Sr${}_{1-x}Na$_x$Fe$_2$As$_2$

Abstract

We report inelastic x-ray scattering measurements of the in-plane polarized transverse acoustic phonon mode propagating along $q\parallel$[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 $q\to 0$ limit and, hence, sensitive to the tetragonal-to-orthorhombic structural phase transition occurring in these compounds. In contrast to a recent report for Ba(Fe${}_{0.94}$Co${}_{0.06}$)${}_2$As${}_2$ [F. 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 Youngs modulus in Ba${}_{1-x}$(K,Na)${}_x$Fe${}_2$As${}_2$ at optimal doping. These results provide an upper limit of about 50 Å for the nematic correlation length for the 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 C4 tetragonal magnetic phase.investigated

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