In spite of antagonism between magnetism and superconductivity, several known superconducting compounds host sublattices of rare-earth local magnetic moments which order inside superconducting state and weakly interact with Cooper pairs. In this situation, the local moments most strongly suppress superconductivity near the magnetic transition, in the regime of strong magnetic fluctuations. A notable example of such a material is iron pnictide RbEuFe4As4 with the superconducting transition at 36.7 K and the magnetic transition at 15 K. As a model for this material, we consider a clean layered superconductor containing magnetic-moments layers in which a magnetic order establishes inside a superconducting state without destruction of superconductivity. We investigate the corrections to the superconducting gap and London penetration depth caused by weak exchange interactions between magnetic and superconducting layers in the regime of correlated magnetic fluctuations , as illustrated in the Figure. The influence of nonuniform exchange field on superconducting parameters is very 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, see Figure. We quantified this 'scattering-to-smooth' crossover for the case of quasi-two-dimensional magnetic fluctuations realized in RbEuFe4As4. In the ‘scattering’ regime, the suppression of superconductivity is similar to the case of magnetic impurities  and the exchange corrections are proportional to the magnetic scattering rate, which grows linearly with ξh until it remains smaller than ξs. In the opposite limit, when ξh exceeds ξs, smoothening of spatial variations of the exchange field strongly diminishes its effect on superconducting parameters. The crossover between the regimes occurs to be unexpectedly broad: the scattering approximation becomes inaccurate already when ξh is substantially larger than ξs. We applied the developed theoretical framework to modelling the observed behavior of the London penetration depth extracted from the vortex imaging in RbEuFe4As4 . Unexpectedly, we found that the exchange interaction between the magnetic and superconducting subsystems is quite noticeable and leads to strong suppression of the superfluid density near the magnetic transition.
Acknowledgements: This work was supported by the US Department of Energy, Office of Science, Basic Energy Sciences, Materials Sciences and Engineering Division.
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Keywords: Magnetic superconductors, Iron pnictides