We report the first observation of dipolar magnetic order in a diamond lattice, in the RVO4-(Mo03)i2* 3OH2O compounds (R =Gd, Dy, Er). Theory predicts antiferromagnetic order for a diamond lattice of dipoles, with a susceptibility at r=0 depending only on lattice symmetry and spin. We present experimental susceptibilities for ions with different effective spin which are consistent with these predictions, and which confirm the existence of unusually large quantum spin fluctuations in these materials. The fluctuations substantially exceed those of the Heisenberg antiferromagnet.PACS numbers: 75.30.Cr Dipolar magnetic order is an interesting problem because the dipolar Hamiltonian is known exactly, presenting the opportunity for a critical comparison between theory and experiment. Cubic lattices occupy a position of special importance, due to their simplicity and, more importantly, the fact that ion moments are isotropic, resulting in magnetic order that is determined by lattice symmetry alone. Isotropy should also produce the largest spin fluctuations. Among the primitive cubic lattices, bcc and fee are predicted always to be dipolar ferromagnets, while only simple cubic is predicted to be antiferromagnetic [1,2]. The antiferromagnetic case is of particular interest because it is here that quantum fluctuations are most directly observable, as we discuss below. The most accessible model systems for studying the full dipolar Hamiltonian are dilute rare earth insulating compounds. While several such materials exist with fee symmetry [3], it is unfortunate from the experimental standpoint that no simple cubic examples are known.There does exist, however, at least one excellent model system with diamond structure, which we find is also predicted to exhibit dipolar antiferromagnetism. This is the rare earth (R) phosphomolybdate tridecahydrate series, /?PO 4 (MoO3)i2-30H 2 O. We have carried out magnetic measurements on the Gd, Dy, and Er members of this series which are consistent only with antiferromagnetic order [4]. They also confirm the existence of unique and very large spin wave zero-point motion effects, directly observable in the susceptibility.The classical ground state energy per spin of a cubic lattice of point dipoles iswhere A, is a dimensionless, maximal eigenvalue of the dipolar field matrix, and n is the spin density. For diamond, we find ^dia ==s 6.394 [5]. The predicted spin configuration is a layered structure, with four sublattices aligned in pairs along the cubic (110) axes. It is pictured in Fig. 1, using a tetragonal unit cell containing four spins, one from each sublattice. The magnitude of X^ exceeds that for the sc lattice, X sc = 5.352, and also that for ferromagnetic order (assuming the ferromagnet is free to minimize its energy by splitting into domains), ^FM = 4/r/3. This establishes diamond as the most strongly antiferromagnetic and most stable of the cubic dipolar lattices. This result agrees with the observation that dipolar antiferromagnetism is favored by relatively open structures, in ...