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

Magnetic anisotropy is a key feature of rare earth materials from permanent magnets to heavy fermions. We explore the complex interplay of Kondo physics and anisotropy, and their effect on different experimental probes of magnetic anisotropy in a minimal $J=3/2$ Anderson impurity model using the numerical renormalization group. While anisotropy suppresses Kondo screening, virtual valence fluctuations enhance the anisotropy. We find distinct renormalization of the magnetic anisotropy measured via dynamical spin response (inelastic neutron scattering) versus electronic excitations in the impurity spectral function (resonant inelastic x-ray and scanning tunneling spectroscopy). The two measurement types have different responses and dependencies on the temperature and Kondo scales.