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

We analyze the magnetic interactions of a five-orbital model for iron superconductors treated within the Hartree-Fock and Heisenberg approximations. We find that the exchange constants depend nontrivially 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 whereas large hole doping stabilizes checkerboard antiferromagnetism, explaining the change in magnetic interactions upon replacement of Fe by Co or Mn. For intermediate and large values of U, the Hartree-Fock approximation shows results similar to those for strong coupling though with a double-stripe phase instead of ferromagnetism. Itinerancy enhances the stability of the columnar ordering. A comparison of the two approaches reveals a metallic region of the phase diagram where strong-coupling physics is determinant.