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Site-specific electronic and magnetic excitations of the skyrmion material Cu$_2$OSeO$_3$

The manifestation of skyrmions in the Mott-insulator Cu$_2$OSeO$_3$ originates from a delicate balance between magnetic and electronic energy scales. As a result of these intertwined couplings, the two symmetry-inequivalent magnetic ions, Cu-I and Cu-II, bond into a spin S=1 entangled tetrahedron. However, conceptualizing the unconventional properties of this material and the energy of the competing interactions is a challenging task due the complexity of this system. Here we combine X-ray Absorption Spectroscopy and Resonant Inelastic X-ray Scattering to uncover the electronic and magnetic excitations of Cu$_2$OSeO$_3$ with site-specificity. We quantify the energies of the 3d crystal-field splitting for both Cu-I and Cu-II, fundamental to optimize model Hamiltonians. Additionally, we unveil a site-specific magnetic mode, indicating that individual spin character is preserved within the entangled-tetrahedron picture. Our results thus provide experimental constraint for validating theories that describe the interactions of Cu$_2$OSeO$_3$, highlighting the site-selective capabilities of resonant spectroscopies