Interplay between magnetism and superconductivity in Fe-pnictides

We consider phase transitions and potential co-existence of spin-density-wave (SDW) magnetic order and extended s-wave ($s^{+}$) superconducting order within a two-band itinerant model of iron pnictides, in which SDW magnetism and $s^{+}$ superconductivity are competing orders. We show that depending on parameters, the transition between these two states is either first order, or involves an intermediate phase in which the two orders co-exist. We demonstrate that such co-existence is possible when SDW order is incommensurate.