responsible for electron pairing and superconductivity [@scalapino; @dagotto; @palee], over the past 25 years a tremendous effort has focused on characterizing the interplay between magnetism and superconductivity in these materials [@fujita]. In the undoped state, the parent compounds of copper oxide superconductors are Mott insulators and have exactly one valence fermion with spin 1/2 for each copper atom, leading to robust electronic correlations and localized magnetic moments [@dagotto; @palee]. Superconductivity emerges after introducing charge carriers that suppress the static AF order. Although the strong Coulomb repulsion in the parent compounds is screened by the doped charge carriers, the electronic correlations are certainly important for the physics of the doped cuprates, particularly in the underdoped regime [@palee].

Consider now the iron-based superconductors [@johnston; @stewart; @paglione10]. Several parent compounds of these materials, such as LaFeAsO, BaFe$_2$As$_2$, NaFeAs, and FeTe, are not insulators but semimetals [@kamihara; @rotter; @cwchu; @mawkuen2]. In these cases, electronic band structure calculations have revealed that their Fermi Surfaces (FS) are composed of nearly cylindrical hole and electron pockets at the $\Gamma(0,0)$ and $M(1,0)/M(0,1)$ points, respectively [@mazin2011n; @hirschfeld]. The high density of states resulting from the extended momentum space with nearly parallel FS between the hole and electron pockets leads 