We have performed depth dependent muon spin rotation/relaxation studies of the dynamics of single layer films of {it Au}Fe and {it Cu}Mn spin glasses as a function of thickness and of its behavior as a function of distance from the vacuum interface (5-70 nm). A significant reduction in the muon spin relaxation rate as a function of temperature with respect to the bulk material is observed when the muons are stopped near (5-10 nm) the surface of the sample. A similar reduction is observed for the whole sample if the thickness is reduced to e.g. 20 nm and less. This reflects an increased impurity spin dynamics (incomplete freezing) close to the surface although the freezing temperature is only modestly affected by the dimensional reduction.
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