  The assumption of asymptotic flatness for isolated astrophysical bodies may
be considered an approximation when one considers a cosmological context where
a cosmological constant or vacuum energy is present. In this framework we study
the motion of spinning particles in static, spherically symmetric and
asymptotically non-flat spacetimes with repulsive cosmological vacuum energy
and quintessential field. Due to the combined effects of gravitational
attraction and cosmological repulsion, the region where stable circular orbits
are allowed is restricted by an innermost and an outermost stable circular
orbits. We show that taking into account the spin of test particles may enlarge
or shrink the region of allowed stable circular orbits depending on whether the
spin is co-rotating or counter-rotating with the angular momentum of the
particles.
