Competing magnetic double-Q phases and superconductivity-induced reentrance of C2 magnetic stripe order in iron pnictides

We perform a microscopic theoretical study of the generic properties of competing magnetic phases in iron pnictides. As a function of electron filling and temperature, the magnetic stripe (single-Q) order forms a dome, but competing noncollinear and nonuniform double-Q phases exist at the foot of the dome, in agreement with recent experiments. We compute and compare the electronic properties of the different magnetic phases, investigate the role of competing superconductivity, and show how disorder may stabilize double-Q order. Superconductivity is shown to compete more strongly with double-Q magnetic phases, which can lead to reentrance of the C-2 (single-Q) order, in agreement with recent thermal expansion measurements on K-doped Ba-122 crystals.