Coexistence of magnetism and superconductivity: Tunneling characteristics of magnetic superconductors

We compute the superconducting density of states $N_s\left(\omega \right)$ for a magnetically ordered superconductor. In principle, $N_s\left(\omega \right)$ contains valuable information about the magnetic correlations. To illustrate how to extract this information, we numerically solve the full (Eliashberg-like) integral equation for $N_s\left(\omega \right)$. This depends on the magnetic structure factor $S(q,\omega )$. Our results are compared with tunneling measurements on a (proximity-effect-) induced superconducting spin-glass. In general, we find good agreement with experiment for the temperature dependence of the zero-bias conductance for two different models of $S(q,\omega )$ in a spin-glass. These models, which are constrained to satisfy sum rules, are compared with direct neutron measurements. A calculation of the gap ($\Delta$)-dependent spin-exchange lifetime $\frac{1}{{\tau }_s^{\mathrm{eff}}}\equiv \Delta {\{1-{\left[\frac{N_s\mathrm{}\left(0\right)\mathrm{}}{N\left(0\right)\mathrm{}}\right]}^2\}}^{-\frac{1}{2}}$ is found to yield significantly better agreement with experiment than the usual golden rule calculation (which includes inelastic processes). For the spin-glasses our theory predicts a temperature-dependent peak in $\frac{d{N}_s\left(\omega \right)}{d\omega }$ at $\omega \sim T_{\mathrm{sg}}$,, where $T_{\mathrm{sg}}$ is the transition temperature. To observe this feature and others, we urge that further measurements of the tunneling characteristics of intrinsic magnetic superconductors be performed.