The quantum critical antiferromagnetic (AFM) fluctuation spectra measured by inelastic neutron scattering recently in two heavy-fermion superconductors are used together with their other measured properties to calculate their $d$-wave superconducting transition temperatures $T_{\mathrm{c}}$. To this end, the linearized Eliashberg equations for $d$-wave superconductivity induced by AFM fluctuations are solved in models of fermions with various levels of nesting. The results for the ratio of $T_{\mathrm{c}}$ to the characteristic spin-fluctuation energy are well parametrized by a dimensionless coupling constant and the AFM correlation length. Comparing the results with experiments suggests that one may reasonably conclude that superconductivity in these compounds is indeed caused by AFM fluctuations. This conclusion is strengthened by a calculation with the same parameters of the measured coefficient of the normal-state quantum-critical resistivity $\propto T^{3/2}$ characteristic of Gaussian AFM quantum-critical fluctuations. The calculations give details of the superconducting coupling as a function of the correlation length and the integrated fluctuation spectra useful in other compounds.

• Received 8 February 2013

DOI:https://doi.org/10.1103/PhysRevB.88.014510