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 ${\mathrm{Ca}}_3{\mathrm{Ru}}_2{\mathrm{O}}_7$.

中文翻译：

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Ca3Ru2O7的共振非弹性X射线散射研究

我们提出了一种混合氧气 $ķ$双层钌酸盐的X射线边缘吸收光谱和共振非弹性X射线散射（RIXS）研究 ${钙}_3{茹}_2{\mathrm{Ø}}_7$。我们的RIXS实验${钙}_3{茹}_2{\mathrm{Ø}}_7$在重叠的平面和平面间的氧共振上进行，这与根尖的有区别。与等效氧气的比较$ķ$边缘光谱记录在带-莫特绝缘上 ${钙}_2茹{\mathrm{Ø}}_4$制造。与之相反${钙}_2茹{\mathrm{Ø}}_4$ 包含与莫特物理学相关的激发的光谱， ${钙}_3{茹}_2{\mathrm{Ø}}_7$ 光谱仅在内部${Ť}_{2G}$不直接涉及库仑能级的那些 如发现${钙}_2茹{\mathrm{Ø}}_4$，我们解决了两个${Ť}_{2G}$ 激发 ${钙}_3{茹}_2{\mathrm{Ø}}_7$。而且，在${钙}_3{茹}_2{\mathrm{Ø}}_7$ 表现出明显的分散性，揭示了与在 ${钙}_2茹{\mathrm{Ø}}_4$。理论建模支持对这种最低能量激发的解释。${钙}_3{茹}_2{\mathrm{Ø}}_7$ 具有多粒子特征的横向磁模式，而相应的激发 ${钙}_2茹{\mathrm{Ø}}_4$分配给组合的纵向和横向自旋模式。这些基本差异是根据不等价的磁性基态表现形式讨论的。${钙}_2茹{\mathrm{Ø}}_4$ 和 ${钙}_3{茹}_2{\mathrm{Ø}}_7$。