We consider a clean layered magnetic superconductor in which a continuous magnetic transition takes place inside superconducting state and the exchange interaction between superconducting and magnetic subsystems is weak so that superconductivity is not destroyed at the magnetic transition. An example of such material is RbEuFe4As4. We investigate the suppression of the superconducting gap and superfluid density by correlated magnetic fluctuations in the vicinity of the magnetic transition. The influence of nonuniform exchange field on superconducting parameters is sensitive to the relation between the magnetic correlation length, ξh, and superconducting coherence length ξs defining the 'scattering' (ξh<ξs) and 'smooth' (ξh>ξs) regimes. As a small uniform exchange field does not affect the superconducting gap and superfluid density at zero temperature, smoothening of the spatial variations of the exchange field reduces its effects on these parameters. We develop a quantitative description of this 'scattering-to-smooth' crossover for the case of quasi-two-dimensional magnetic fluctuations. Since the magnetic-scattering probability varies at the energy scale comparable with the gap, the quasiclassical approximation is not applicable in the crossover region and microscopic treatment is required. We find that the corrections to both the gap and superfluid density grow proportionally to ξh until it remains much smaller than ξs. When ξh exceeds ξs, both parameters have much weaker dependence on ξh. Moreover, the gap correction may decrease with increasing of ξh in the vicinity of the magnetic transition. We also find that the crossover is unexpectedly broad: the standard scattering approximation becomes sufficient only when ξh is substantially smaller than ξs.
The AG theory is only relevant for quenched magnetic disorder, but I assume there is some dynamics to magnetic fluctuations.
Also, what is the pairing symmetry of the superconducting order parameter? If it's not s-wave any disorder, even non-magnetic should lead to the AG suppression.