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, charge transfer multiplet calculation, and density functional theory study of size-selected free chromium-doped gold clusters. The observed size dependence of the local magnetic moment can be understood as a transition from a local moment to a mixed valence regime. This shows that the Anderson impurity model essentially describes finite systems even though the discrete density of states introduces a significant deviation from a bulk metal, and the free electron gas is only formed by less than 10 electrons. Electronic shell closure in the gold host minimizes the interaction of localized impurity states with the confined free electron gas and preserves the magnetic moment of 5μB fully in CrAu2+ and almost fully in CrAu6+. 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 stabilizes the local magnetic moment of the impurity atom.
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