Mixed-parity superconductivity in ${\mathrm{Sr}}_2{\mathrm{RuO}}_4$

We show that in ${\mathrm{Sr}}_2{\mathrm{RuO}}_4$ the Fermi surface geometry as inferred from angle resolved photoemission experiments has important implications for a pairing interaction dominated by incommensurate, strongly anisotropic, spin fluctuations. For a spin fluctuation spectrum consistent with inelastic neutron-scattering experiments the system is close to an accidental degeneracy between even parity spin singlet and odd parity spin triplet channels. This opens the possibility of a mixed parity order parameter state in ${\mathrm{Sr}}_2{\mathrm{RuO}}_4.$ We determine the stable and metastable order parameter phases at low-temperatures and discuss especially phases with order parameter nodes.