Constraints on superconducting transition temperatures in the cuprates: Antiferromagnetic spin fluctuations

Recently, several authors have suggested that antiferromagnetic spin fluctuations provide the pairing mechanism in the high-temperature superconductors. In this paper, we discuss this spin-fluctuation mechanism in the Fermi-surface-restricted Eliashberg formalism using a dynamical susceptibility whose form is constrained by neutron-scattering data. For definiteness, we consider the ${\mathrm{YBa}}_2$${\mathrm{Cu}}_3$${\mathrm{O}}_{7\mathrm{-}\mathrm{\delta }}$ family of superconductors, which we model with a realistic model band structure. Furthermore, we choose the electron-spin fluctuation coupling constant λ to yield agreement with low-frequency ac conductivity measurements. We find that spin-singlet pairing can occur only for ${\mathit{B}}_1$ and ${\mathit{A}}_2$ symmetries and that the former symmetry yields the higher critical temperature ${\mathit{T}}_{\mathit{c}}$. The ${\mathit{T}}_{\mathit{c}}$ associated with the ${\mathit{B}}_1$ symmetry is large in the weak-coupling limit, but is greatly reduced when strong-coupling effects are included. Finally, we observe that even for anisotropic pairing schemes, transport data that constrain λ provide stringent limits on the critical temperature.