It is proposed to study the low-temperature magnetic properties of several highly symmetric structures containing rare-earth and/or transition-metal ions. They aim to: a) provide stringent tests of theoretical predictions for the ordered state of purely dipolar magnets with high symmetry, particularly cubic lattices, b) explore magnetic order in some new cubic materials containing two competing sublattices of ions, one with primarily dipolar interactions, the other with "exchange"; and c) test recent predictions of "order induced by disorder" in frustrated exchange-coupled systems, focusing on f.c.c. Heisenberg antiferromagnets.
