  Co-doped ZnO is the prototypical dilute magnetic oxide showing many of the
characteristics of ferromagnetism. The microscopic origin of the long range
order however remains elusive, since the conventional mechanisms for the
magnetic interaction, such as super-exchange and double exchange, fail either
at the fundamental or at a quantitative level. Intriguingly, there is a growing
evidence that defects both in point-like or extended form play a fundamental
role in driving the magnetic order. Here we explore one of such possibilities
by performing {\it ab initio} density functional theory calculations for the
magnetic interaction of Co ions at or near a ZnO \{10$\bar{1}$0\} surface. We
find that extended surface states can hybridize with the $e$-levels of Co and
efficiently mediate the magnetic order, although such a mechanism is effective
only for ions placed in the first few atomic planes near the surface. We also
find that the magnetic anisotropy changes at the surface from an hard-axis
easy-plane to an easy axis, with an associated increase of its magnitude. We
then conclude that clusters with high densities of surfacial Co ions may
display blocking temperatures much higher than in the bulk.
