  Inelastic spin flip excitations associated with single-ion magnetic
anisotropy of quantum spins, can be strongly renormalized by Kondo exchange
coupling to the conduction electrons in the substrate, as shown recently for
the case of Co adatoms on CuN$_2$ islands. In this case differential
conductance spectra show zero-bias anomalies due to a Kondo effect of the
doubly degenerate ground state, and finite-bias step features due to spin flip
excitations. Here I consider spin-1 quantum magnets with positive uniaxial
anisotropy, where the ground state is non-degenerate and hence the Kondo effect
does not take place. Nevertheless the renormalization of inelastic spin
excitations due to exchange coupling by hybridization of the quantum spin with
the conduction electrons still takes place despite the complete absence of the
Kondo effect in the ground state. Additionally, I show that away from
particle-hole symmetry, charge fluctuations have a similar effect to Kondo
exchange coupling, leading to the renormalization of spin flip excitations.
However, in contrast to the renormalization by Kondo exchange, charge
fluctuations lead to asymmetric spectra, which for strong charge fluctuations
can mimic Fano behavior.
