Upper critical magnetic field for antiferromagnetically correlatedd-wave superconductors

We have obtained strong-coupling equations for the superconducting gap of a two-dimensional d-wave superconductor subjected to a perpendicular external magnetic field. The superconductor is described as a nearly antiferromagnetic Fermi liquid with pairing between the planar quasiparticles due to the exchange of antiferromagnetic spin fluctuations. We solve the equations numerically to find the upper-critical magnetic field as a function of temperature assuming that the pairing interaction mirrors the wave-vector and frequency dependence of the phenomenological dynamic spin susceptibility proposed by Millis, Monien, and Pines for the high-${T}_{c}$ superconducting cuprates. A single tight-binding energy band with first- and second-nearest-neighbor hopping is considered. One parameter in the energy-dispersion relation allows for anisotropy between the a and b directions and, consequently, for the possibility of considering a mixture of s- and d-wave gaps. We show results for different sets of parameters.