Ferromagnetic ordering of magnetic impurities mediated by supercurrents in the presence of spin-orbit coupling

We investigate the behavior of magnetic impurities placed on the surface of superconductor thin films with spin-orbit coupling. Our study reveals long-range interactions between the impurities, which decay according to a power law, mediated by the interplay between the superfluid response described by the London equations and the anomalous supercurrents due to magnetoelectric effects. Importantly, these interactions possess a ferromagnetic component when considering the influence of the electromagnetic field, leading to the parallel alignment of the magnetic moments in the case of two impurities. In a Bravais lattice of magnetic impurities, superconductivity facilitates the establishment of ferromagnetic order within specific parameter ranges. These findings challenge the conventional understanding that ferromagnetism and superconductivity are mutually exclusive phenomena. Our theoretical framework provides a plausible explanation for the recently observed remanent flux and transport signature of ferromagnetism in iron-based superconductors, particularly Fe(Se,Te).