Suppression of superconductivity by Neel-type magnetic fluctuations in the iron pnictides

Motivated by recent experimental detection of Neel-type ($(\pi ,\pi )$) magnetic fluctuations in some iron pnictides, we study the impact of competing $(\pi ,\pi )$ and $(\pi ,0)$ spin fluctuations on the superconductivity of these materials. We show that, counter-intuitively, even short-range, weak Neel fluctuations strongly suppress the $s^{+-}$ state, with the main effect arising from a repulsive contribution to the $s^{+-}$ pairing interaction, complemented by low frequency inelastic scattering. Further increasing the strength of the Neel fluctuations leads to a low-$T_c$ d-wave state, with a possible intermediate $s+id$ phase. The results suggest that the absence of superconductivity in a series of hole-doped pnictides is due to the combination of short-range Neel fluctuations and pair-breaking impurity scattering, and also that $T_c$ of optimally doped pnictides could be further increased if residual $(\pi ,\pi )$ fluctuations were reduced.