  We investigate the fate of the orthorhombic stripe-type magnetic state
(ordering vectors $\left(\pi,0\right)$/$\left(0,\pi\right)$), observed in most
iron-pnictide superconductors, in the presence of localized magnetic moments
that tend to form a Neel state (ordering vector $\left(\pi,\pi\right)$). We
show that before long-range Neel order sets in, the coupling between the
conduction electrons and the fluctuations of the local moments favors an
unusual magnetic state consisting of a coherent superposition of the
$\left(\pi,0\right)$ and $\left(0,\pi\right)$ orders that preserves tetragonal
symmetry. The magnetization of this state is non-uniform and induces a
simultaneous checkerboard charge order. We discuss signatures of this magnetic
configuration on the electronic spectrum and its impact on the superconducting
state, showing that its phase space for coexistence with the $s^{+-}$ state is
smaller than the stripe-type state. Our results shed light on recent
experimental observations on $\mathrm{Ba(Fe_{1-x}Mn_{x})_{2}As_{2}}$ compounds,
where the Neel-type local Mn moments interact with the Fe conduction electrons.

Strongly Correlated Electrons;Superconductivity