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Superconductivity tuned by the iron vacancy order in K$_{\bf x}$Fe$_{\bf 2-y}$Se$_2$

Combining in-depth neutron diffraction and systematic bulk studies, we discover that the $\sqrt{5}\times\sqrt{5}$ Fe vacancy order with its associated block antiferromagnetic order is the ground state, with varying occupancy ratio of the iron 16i and vacancy 4d sites, across the phase-diagram of K$_{\bf x}$Fe$_{\bf 2-y}$Se$_2$. The orthorhombic order with one of the four Fe sites vacant appears only at intermediate temperature as a competing phase. The material experiences an insulator to metal crossover when the $\sqrt{5}\times\sqrt{5}$ order has highly developed. Superconductivity occurs in such a metallic phase.