The interplay between superconductivity and magnetism is one of the oldest enigmas in physics. Usually, the strong exchange field of ferromagnet suppresses singlet superconductivity via the paramagnetic effect. In EuFe₂(As_0.79P_0.21)₂, a material that becomes not only superconducting at 24.2 K but also ferromagnetic below 19 K, the coexistence of the two antagonistic phenomena becomes possible because of the unusually weak exchange field produced by the Eu subsystem. We demonstrate experimentally and theoretically that when the ferromagnetism adds to superconductivity, the Meissner state becomes spontaneously inhomogeneous, characterized by a nanometer-scale striped domain structure. At yet lower temperature and without any externally applied magnetic field, the system locally generates quantum vortex-antivortex pairs and undergoes a phase transition into a domain vortex-antivortex state characterized by much larger domains and peculiar Turing-like patterns. We develop a quantitative theory of this phenomenon and put forth a new way to realize superconducting superlattices and control the vortex motion in ferromagnetic superconductors by tuning magnetic domains—unprecedented opportunity to consider for advanced superconducting hybrids.

The ${\mathbb{Z}}_2$ topological metals $R{\mathrm{V}}_3{\mathrm{Sb}}_5$ ($R$ = K, Rb, Cs) with a layered kagome structure provide a unique opportunity to investigate the interplay between charge order, superconductivity, and topology. Here, we report muon-spin relaxation/rotation ($\mu \mathrm{SR}$) measurements performed on $\mathrm{Cs}{\mathrm{V}}_3{\mathrm{Sb}}_5$ across a broad temperature range, in order to uncover the nature of the charge density wave order and superconductivity in this material. From zero-field $\mu \mathrm{SR}$, we find that spontaneous magnetic fields appear below 50 K, which is well below the charge density wave transition ($T^{*}\sim 93$ K). We show that these spontaneous fields are dynamic in nature making it difficult to associate them with a hidden static order. The superconducting state of $\mathrm{Cs}{\mathrm{V}}_3{\mathrm{Sb}}_5$ is found to preserve time-reversal symmetry, and the transverse-field $\mu \mathrm{SR}$ results are consistent with a superconducting state that has two fully open gaps.

Chiral superconductors are novel topological materials with finite angular momentum Cooper pairs circulating around a unique chiral axis, thereby spontaneously breaking time-reversal symmetry. They are rather scarce and usually feature triplet pairing: a canonical example is the chiral p-wave state realized in the A-phase of superfluid He³. Chiral triplet superconductors are, however, topologically fragile with the corresponding gapless boundary modes only weakly protected against symmetry-preserving perturbations in contrast to their singlet counterparts. Using muon spin relaxation measurements, here we report that the weakly correlated pnictide compound LaPt₃P has the two key features of a chiral superconductor: spontaneous magnetic fields inside the superconducting state indicating broken time-reversal symmetry and low temperature linear behaviour in the superfluid density indicating line nodes in the order parameter. Using symmetry analysis, first principles band structure calculation and mean-field theory, we unambiguously establish that the superconducting ground state of LaPt₃P is a chiral d-wave singlet.