  We analyze the phase diagram associated with a pair of magnetic impurities
trapped in a superconducting host. The natural interplay between Kondo
screening, superconductivity and exchange interactions leads to a rich array of
competing phases, whose transitions are characterized by discontinuous changes
of the total spin. Our analysis is based on a combination of numerical
renormalization group techniques as well as semi-classical analytics. In
addition to the expected screened and unscreened phases, we observe a new
molecular doublet phase where the impurity spins are only partially screened by
a single extended quasiparticle. Direct signatures of the various Shiba
molecule states can be observed via RF spectroscopy.
