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 [1], 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, ξ_h, and superconducting coherence length ξ_s defining the 'scattering' (ξ_h < ξ_s) and 'smooth' (ξ_h > ξ_s) 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 [2] and the exchange corrections are proportional to the magnetic scattering rate, which grows linearly with ξ_h until it remains smaller than ξ_s. In the opposite limit, when ξ_h exceeds ξ_s, 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 ξ_h is substantially larger than ξ_s. We applied the developed theoretical framework to modelling the observed behavior of the London penetration depth extracted from the vortex imaging in RbEuFe₄As₄ [3]. 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.

References:
[1] A. E. Koshelev, “Suppression of superconducting parameters by correlated quasi-two-dimensional magnetic fluctuations”, Phys. Rev. B 100, 014518 (2019).
[2] A. A. Abrikosov and L. P. Gor’kov, “Contribution to the theory of superconducting alloys with paramagnetic impurities”, Sov. Phys. JETP 12, 1243 (1961); S. Skalski, O. Betbeder-Matibet, and P. R. Weiss, “Properties of superconducting alloys containing paramagnetic impurities”, Phys. Rev. 136, A1500 (1964); V. G. Kogan, R. Prozorov, and V. Mishra, “London penetration depth and pair breaking”, Phys. Rev. B 88, 224508 (2013).
[3] D. Collomb et al., “Observing the suppression of superconductivity in RbEuFe4As4 by correlated magnetic fluctuations”, Phys. Rev. Lett. 126, 157001 (2021).

Keywords: Magnetic superconductors, Iron pnictides