Quantum order by disorder in frustrated diamond lattice antiferromagnets

We present a quantum theory of frustrated diamond lattice antiferromagnets. Considering quantum fluctuations as the predominant mechanism relieving spin frustration, we find a rich phase diagram comprising of six phases with coplanar spiral ordering in addition to the Neel phase. By computing the specific heat of these ordered phases, we obtain a remarkable agreement between (k, k, 0) spiral ordering and the experimental specific heat data for the diamond lattice spinel compounds MnSc(2)S(4), Co(3)O(4), and CoRh(2)O(4), i.e., specific heat data is a strong evidence for (k, k, 0) spiral ordering in all of these materials. This prediction can be tested in future neutron scattering experiments on Co(3)O(4) and CoRh2O4, and is consistent with existing neutron scattering data on MnSc(2)S(4). Based on this agreement, we infer a monotonically increasing relationship between frustration and the strength of quantum fluctuations.