  The magnetic moment of a single impurity atom in a finite free electron gas
is studied in a combined x-ray magnetic circular dichroism spectroscopy and
density functional theory study of size-selected free chromium-doped gold
clusters. The observed size-dependence of the local magnetic moment can
essentially be understood in terms of the Anderson impurity model. Electronic
shell closure in the host metal minimizes the interaction of localized impurity
states with the confined free electron gas and preserves the full magnetic
moment of $\unit[5]{\mu_B}$ in $\mathrm{CrAu}_{2}^{+}$ and
$\mathrm{CrAu}_{6}^{+}$ clusters. Even for open-shell species, large local
moments are observed that scale with the energy gap of the gold cluster. This
indicates that an energy gap in the free electron gas generally stabilizes the
local magnetic moment of the impurity.
