Measurement of f orbital hybridization in rare earths through electric dipole-octupole interference in X-ray Absorption Spectroscopy

This work provides a direct route to measure the degree of hybridization of f states in rare earths. The interference between electric dipole and octupole transitions is measured at the L1 edge of Gd in Gd3Ga5O12 using X-ray Natural Linear Dichroism (XNLD) and high energy resolution fluorescence detection. The Gd 4f-6p admixture is quantified through the integral of the dipole-octupole XNLD using a new sum rule easily applicable to experimental data. The mixing of the Gd valence states with the O ligand orbitals, calculated from first-principles, reveals that despite their localized character, the Gd 4f orbitals mix with the O 2p and 2s orbitals with an antibonding and bonding character, respectively.