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Unconventional superconductors have Cooper pairs with lower symmetries than in conventional superconductors. In most unconventional superconductors, the additional symmetry breaking occurs in relation to typical ingredients such as strongly correlated Fermi liquid phases, magnetic fluctuations, or strong spin-orbit coupling in noncentrosymmetric structures. In this article, we show that the time-reversal symmetry breaking in the superconductor LaNiGa2 is enabled by its previously unknown topological electronic band structure, with Dirac lines and a Dirac loop at the Fermi level. Two symmetry related Dirac points even remain degenerate under spin-orbit coupling. These unique topological features enable an unconventional superconducting gap in which time-reversal symmetry can be broken in the absence of other typical ingredients. Our findings provide a route to identify a new type of unconventional superconductors based on nonsymmorphic symmetries and will enable future discoveries of topological crystalline superconductors.

The anomalous Hall effect (AHE), typically observed in ferromagnetic (FM) metals with broken time-reversal symmetry, depends on electronic and magnetic properties. In Co3Sn2-xInxS2, a giant AHE has been attributed to Berry curvature associated with the FM Weyl semimetal phase, yet recent studies report complicated magnetism. We use neutron scattering to determine the spin dynamics and structures as a function of x and provide a microscopic understanding of the AHE and magnetism interplay. Spin gap and stiffness indicate a contribution from Weyl fermions consistent with the AHE. The magnetic structure evolves from c-axis ferromagnetism at $$x = 0$$ x = 0 to a canted antiferromagnetic (AFM) structure with reduced c-axis moment and in-plane AFM order at $$x = 0.12$$ x = 0.12 and further reduced c-axis FM moment at $$x = 0.3$$ x = 0.3 . Since noncollinear spins can induce non-zero Berry curvature in real space acting as a fictitious magnetic field, our results revealed another AHE contribution, establishing the impact of magnetism on transport.