  We unveil the novel physical origin of the insulating block checkerboard
antiferromagnetism in vacancy-ordered K2Fe4Se5. Our first-principles electronic
structure analysis reveals its incompatibility with a simple Fermi-surface
nesting or Mott insulator scenario, and suggests the picture of coexisting
itinerant and localized electronic states. Consistently, we demonstrate that it
can be unified with the metallic collinear or bicollinear antiferromagnetism of
the vacancy-free parent compounds LaOFeAs, BaFe2As2, or FeTe in the
spin-fermion model. These results indicate that the blocking effects of Hund's
rule coupling and the resulting electron correlation are crucial to the
electronic and magnetic structures of iron-based superconductors.
