Magnetic excitations and their possible role in the superconducting pairing in Sr${}_2$RuO${}_4$

The mechanism of the unconventional superconductivity in Sr${}_2$RuO${}_4$ is subject of ongoing debate opposing the impact of antiferromagnetic (AFM) and ferromagnetic (FM) fluctuations. Indirect evidence for FM fluctuations can be deduced from the metallic FM SrRuO${}_3$, while isovalent Ca${}_2$RuO${}_4$ is an AFM Mott insulator. With the recent progress in inelastic neutron scattering, we could follow the AFM signal associated with quasi-one-dimensional bands across the superconducting transition down to very low energies. Even well below twice the superconducting gap, there is no change in the magnetic response in Sr${}_2$RuO${}_4$, which seems incompatible with the picture of a large gap on these Fermi-surface sheets. The quantitative analysis of FM fluctuations in Sr${}_2$RuO${}_4$ was performed with polarized neutron scattering yielding good agreement with reports of specific heat, magnetic susceptibility and NMR. Incorporating this ferromagnetic response into the BCS gap equation, however, does not stabilize a triplet pairing.