Resonant inelastic x-ray scattering study of Ca 3 Ru 2 O 7

We present a combined oxygen $K$-edge x-ray absorption spectroscopy and resonant inelastic x-ray scattering (RIXS) study of the bilayer ruthenate ${\mathrm{Ca}}_{3}{\mathrm{Ru}}_{2}{\mathrm{O}}_{7}$. Our RIXS experiments on ${\mathrm{Ca}}_{3}{\mathrm{Ru}}_{2}{\mathrm{O}}_{7}$ were carried out on the overlapping planar and interplanar oxygen resonances, which are distinguishable from the apical one. Comparison to equivalent oxygen $K$-edge spectra recorded on band-Mott insulating ${\mathrm{Ca}}_{2}\mathrm{Ru}{\mathrm{O}}_{4}$ is made. In contrast to ${\mathrm{Ca}}_{2}\mathrm{Ru}{\mathrm{O}}_{4}$ spectra, which contain excitations linked to Mott physics, ${\mathrm{Ca}}_{3}{\mathrm{Ru}}_{2}{\mathrm{O}}_{7}$ spectra feature only intra-${t}_{2g}$ ones that do not directly involve the Coulomb energy scale. As found in ${\mathrm{Ca}}_{2}\mathrm{Ru}{\mathrm{O}}_{4}$, we resolve two intra-${t}_{2g}$ excitations in ${\mathrm{Ca}}_{3}{\mathrm{Ru}}_{2}{\mathrm{O}}_{7}$. Moreover, the lowest lying excitation in ${\mathrm{Ca}}_{3}{\mathrm{Ru}}_{2}{\mathrm{O}}_{7}$ shows a significant dispersion, revealing a collective character different from what is observed in ${\mathrm{Ca}}_{2}\mathrm{Ru}{\mathrm{O}}_{4}$. Theoretical modeling supports the interpretation of this lowest energy excitation in ${\mathrm{Ca}}_{3}{\mathrm{Ru}}_{2}{\mathrm{O}}_{7}$ as a magnetic transverse mode with multiparticle character, whereas the corresponding excitation in ${\mathrm{Ca}}_{2}\mathrm{Ru}{\mathrm{O}}_{4}$ is assigned to combined longitudinal and transverse spin modes. These fundamental differences are discussed in terms of the inequivalent magnetic ground-state manifestations in ${\mathrm{Ca}}_{2}\mathrm{Ru}{\mathrm{O}}_{4}$ and ${\mathrm{Ca}}_{3}{\mathrm{Ru}}_{2}{\mathrm{O}}_{7}$.