Disorder-promoted C4 -symmetric magnetic order in iron-based superconductors

In most iron-based superconductors, the transition to the magnetically ordered state is closely linked to a lowering of structural symmetry from tetragonal (C4) to orthorhombic (C2). However, recently, a regime of C4-symmetric magnetic order has been reported in certain hole-doped iron-based superconductors. This novel magnetic ground state can be understood as a double-Q spin density wave characterized by two order parameters M1 and M2 related to each of the two Q vectors. Depending on the relative orientations of the order parameters, either a noncollinear spin-vortex crystal or a nonuniform charge-spin density wave could form. Experimentally, Mössbauer spectroscopy, neutron scattering, and muon spin rotation established the latter as the magnetic configuration of some of these optimally hole-doped iron-based superconductors. Theoretically, low-energy itinerant models do support a transition from single-Q to double-Q magnetic order, but with nearly degenerate spin-vortex crystal and charge-spin density wave states. In fact, extensions of these low-energy models including additional electronic interactions tip the balance in favor of the spin-vortex crystal, in apparent contradiction with the recent experimental findings. In this paper we revisit the phase diagram of magnetic ground states of low-energy multiband models in the presence of weak disorder. We show that impurity scattering not only promotes the transition from C2 to C4-magnetic order, but it also favors the charge-spin density wave over the spin-vortex crystal phase. Additionally, in the single-Q phase, our analysis of the nematic coupling constant in the presence of disorder supports the experimental finding that the splitting between the structural and stripe-magnetic transition is enhanced by disorder.