  Elucidating the nature of the magnetic ground state of iron-based
superconductors is of paramount importance in unveiling the mechanism behind
their high temperature superconductivity. Until recently, it was thought that
superconductivity emerges only from an orthorhombic antiferromagnetic stripe
phase, which can in principle be described in terms of either localized or
itinerant spins. However, we recently reported that tetragonal symmetry is
restored inside the magnetically ordered state of a hole-doped BaFe2As2. This
observation was interpreted as indirect evidence of a new double-Q magnetic
structure, but alternative models of orbital order could not be ruled out.
Here, we present Mossbauer data that show unambiguously that half of the iron
sites in this tetragonal phase are non-magnetic, establishing conclusively the
existence of a novel magnetic ground state with a non-uniform magnetization
that is inconsistent with localized spins. We show that this state is naturally
explained as the interference between two spin-density waves, demonstrating the
itinerant character of the magnetism of these materials and the primary role
played by magnetic over orbital degrees of freedom.
