Knight Shift and Leading Superconducting Instability from Spin Fluctuations in Sr_{2}RuO_{4}

Recent nuclear magnetic resonance studies [A. Pustogow et al., Nature 574, 72 (2019)] have challenged the prevalent chiral triplet pairing scenario proposed for Sr_{2}RuO_{4}. To provide guidance from microscopic theory as to which other pair states might be compatible with the new data, we perform a detailed theoretical study of spin fluctuation mediated pairing for this compound. We map out the phase diagram as a function of spin-orbit coupling, interaction parameters, and band structure properties over physically reasonable ranges, comparing when possible with photoemission and inelastic neutron scattering data information. We find that even-parity pseudospin singlet solutions dominate large regions of the phase diagram, but in certain regimes spin-orbit coupling favors a near-nodal odd-parity triplet superconducting state, which is either helical or chiral depending on the proximity of the γ band to the van Hove points. A surprising near degeneracy of the nodal s^{'} and d_{x^{2}-y^{2}} wave solutions leads to the possibility of a near-nodal time-reversal symmetry broken s^{'}+id_{x^{2}-y^{2}} pair state. Predictions for the temperature dependence of the Knight shift for fields in and out of plane are presented for all states.