Coexistence of magnetism and superconductivity: Tunneling characteristics of magnetic superconductors

We compute the superconducting density of states Ns(ω) for a magnetically ordered superconductor. In principle, Ns(ω) contains valuable information about the magnetic correlations. To illustrate how to extract this information, we numerically solve the full (Eliashberg-like) integral equation for Ns(ω). This depends on the magnetic structure factor S(q,ω). 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,ω) in a spin-glass. These models, which are constrained to satisfy sum rules, are compared with direct neutron measurements. A calculation of the gap (Δ)-dependent spin-exchange lifetime 1τseffΔ{1-[Ns(0)N(0)]2}-12 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 dNs(ω)dω at ω∼Tsg, where Tsg 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. © 1981 The American Physical Society.