  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.
