We have measured the polarization of very slow positive muons (kinetic
energy approximately 10 eV) obtained from the moderation of a 100% po
larized surface muon bean in rare gas solid layers. We find that the m
uons nearly retain their initial polarization, indicating that the mod
eration process is very fast compared to depolarizing mechanisms. This
result opens the possibility of producing beams of very low energy po
larized muons, which have a wide range of possible applications, e.g.,
as a magnetic microprobe of surfaces and thin films.