Suppression of superconducting parameters by correlated quasi-two-dimensional magnetic fluctuations

We consider a clean layered magnetic superconductor in which a continuous magnetic transition takes place inside a superconducting state. We assume that the exchange interaction between superconducting and magnetic subsystems is weak so that superconductivity is not destroyed at the magnetic transition. A representative 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 very sensitive to the relation between the magnetic correlation length 4" h and superconducting coherence length xi(s), defining the 'scattering' (xi(h) < xi(s)) and 'smooth' (xi(h) > xi(s)) 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 realized in RbEuFe4As4. Since the magnetic-scattering energy scale is comparable with the gap in the crossover region, the standard quasiclassical approximation is not applicable and full microscopic treatment is required. We find that the corrections to both the gap and superfluid density increase proportionally to xi(h) until it remains much smaller than xi(s). In the opposite limit, when the correlation length exceeds the coherence length both parameters have much weaker dependence on xi(h). Moreover, the gap correction may decrease with increasing of xi(h) in the immediate vicinity of the magnetic transition if it is located at temperature much lower than the superconducting transition. We also find that the crossover between the two regimes is unexpectedly broad: The standard scattering approximation becomes sufficient only when xi(h) is substantially smaller than xi(s).