Distinct orbital contributions to electronic and magnetic structures in La$_{4}$Ni$_{3}$O$_{10}$

Abstract: High-T$<em>c$ superconductivity has recently been discovered in Ruddlesden-Popper phase nickelates under pressure, where the low-energy electronic structure is dominated by Ni $d</em>{x² - y<sup>2}$ and $d_{z<sup>2}$ orbitals. However, the respective roles of these orbitals in superconductivity remain unclear. Here, by combining X-ray absorption, electron energy loss spectroscopy, and density functional theory calculations on La$<em>{4}$Ni$</em>{3}$O$<em>{10}$ single crystals, we identify ligand holes in the $p</em>{x,y}$ orbitals of planar oxygen and the $p_z$ orbitals of apical oxygen, which hybridize with the Ni $d_{x<sup>2-y<sup>2}$ and $d_{z<sup>2}$ orbitals, respectively. These ligand holes enable orbital-selective O K-edge resonant inelastic X-ray scattering (RIXS) study, which reveals that $d_{x<sup>2-y<sup>2}$ states dominate the low-energy charge excitations and are more itinerant. We also observe a $\sim$0.1 eV bimagnon through RIXS and Raman spectroscopy, which leads to an interlayer superexchange interaction J$<em>z$ of $\sim$50 meV. Our results reveal distinct contributions of Ni $d</em>{x<sup>2-y<sup>2}$ and $d_{z<sup>2}$ orbitals to the electronic and magnetic structure and provide direct experimental insights to understand the RP-phase nickelate superconductors.