  When the exchange interaction between the impurity spin and the spins of
itinerant quasiparticles are strong or weak enough, the ground states for a
magnetic impurity in a superconductor are the screened or free spins,
respectively. In both cases, the lowest excited state is a bound state within
the superconducting gap, known as the Yu-Shiba-Rusinov (YSR) state. The YSR
state is spatially localized, energetically isolated, and fully spin-polarized,
leading to applications such as functional scanning probes. While any
application demands identifying whether the impurity spin is screened or free,
a suitable experimental technique has been elusive. Here we demonstrate an
unambiguous way to determine the impurity ground state using the Zeeman effect.
We performed ultra-low temperature scanning tunneling spectroscopy of junctions
formed between a Cu(111) surface and superconducting Nb tips decorated by
single magnetic Fe atoms. Depending on the condition of the Fe adsorbate, the
YSR peak in the spectrum either splits or shifts in a magnetic field,
signifying that the Fe spin is screened or free, respectively. Our observations
provide renewed insights into the competition between magnetism and
superconductivity and constitute a basis for the applications of the YSR state.
