  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 in a minimal impurity model using numerical renormalization
group. While anisotropy suppresses Kondo physics, Kondo physics enhances the
anisotropy. Importantly, 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-rays and scanning tunneling spectroscopy). The two measurement
types have different responses and dependences on the temperature and Kondo
scales.
