Distinct effect of Kondo screening on crystal field splitting in electron and spin spectroscopies

Magnetic anisotropy has a complex interplay with Kondo physics, which can either enhance or suppress it. We explored this interplay in a minimal J = 3/2 Anderson impurity model with anisotropic hybridization using the numerical renormalization group, where we find a distinct renormalization of the magnetic anisotropy as measured by the dynamical spin response, as in inelastic neutron scattering, versus the splitting of electronic excitations in the impurity spectral function, as measured by resonant inelastic x-rays, photoemission and scanning tunneling spectroscopy. The two measurements are distinct, particularly with larger degrees of mixed valency, and have different dependences on the temperature and materials parameters. We also explore how the magnetic anisotropy energy is renormalized in magnetic field and temperature.