  Interfacing magnetism with superconducting condensates is rapidly emerging as
a viable route for the development of innovative quantum technologies. In this
context, the development of rational design strategies to controllably tune the
interaction between magnetic moments is crucial. In the metallic regime, the
indirect interaction mediated by conduction electrons, the so-called RKKY
coupling, has been proven to be remarkably fertile in creating and controlling
magnetic phenomena. However, despite its potential, the possibility of using
superconductivity to control the sign and the strength of indirect interactions
between magnet moments remains largely unexplored. Here we address this problem
at its ultimate limit, demonstrating the possibility of maximally tuning the
interaction between local spins coupled through a superconducting condensate
with atomic scale precision. By using Cr atoms coupled to superconducting Nb as
a prototypical system, we use atomic manipulation techniques to precisely
control the relative distance between local spins along different
crystallographic directions while simultaneously sensing their coupling by
scanning tunneling spectroscopy. Our results reveal the existence of highly
anisotropic superconductor-mediated indirect couplings between the local spins,
lasting up to very long distances, up to 12 times the lattice constant of Nb.
Moreover, we demonstrate the possibility of controllably crossing a quantum
phase transition by acting on the direction and interatomic distance between
spins. The extremely high tunability provides novel opportunities for the
realization of exotic phenomena such as topological superconductivity and the
rational design of magneto-superconducting interfaces.
