Title: Spin and charge excitations in the correlated multiband metal Ca3Ru2O7

Abstract: We use Ru $L_3$-edge resonant inelastic x-ray scattering (RIXS) to study the full range of excitations in Ca$_3$Ru$_2$O$_7$ from meV-scale magnetic dynamics through to the eV-scale interband transitions. This bilayer $4d$-electron correlated metal expresses a rich phase diagram, displaying long range magnetic order below 56 K followed by a concomitant structural, magnetic and electronic transition at 48 K. In the low temperature phase we observe a magnetic excitation with a bandwidth of $\sim$30 meV and a gap of $\sim$8 meV at the zone center, in excellent agreement with inelastic neutron scattering data. The dispersion can be modeled using a Heisenberg Hamiltonian for a bilayer $\mathrm{S}=1$ system with single ion anisotropy terms. At a higher energy loss, $dd$-type excitations show heavy damping in the presence of itinerant electrons, giving rise to a fluorescence-like signal appearing between the $t_{2g}$ and $e_g$ bands. At the same time, we observe a resonance originating from localized $t_{2g}$ excitations, in analogy to the structurally related Mott-insulator Ca$_2$RuO$_4$. But whereas Ca$_2$RuO$_4$ shows sharp separate spin-orbit excitations and Hund's-rule driven spin-state transitions, here we identify only a single broad asymmetric feature. These results indicate that local intra-ionic interactions underlie the correlated physics in Ca$_3$Ru$_2$O$_7$, even as the excitations become strongly mixed in the presence of itinerant electrons.