Competing orders in FeAs layers.

Using the unrestricted Hartree-Fock approximation and Landau theory we identify possible phases competing with superconductivity in FeAs layers. We find that close to half-filling the transition from the paramagnet to the magnetically ordered phase is first order, making anharmonicities relevant and leading to a rich phase diagram. Between the already known one-dimensionally modulated magnetic stripe phase and the paramagnet we find a new phase which has the same structure factor as the former but in which magnetic moments at nearest-neighbor sites are at right angles making electrons acquire a nontrivial phase when circulating a plaquette at strong coupling. Another competing phase has magnetic and charge order and may be stabilized by charged impurities.