Patterns of symmetry breaking in systems of coupled tetrahedra

The phases of a system of weakly coupled tetrahedra (S = 1/2), in the presence of both Heisenberg and antisymmetric Dzyaloshinsky-Moriya interactions, are discussed. While non-magnetic dimer order is dominant for the specific interactions considered, we find that Dzyaloshinsky-Moriya induced magnetic long-range order can also emerge. The presence of antisymmetric interactions also leads to non-trivial effects (e.g. ordering) in an external magnetic field.