  At the interface of an s-wave superconductor and a three-dimensional
topological insulator, Ma- jorana zero modes and Majorana helical states have
been proposed to exist respectively around magnetic vortices and geometrical
edges. Here we first show that a single magnetic impurity at such an interface
splits each resonance state of a given spin channel outside the superconducting
gap, and also induces two new symmetric impurity states inside the gap. Next we
find that an increase in the superconducting gap suppresses both the
oscillation magnitude and period of the RKKY inter- action between two
interface magnetic impurities mediated by BCS quasi-particles. Within a mean
field approximation, the ferromagnetic Curie temperature is found to be
essentially independent of the superconducting gap, an intriguing phenomenon
due to a compensation effect between the short-range ferromagnetic and
long-range anti-ferromagnetic interactions. The existence of persis- tent
ferromagnetism at the interface allows realization of a novel topological phase
transition from a non-chiral to a chiral superconducting state at sufficiently
low temperatures, providing a new platform for topological quantum computation.
