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The superconductor Sr2RuO4 has been the subject of enormous interest overmore than two decades, but until now the form of its order parameter has notbeen determined. Since groundbreaking NMR experiments revealed that the pairsare of dominant spin-singlet character, attention has focused on time-reversalsymmetry breaking linear combinations of $s$-, $d$- and $g$-waveone-dimensional (1D) irreducible representations. However, a state of the form$d_{xz}+id_{yz}$ has also been proposed. We present a systematic study of thestability of various superconducting candidate states, assuming that pairing isdriven by the fluctuation exchange mechanism, including a realisticthree-dimensional Fermi surface, full treatment of both local and non-localspin-orbit couplings, and a wide range of interaction parameters $U,J,U',J'$.The leading superconducting instabilities are found to exhibit nodaleven-parity $A_{1g} (s')$ or $B_{1g} (d_{x^2-y^2})$ symmetries, similar to thefindings in two-dimensional models without longer-range Coulomb interactionwhich tends to favor $d_{xy}$ over $d_{x^2-y^2}$. Within the so-called Hund'scoupling mean-field pairing scenario, the $E_g (d_{xz}/d_{yz})$ solution can bestabilized for large $J$ and specific forms of the spin-orbit coupling, but forall cases studied here the eigenvalues of other superconducting solutions aresignificantly larger when the full fluctuation exchange vertex is included inthe pairing kernel. Additionally, we compute the spin susceptibility inrelevant superconducting candidate phases and compare to recent neutronscattering and NMR Knight shift measurements.

Leading superconducting instabilities in three-dimensional models for Sr2RuO4