Suppression of superconducting parameters in magnetic layered superconductors by correlated quasi-two-dimensional magnetic fluctuations*

Motivated by physics of RbEuFe₄As₄, we consider a layered magnetic superconductor in which a magnetic transition takes place inside a superconducting state and the exchange interaction between superconducting and magnetic subsystems is weak. We investigate the suppression of the superconducting gap and superfluid density by correlated magnetic fluctuations near the magnetic transition. The behavior is very sensitive to the relation between the magnetic correlation length, ξ_h, and superconducting coherence length ξ_s defining the 'scattering' (ξ_h<ξ_s) and 'smooth' (ξ_h>ξ_s) regimes. We quantified this 'scattering-to-smooth' crossover for the case of quasi-two-dimensional magnetic fluctuations. We find that the corrections to both parameters increase proportionally to ξ_h until it remains much smaller than ξ_s. In the opposite limit, when ξ_h exceeds ξ_s, both parameters have much weaker dependence on ξ_h. Moreover, the gap correction may decrease with increasing of ξ_h close to the magnetic transition. The crossover between the two regimes is unexpectedly broad: the scattering approximation becomes sufficient only when ξ_h is substantially smaller than ξ_s.