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Antiferromagnetic fluctuations are believed to be a promising glue to drivehigh-temperature superconductivity especially in cuprates. Here, we perform aclose inspection of the superconducting mechanism from spin fluctuations in theEliashberg framework by employing a typical one-band model on a square lattice.While spin fluctuations can eventually drive superconductivity as is wellestablished, we find that the superconducting tendency is suppressedsubstantially by a seemingly negligible contribution from a small momentumtransfer far away from (pi,pi). This suppression comes from phase frustrationof the pairing gap and is expected to be a general feature due to the repulsivepairing interaction of spin fluctuations. Furthermore, we find that themomentum dependence of the pairing gap largely deviates from the functionalform of cos kx - cos ky, although this form is well established in cupratesuperconductors. We argue that an instantaneous magnetic interaction plays theimportant role to understand high-critical temperature of superconductivity aswell as the momentum dependence of the pairing gap.

Spin-fluctuation glue disfavors high-critical temperature of superconductivity?