A class of Heisenberg models with orthogonal dimer ground states

Extensions of the Shastry-Sutherland model are possible in various ways. In particular, it is possible to construct a natural model in three dimensions which has the exact dimer ground state. The recently found spin gap system SrCu₂(BO₃)₂ has this structure. The exchange constants between the layers are expected to be smaller than the intra-layer couplings. However, the exactness of the dimer state for the three dimensional structure is important for understanding why the magnetic properties of SrCu₂(BO₃)₂ are described well by the two dimensional model.