Contrasting dynamic spin susceptibility models and their relation to high-temperature superconductivity.

We compare the normal-state resistivities ρ and the critical temperatures Tc for superconducting dx2−y2 pairing due to antiferromagnetic (AF) spin fluctuation exchange in the context of the two phenomenological dynamical spin susceptibility models, recently proposed by Millis, Monien, and Pines (MMP) and Monthoux and Pines (MP) and, respectively, by Radtke, Ullah, Levin, and Norman (RULN), for the cuprate high-Tc materials. Assuming comparable electronic bandwidths and resistiviies in both models, we show that the RULN model gives a much lower d-wave Tc ( < ∼ 20K) than the MMP model (with Tc ∼ 100K). We demonstrate that these profound differences in the Tc’s arise from fundamental differences in the spectral weight distributions of the two model susceptibilities and are not primarily caused by differences in the calculational techniques employed by MP and RULN. The MMP model, claimed to fit NMR data in YBCO, exhibits substantial amounts of spin fluctuation spectral weight up to an imposed cut-off of 400meV, whereas, in the RULN model, claimed to fit YBCO neutron scattering data, the weight is narrowly peaked and effectively cut-off by 100meV. Further neutron scattering experiments, to explore the spectral weight distribution at all wavevectors over a sufficiently large excitation energy range, will thus be of crucial importance to resolve the question whether AF spin fluctuation exchange provides a viable mechanism to account for high-Tc superconductivity. The large highfrequency boson spectral weight, needed to generate both a high d-wave Tc and a low normal-state resistivity, also implies large values, of order unity, for the Migdal smallness parameter, thus casting serious doubt on the validity of the very Migdal approximation on which high-Tc spin fluctuation exchange models are based. PACS numbers: 74.20.Mn, 74.25.-q, 74.25.Fy, 74.25.Ha Typeset using REVTEX