We examine the competition of the observed stripe spin density wave (SDW) with other commensurate and incommensurate SDW phases in a two-band model of the pnictides. Starting from this microscopic model, we rigorously derive an expansion of the free energy in terms of the different order parameters at the mean-field level. We show that three distinct commensurate SDW states are possible and study their appearance as a function of the doping and the electronic structure. We show that the stripe phase is generally present, but its extent in the phase diagram depends strongly upon the number of hole Fermi pockets that are nested with the electron Fermi pockets. Electron pockets competing for the same portion of a hole pocket play a crucial role. We discuss the relevance of our results for the antiferromagnetism of the pnictides.

Some of the iron pnictides show coexisting superconductivity and spin-density-wave order. We study the superconducting pairing instability in the spin-density-wave phase. Assuming that the pairing interaction is due to spin fluctuations, we calculate the effective pairing interactions in the singlet and triplet channels by summing the bubble and ladder diagrams taking the reconstructed band structure into account. The leading pairing instabilities and the corresponding superconducting gap structures are then obtained from the superconducting gap equation. We illustrate this approach for a minimal two-band model of the pnictides. Analytical and numerical results show that the presence of spin and charge fluctuations in the spin-density-wave phase strongly enhances the pairing. Over a limited parameter range, a px-wave state is the dominant instability. It competes with various states, which have mostly s ± -type structures. We analyze the effect of various symmetry-allowed interactions on the pairing in some detail.

We study the doping dependence of the spin-density-wave (SDW) state in four models of the 1111 pnictides. The random-phase approximation is used to determine the ordering temperature and the ordering vector as functions of doping, and to evaluate the contribution of the various orbitals to the SDW instability. In addition to the usual assumption of orbitally rotation-invariant interactions, we consider the effect of reduced interactions involving the xy orbital, which are anticipated by crystal-structure considerations. We find that changing the relative strength of the interaction in the xy orbital tunes the system between different nesting instabilities leading to similar SDW order. We identify two models as showing reasonable agreement with experiments, while the other two display significant discrepancies, and discuss the underlying differences between the models.Comment: 10 pages, 10 figure