  We show that the magnetic ordering of coupled atomic dimers on a
superconductor is revealed by their intra-gap spectral features. Chromium atoms
on the superconductor $\beta$-Bi$_2$Pd surface display Yu-Shiba-Rusinov bound
states, detected as pairs of intra-gap excitations in the tunneling spectra. We
formed Cr dimers by atomic manipulation and found that their intra-gap features
appear either shifted or split with respect to single atoms. The spectral
variations reveal that the magnetic coupling of the dimer changes between
ferromagnetic and antiferromagnetic depending on its disposition on the
surface, in good agreement with density functional theory simulations. These
results prove that superconducting intra-gap state spectroscopy is an accurate
tool to detect the magnetic ordering of atomic scale structures.
