  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.
