Determination of the electron-paramagnon coupling parameter of a transition metal from superconducting tunneling experiments

In a recent paper Burnell et al. presented a novel method of analysis for obtaining experimental estimates of the electron-phonon and electron-paramagnon coupling parameters ${\lambda }_{\mathrm{ph}}$ and ${\lambda }_s$, respectively, for transition metals. Their analysis provides convincing evidence for strong paramagnon suppression of $T_c$ in Nb and V. We show that this analysis can be improved by removing two unnecessary assumptions each of which can have a significant effect on the determination of ${\lambda }_s$. The experimental uncertainty in the estimate of ${\lambda }_s$ then depends primarily on uncertainties in the characteristic paramagnon frequency ${\Omega }_s$ and the usual Coulomb interaction parameter ${\mu }_{\mathrm{ph}}^{*}$. We calculate ${\lambda }_s$ for a reasonable range of values for these parameters and obtain estimates of ${\lambda }_s$ that are a factor of ∼2 larger than those of Burnell et al. for the same choice of ${\mu }_{\mathrm{ph}}^{*}$ and ${\Omega }_s\sim 1$ eV.