Theory of the upper critical field of a magnetic superconductor

We have derived a general set of microscopic equations for the upper critical field of a magnetic superconductor which is valid for any concentration of normal impurity scattering and includes fully the dynamics of the phonons and of the spin fluctuations. As spin correlations can be long range, we avoid, in our derivation, the usual contact approximation and get an expression which behaves properly near the magnetic transition. Numerical estimates for various possible values of the magnetic parameters reveal that, for some regimes, the dynamics of the spin diffusions can be important. In addition it is found, from general symmetry considerations, that singlet-triplet amplitude mixing can occur in dirty superconductors with large band-splitting effects due to internal magnetization