  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.
