High temperature superconductivity in iron pnictides and chalcogenides emerges when a magnetic phase is suppressed. The multi-orbital character and the strength of correlations underlie this complex phenomenology, involving magnetic softness and anis
otropies, with Hunds coupling playing an important role. We review here the different theoretical approaches used to describe the magnetic interactions in these systems. We show that taking into account the orbital degree of freedom allows us to unify in a single phase diagram the main mechanisms proposed to explain the (pi,0) order in iron pnictides: the nesting-driven, the exchange between localized spins, and the Hund induced magnetic state with orbital differentiation. Comparison of theoretical estimates and experimental results helps locate the Fe superconductors in the phase diagram. In addition, orbital physics is crucial to address the magnetic softness, the doping dependent properties, and the anisotropies.
To clarify the nature of correlations in Hund metals and its relationship with Mott physics we analyze the electronic correlations in multiorbital systems as a function of intraorbital interaction U, Hunds coupling JH and electronic filling n. We sho
w that the main process behind the enhancement of correlations in Hund metals is the suppression of the double-occupancy of a given orbital, as it also happens in the Mott-insulator at half-filling. However, contrary to what happens in Mott correlated states the reduction of the quasiparticle weight Z with JH can happen on spite of increasing charge fluctuations. Therefore, in Hund metals the quasiparticle weight and the mass enhancement are not good measurements of the charge localization. Using simple energetic arguments we explain why the spin polarization induced by Hunds coupling produces orbital decoupling. We also discuss how the behavior at moderate interactions, with correlations controlled by the atomic spin polarization, changes at large $U$ and $J_H$ due to the proximity to a Mott insulating state.
