Recent $\mu \mathrm{SR}$ measurements revealed remarkable signatures of spontaneous magnetism coexisting with superconductivity in elemental rhenium. Thus, pure rhenium could be the first elemental crystal where unconventional superconductivity is realized in nature. Here we provide a quantitative theory that uncovers the nature of the superconducting instability by incorporating every details of the electronic structure together with spin-orbit coupling and multiorbital physics. We show that conventional $s$-wave superconductivity combined with strong spin-orbit coupling is inducing even-parity odd-orbital spin triplet Cooper pairs, and in presence of a screw-axis Cooper pairs' migration between the induced equal-spin triplet component leads to an exotic magnetic state with atomic-scale texture. Our first-principles-based model contains two phenomenological parameters that characterizes the pairing interaction fixed by the experimental value of the superconducting transition temperature and the slope of the specific heat, and allows quantitative prediction of the magnetic structure.

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• Magnetic texture
• Multiband superconductivity
• Pairing mechanisms
• Spin-orbit coupling
• Spin-triplet pairing
• Superconducting order parameter