Magnetically mediated superconductivity in quasi-two and three dimensions

We compare predictions of the mean-field theory of superconductivity for nearly antiferromagnetic and nearly ferromagnetic metals in two and three dimensions. The calculations are based on a parametrization of the effective interaction arising from the exchange of magnetic fluctuations. The results show that for comparable parameters, magnetic pairing is more robust in quasi-two-dimensions than in three dimensions, for either p-wave (spin triplet) pairing in nearly ferromagnetic metals or d-wave (spin singlet) pairing in nearly antiferromagnetic metals. Moreover we find higher mean-field transition temperatures for d-wave pairing than for p-wave pairing (for comparable parameters), regardless of dimensionality. We present intuitive arguments for why quasi-two-dimensional d-wave pairing is a particularly favorable case.