$d$-spacing distributions as a probe of nematoelastic response in iron-based superconductors

Electronic nematicity in iron-based superconductors (FeSCs) couples bilinearly to orthorhombic strain, allowing nematic correlations to appear in the lattice response. Here we use neutron Larmor diffraction to measure the temperature-dependent distribution of relative $d$ spacings in electron-doped Ba(Fe$_{1-x}$Co$_x$)$_2$As$_2$, hole-doped Ba$_{0.83}$K$_{0.17}$Fe$_2$As$_2$, FeSe, and Fe$_{1.07}$Te. In Ba(Fe$_{1-x}$Co$_x$)$_2$As$_2$ crystals without intentionally applied uniaxial stress, the in-plane distribution width, $\varepsilon_{\rm FWHM}$, increases on cooling in the tetragonal phase and can be described phenomenologically by a Curie--Weiss-like form. The fitted scale $T^*$ decreases with Co doping and evolves similarly to the nematic phase diagram inferred from elastoresistance, although the two experiments probe different response functions. Related broadening in Ba$_{0.83}$K$_{0.17}$Fe$_2$As$_2$ and FeSe supports extending this interpretation beyond electron-doped BaFe$_2$As$_2$. By contrast, Fe$_{1.07}$Te shows no extended Curie--Weiss-like regime without applied stress, whereas uniaxial pressure produces a strongly anisotropic broadening that can contain contributions from both the field-biased lattice response and inhomogeneous loading. A mean-field model with bilinear nematoelastic coupling and spatially varying symmetry-breaking stress explains the Curie--Weiss-like broadening in terms of the renormalized orthorhombic compliance. Neutron Larmor diffraction therefore provides a bulk-sensitive probe of nematic-related lattice broadening that complements electronic and elastic measurements.