Measurement of f orbital hybridization in rare earths through electric dipole-octupole interference in x-ray absorption spectroscopy

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Hybridization between $f$ and $p$ orbitals is relevant in many applications of rare-earth materials (catalysis, magnetism, nuclear industry) and in fundamental research (Kondo and heavy fermion systems). The authors investigated the ground state mixing between $f$ and $p$ orbitals in rare earths using high resolution x-ray absorption spectroscopy with linearly polarized x-rays, through the interference between electric dipole (\ensuremath{\Delta}L=1) and octupole (\ensuremath{\Delta}L=3) transitions. The $f\ensuremath{-}p$ hybridization was quantified by an hexadecapole moment using a sum rule. This approach has been put to the test on Gadolinium Gallium Garnet where $4f$ states are expected to be localized.