Magnetism, Superconductivity, and Spontaneous Orbital Order in Iron-Based Superconductors: Which Comes First and Why?

Magnetism and nematic order are the two nonsuperconducting orders observed in iron-based superconductors. To elucidate the interplay between them and ultimately unveil the pairing mechanism, several models have been investigated. In models with quenched orbital degrees of freedom, magnetic fluctuations promote stripe magnetism, which induces orbital order. In models with quenched spin degrees of freedom, charge fluctuations promote spontaneous orbital order, which induces stripe magnetism. Here, we develop an unbiased approach, in which we treat magnetic and orbital fluctuations on equal footing. Key to our approach is the inclusion of the orbital character of the low-energy electronic states into renormalization group (RG) analysis. We analyze the RG flow of the couplings and argue that the same magnetic fluctuations, which are known to promote s(+-) superconductivity, also promote an attraction in the orbital channel, even if the bare orbital interaction is repulsive. We next analyze the RG flow of the susceptibilities and show that, if all Fermi pockets are small, the system first develops a spontaneous orbital order, then s(+-) superconductivity, and magnetic order does not develop down to T = 0. We argue that this scenario applies to FeSe. In systems with larger pockets, such as BaFe2As2 and LaFeAsO, we find that the leading instability is either towards a spin-density wave or superconductivity. We argue that in this situation nematic order is caused by composite spin fluctuations and is vestigial to stripe magnetism. Our results provide a unifying description of different iron-based materials.