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Magnetic interactions in iron superconductors studied with a five-orbital model within the Hartree-Fock and Heisenberg approximations

We have analyzed the magnetic interactions of a five orbital model for iron superconductors treated both within Hartree-Fock and Heisenberg approximations. We have found that the exchange constants depend non-trivially on the Fe-As-Fe angle and on the charge and orbital filling. Within the localized picture, columnar ordering is found for intermediate Hund's coupling J_H. At smaller J_H, an unusual orbital reorganization stabilizes checkerboard ordering. Ferromagnetism appears at large J_H. Ferromagnetic correlations are enhanced with electron doping while large hole doping stabilizes checkerboard antiferromagnetism, explaining the change in magnetic interactions upon substitution of Fe by Co or Mn. For intermediate and large values of U, Hartree-Fock shows similar results as strong coupling though with a double stripe phase instead of ferromagnetism. Itinerancy enhances the stability of the columnar ordering. Comparison of the two approaches reveals a metallic region of the phase diagram where strong coupling physics is determinant.