  Here we follow, both experimentally and theoretically, the development of
magnetism in Tb clusters from the atomic limit, adding one atom at a time. The
exchange interaction is, surprisingly, observed to drastically increase
compared to that of bulk, and to exhibit irregular oscillations as a function
of the interatomic distance. From electronic structure theory we find that the
theoretical magnetic moments oscillate with cluster size in exact agreement
with experimental data. Unlike the bulk, the oscillation is not caused by the
RKKY mechanism. Instead, the inter-atomic exchange is shown to be driven by a
competition between wave-function overlap of the 5d shell and the on-site
exchange interaction, which leads to a competition between ferromagnetic
double-exchange and antiferromagnetic super-exchange. This understanding opens
up new ways to tune the magnetic properties of rare-earth based magnets with
nano-sized building blocks.
