Impurity Effects in Highly Frustrated Diamond-Lattice Antiferromagnets

We consider the effects of local impurities in highly frustrated diamond lattice antiferromagnets, which exhibit large but non-extensive ground state degeneracies. Such models are appropriate to many A-site magnetic spinels. We argue very generally that sufficiently dilute impurities induce an {\sl ordered} magnetic ground state, and provide a mechanism of degeneracy breaking. The states which are selected can be determined by a ``swiss cheese model'' analysis, which we demonstrate numerically for a particular impurity model in this case. Moreover, we present criteria for estimating the stability of the resulting ordered phase to a competing frozen (spin glass) one. The results may explain the contrasting finding of frozen and ordered ground states in CoAl$_2$O$_4$ and MnSc$_2$S$_4$, respectively.