Vortex state in iron-based superconductors with collinear antiferromagnetic cores

Magnetism in the FeAs stoichiometric compounds and its interplay with superconductivity in vortex states are studied by self-consistently solving the BdG equations based on a two-orbital model with including the on-site interactions between electrons in the two orbitals. It is revealed that for the parent compound, magnetism is caused by the strong Hund's coupling, and the Fermi surface topology aids to select the spin-density-wave (SDW) pattern. The superconducting (SC) order parameter with $s_{\pm}=\Delta_{0}\cos(k_{x})\cos(k_{y})$ symmetry is found to be the most favorable pairing for both the electron- and hole-doped cases, while the local density-of-states (LDOS) exhibits the characteristic of nodal gap for the former and full gap for the latter. In the vortex state, the emergence of the field-induced SDW depends on the strength of the Hund's coupling and the Coulomb repulsions. The field-induced SDW gaps the finite energy contours on the electron and hole pocket sides, leading to the dual structures with one reflecting the SC pairing and the other being related to the SDW order. These features can be discernable in STM measurements for identifying the interplay between the field-induced SDW order and the SC order around the core region.