Horizontal Line Nodes in Sr2RuO4 Proved by Spin Resonance

We investigated the low-energy incommensurate (IC) magnetic fluctuations in Sr${}_2$RuO${}_4$ by the high-resolution inelastic neutron scattering measurements and random phase approximation (RPA) calculations. We observed a spin resonance with energy of $\mathrm{\hslash }{\omega }_{\text{res}}=0.56$~meV centered at a characteristic wavevector ${\mathbf{Q}}_{\text{res}}=(0.3,0.3,0.5)$. The resonance energy corresponds well to the superconducting gap $2\mathrm{\Delta }=0.56$~meV estimated by the tunneling spectroscopy. The spin resonance shows the $L$ modulation with a maximum at around $L=0.5$. The $L$ modulated intensity of the spin resonance and our RPA calculations indicate that the superconducting gaps regarding the quasi-one-dimensional $\alpha$ and $\beta$ sheets at the Fermi surfaces have the horizontal line nodes. These results may set a strong constraint on the pairing symmetry of Sr${}_2$RuO${}_4$. We also discuss the implications on possible superconducting order parameters.