  We address the tunneling conductance and spin inelastic tunneling
spectroscopy of localized paramagnetic moments in a superconducting
environment, pertaining to recent measurements on
Fe-octaethylporphyrin-chloride using superconducting scanning tunneling
microscopy. We demonstrate that the Cooper pair correlations in the tip and
substrate generate a finite uniaxial anisotropy field acting on the local spin
moment, and we argue that this field may be a source for the observed changes
in the conductance spectrum for decreasing distance between the scanning
tunneling tip and the local magnetic moment. We make a side-by-side comparison
between the superconductor-superconductor junction and
normal-metal--superconductor junction, and find qualitative agreement between
the two setups while quantitative differences become explicit.
  When simulating the effects of electron pumping, we obtain additional peaks
in the conductance spectrum that can be attributed to excitations between
higher-energy spin states. The transverse anisotropy field couples basis states
of the local spin which opens for transitions between spin states that are
otherwise forbidden by conservation of angular momentum. Finally, we explore
the influences of temperature, which tend to enable in-gap transitions, and an
external magnetic field, which enables deeper studies of the spin excitation
spectrum. We especially notice the appearance of a low and high excitation peak
on each side of the main coherence peak as an imprint of transitions between
the Zeeman split ground states.
