Surface alloys are highly flexible materials for tailoring the spin-dependent properties of surfaces. Here, we study the spin-dependent band structure of a DyAg$_2$ surface alloy formed on an Ag(111) crystal. We find a significant exchange spin-splitting of the localized Dy 4f states pointing to a ferromagnetic coupling between the localized Dy moments at $40,$K. The magnetic coupling between these moments is mediated by an indirect, RKKY-like exchange coupling via the spin-polarized electrons of the hole-like Dy-Ag hybrid surface state.
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