Suppression of superconductivity by spin fluctuations in iron-based superconductors

We study the superconducting instability mediated by spin fluctuations in the Eliashberg theory for a minimal two-band model of iron-based superconductors. While antiferromagnetic spin fluctuations can drive superconductivity (SC) as is well established, we find that spin fluctuations necessarily contain a contribution to suppress SC even though SC can eventually occur at lower temperatures. This self-restraint effect stems from a general feature of the spin-fluctuation mechanism, namely the repulsive pairing interaction, which leads to phase frustration of the pairing gap and consequently the suppression of SC.