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We use the numerical renormalization group theory to investigate theYu-Shiba-Rusinov (YSR) bound state properties of single magnetic moleculesplaced in an s-wave superconducting substrate. The molecule consist of a largecore spin and a single orbital, coupled via an exchange interaction. Thecritical Coulomb interaction for the singlet/doublet transition decreases inthe presence of this exchange interaction for both ferro and anti-ferromagneticcouplings. The number of YSR states also increase to two pairs, however, in thesinglet phase, one of the pairs have zero spectral weight. We explore theevolution of the in-gap states using the Anderson model. Away from theparticle-hole symmetry point, the results suggest a doublet-singlet-doublettransition as the on-site energy is lowered while keeping the Coulombinteraction fixed. To understand these results, we write down an effectivemodel for the molecule in the limit of large superconducting order parameter.Qualitatively, it explains the various phase transitions and spectral nature ofthe in-gap states. Finally, we analyze the effects of magnetic anisotropicfields of the core spin on in-gap states. Due to internal degrees of freedom ofthe spin excited states, a multitude of new states emerges within the gap.Depending on the sign and strength of the uniaxial anisotropic field, theresults indicate up to three pairs of YSR states.

Yu-Shiba-Rusinov states of single magnetic molecule in an $s-wave$ superconductor