Correlated disorder-to-order crossover in the local structure of KxFe2−ySe2−zSz

A detailed account of the local atomic structure and disorder at 5 K across the phase diagram of the high-temperature superconductor ${\mathrm{K}}_x{\mathrm{Fe}}_{2\ensuremath{-}y}{\mathrm{Se}}_{2\ensuremath{-}z}{\mathrm{S}}_z$ $(0\ensuremath{\le}z\ensuremath{\le}2)$ is obtained from neutron total scattering and associated atomic pair distribution function (PDF) approaches. Various model-independent and model-dependent aspects of the analysis reveal a high level of structural complexity on the nanometer length scale. Evidence is found for considerable disorder in the $c$-axis stacking of the ${\mathrm{FeSe}}_{1\ensuremath{-}x}{\mathrm{S}}_x$ slabs without observable signs of turbostratic character of the disorder. In contrast to the related FeCh (Ch = S, Se)-type superconductors, substantial Fe-vacancies are present in ${\mathrm{K}}_x{\mathrm{Fe}}_{2\ensuremath{-}y}{\mathrm{Se}}_{2\ensuremath{-}z}{\mathrm{S}}_z$, deemed detrimental for superconductivity when ordered. Our study suggests that the distribution of vacancies significantly modifies the iron-chalcogen bond-length distribution, in agreement with observed evolution of the PDF signal. A crossoverlike transition is observed at a composition of $z\ensuremath{\approx}1$, from a correlated disorder state at the selenium end to a more vacancy-ordered (VO) state closer to the sulfur end of the phase diagram. The S-content-dependent measures of the local structure are found to exhibit distinct behavior on either side of this crossover, correlating well with the evolution of the superconducting state to that of a magnetic semiconductor toward the $z\ensuremath{\approx}2$ end. The behavior reinforces the idea of the intimate relationship of correlated Fe-vacancy order in the local structure and the emergent electronic properties.