Strontium copper borate SrCu₂(BO₃)₂ is a novel material with a spin gapped ground state. Its crystal structure is topologically equivalent to the Shastry Sutherland lattice. We have studied the spin-1/2 models on the Shastry Sutherland lattice in undoped case and doped cases, by using exact diagonalization method on the 32-site lattice. In the undoped case, we study magnon (triplet) dispersions of the Heisenberg model with the Dzyaloshinskii-Moriya (DM) interactions. Fine features on the first branch of magnon dispersions in SrCu₂(BO₃)₂ can be explained by using relatively small DM interactions. We also study the effects of these anisotropic couplings on the first branch of magnon dispersions and extract their magnitudes from the experimental data. They will be useful in describing fine...[ Read more ]

Strontium copper borate SrCu₂(BO₃)₂ is a novel material with a spin gapped ground state. Its crystal structure is topologically equivalent to the Shastry Sutherland lattice. We have studied the spin-1/2 models on the Shastry Sutherland lattice in undoped case and doped cases, by using exact diagonalization method on the 32-site lattice. In the undoped case, we study magnon (triplet) dispersions of the Heisenberg model with the Dzyaloshinskii-Moriya (DM) interactions. Fine features on the first branch of magnon dispersions in SrCu₂(BO₃)₂ can be explained by using relatively small DM interactions. We also study the effects of these anisotropic couplings on the first branch of magnon dispersions and extract their magnitudes from the experimental data. They will be useful in describing fine features on other branches of magnon dispersions. In the doped case, we study the spin and the hole properties of the t-J model on the Shastry Sutherland lattice with up to two holes. We have found that two dominant spin orders, the diagonal dimer order and the anti-ferromagnetic long range order, are enhanced at different signs of t' /t. We also argue that the effects of geometrical frustration are influenced by the doping level. However, we have not found any hole pairing across a diagonal in the diagonal dimer region at the realistic t/J value. Therefore, this is an example where doping a spin gapped system does not guarantee hole pairing.