Critical temperature and the giant isotope effect in the presence of paramagnons

Abstract

We reconsider the long-standing problem of the effect of spin fluctuations on the criticaltemperature and the isotope effect in a phonon-mediated superconductor. We discuss thegeneral physics of the interplay between phonons and paramagnons, and show that thepreviously used approximate formulas fail to describe the correct behavior ofTc for generalphonon and paramagnon spectra. Using a controllable approximation, we derive an analytical formulafor Tc which agrees well with exact numerical solutions of the Eliashberg equations for a broad rangeof parameters. On the basis of both numerical and analytical results, we predict a strongenhancement of the isotope effect when the frequencies of spin fluctuation and phonons areof the same order. We discuss application to near-magnetic superconductors such asMgCNi3.