Short-range nematic fluctuations in Sr1-xNaxFe2As2 superconductors

Interactions between nematic fluctuations, magnetic order and superconductivity are central to the physics of iron-based superconductors. Here we report on in-plane transverse acoustic phonons in hole-doped Sr${}_{1-x}$Na${}_x$Fe${}_2$As${}_2$ measured via inelastic X-ray scattering, and extract both the nematic susceptibility and the nematic correlation length. By a self-contained method of analysis, for the underdoped ($x=0.36$) sample, which harbors a magnetically-ordered tetragonal phase, we find it hosts a short nematic correlation length $\xi$ ~ 10 $\mathring{A}$ and a large nematic susceptibility ${\chi }_{\mathrm{n}\mathrm{e}\mathrm{m}}$. The optimal-doped ($x=0.55$) sample exhibits weaker phonon softening effects, indicative of both reduced $\xi$ and ${\chi }_{\mathrm{n}\mathrm{e}\mathrm{m}}$. Our results suggest short-range nematic fluctuations may favor superconductivity, placing emphasis on the nematic correlation length for understanding the iron-based superconductors.