Recent mu 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.
