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$

TL;DR

This study uses inelastic x-ray scattering to measure phonon modes in hole-doped Ba and Sr iron-based superconductors, revealing insights into their shear modulus and nematic correlations near structural and magnetic phase transitions.

Contribution

It provides a detailed comparison of shear modulus measurements from phonon spectroscopy with elastic measurements, and explores nematic correlations across different doping levels and phases.

Findings

Qualitative agreement between phonon-derived and Young's modulus shear modulus values.

Upper limit of ~50 Å for nematic correlation length in optimally hole-doped compounds.

Observation of shear modulus behavior in compounds with magnetic orthorhombic and tetragonal phases.

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 $q \rightarrow 0$ 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 {\AA} 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