We have computed ${\alpha }^{2}F$’s for the hole-doped cuprates within the framework of the one-band Hubbard model, where the full magnetic response of the system is treated properly. The $d$-wave pairing weight ${\alpha }^2{F}_d$ is found not only to contain a low-energy peak due to excitations near $\left(\pi ,\pi \right)$ expected from neutron-scattering data but also to display substantial spectral weight at higher energies due to contributions from other parts of the Brillouin zone as well as pair-breaking ferromagnetic excitations at low energies. The resulting solutions of the Eliashberg equations yield transition temperatures and gaps comparable to the experimentally observed values, suggesting that magnetic excitations of both high and low energies play an important role in providing the pairing glue in the cuprates.

• Received 17 July 2007

DOI:https://doi.org/10.1103/PhysRevB.78.134513