  Nowadays ferromagnetism is often found in potential diluted magnetic
semiconductor systems. However, many authors argue that the observed
ferromagnetism stems from ferromagnetic precipitates or spinodal decomposition
rather than from carrier mediated magnetic impurities, as required for a
diluted magnetic semiconductor. In the present paper we answer this question
for Fe-implanted ZnO single crystals comprehensively. Different implantation
fluences and temperatures and post-implantation annealing temperatures have
been chosen in order to evaluate the structural and magnetic properties over a
wide range of parameters. Three different regimes with respect to the Fe
concentration and the process temperature are found: 1) Disperse Fe$^{2+}$ and
Fe$^{3+}$ at low Fe concentrations and low processing temperatures, 2)
FeZn$_2$O$_4$ at very high processing temperatures and 3) an intermediate
regime with a co-existence of metallic Fe (Fe$^0$) and ionic Fe (Fe$^{2+}$ and
Fe$^{3+}$). Ferromagnetism is only observed in the latter two cases, where
inverted ZnFe$_2$O$_4$ and $\alpha$-Fe nanocrystals are the origin of the
observed ferromagnetic behavior, respectively. The ionic Fe in the last case
could contribute to a carrier mediated coupling. However, their separation is
too large to couple ferromagnetically due to the lack of p-type carrier. For
comparison investigations of Fe-implanted epitaxial ZnO thin films are
presented.
