  Local spins coupled to superconductors give rise to several emerging
phenomena directly linked to the competition between Cooper pair formation and
magnetic exchange. These effects are generally scrutinized using a
spectroscopic approach which relies on detecting the in-gap bound modes arising
from Cooper pair breaking, the so-called Yu-Shiba-Rusinov (YSR) states.
However, the impact of local magnetic impurities on the superconducting order
parameter remains largely unexplored. Here, we use scanning Josephson
spectroscopy to directly visualize the effect of magnetic perturbations on
Cooper pair tunneling between superconducting electrodes at the atomic scale.
By increasing the magnetic impurity orbital occupation by adding one electron
at a time, we reveal the existence of a direct correlation between Josephson
supercurrent suppression and YSR states. Moreover, in the metallic regime, we
detect zero bias anomalies which break the existing framework based on
competing Kondo and Cooper pair singlet formation mechanisms. Based on
first-principle calculations, these results are rationalized in terms of
unconventional spin-excitations induced by the finite magnetic anisotropy
energy. Our findings have far reaching implications for phenomena that rely on
the interplay between quantum spins and superconductivity.
