  A superconductor (SC) in proximity to a ferromagnetic insulator (FMI) is
predicted to exhibit mixed singlet and triplet pair correlations. The magnetic
proximity effect of FMI spin-splits the energy of Bogoliubov excitations and
leads to a spin polarization at the surface for superconducting films thinner
than the superconducting coherence length. In this work, we study
manifestations of these phenomena in the properties of a magnetic impurity
coupled via Kondo coupling to this FMI/SC system. Using the numerical
renormalization group (NRG) method, we compute the properties of the ground
state and low-lying excited states of a model that incorporates the Kondo
interaction and a Ruderman-Kittel-Kasuya-Yosida (RKKY)-like interaction with
the surface spin polarization. Our main finding is an energy splitting of the
lowest even fermion-parity states caused by the proximity to the FMI. As the
Kondo coupling increases, the splitting grows and saturates to a universal
value equal to twice the exchange field of the FMI. We introduce a two-site
model that can be solved analytically and provides a qualitative understanding
of this and other NRG results. In addition, using perturbation theory we
demonstrate that the mechanism behind the splitting involves the RKKY field and
the triplet correlations of the spin-split superconductor. A scaling analysis
combined with NRG shows that the splitting can be written as a single-parameter
scaling function of the ratio of the Kondo temperature and the superconducting
gap, which is also numerically obtained.
