By simultaneously displaying magnetism and superconductivity in a single phase, the iron-based superconductors provide a model system for the study of magnetism's role in superconductivity. The class of intercalated iron selenide superconductors is unique among these in having the additional property of phase separation and coexistence of two distinct phases-one majority phase with iron vacancy ordering and strong antiferromagnetism, and the other a poorly understood minority microscopic phase with a contested structure. Adding to the intrigue, the majority phase has never been found to show superconductivity on its own while the minority phase has never been successfully synthesized separate from the majority phase. In order to better understand this minority phase, a series of high-quality CsxFe(2)-ySe(2) single crystals with ( 0.8 <= x <= 1; 0 <= y <= 0.3) were grown and studied. Neutron and x-ray powder diffraction performed on ground crystals show that the average I4/mmm structure of the minority phase is distinctly different from the high-temperature I4/mmm parent structure. Moreover, single-crystal diffraction reveals the presence of discrete superlattice reflections that remove the degeneracy of the Cs sites in both the majority and minority phases and reduce their structural symmetries from body centered to primitive. Group theoretical analysis in conjunction with structural modeling shows that the observed superlattice reflections originate from three-dimensional Cs vacancy ordering. This model predicts a 25 vacancy of the Cs site in the minority phase which is consistent with the site's refined occupancy. Magnetization measurements performed in tandem with neutron single-crystal diffraction provide evidence that the minority phase is the host of superconductivity. Our results also reveal a superconducting dome in which the superconducting transition temperature varies as a function of the nominal valence of iron.
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