We study the dispersion of the magnons ͑triplet states͒ in SrCu 2 ͑BO 3 ͒ 2 including all symmetry-allowed Dzyaloshinskii-Moriya interactions ͓J. Phys. Chem. Solids 4, 241 ͑1958͒; Phys. Rev. 120, 91 ͑1960͔͒. We can reduce the complexity of the general Hamiltonian to a simpler form by appropriate rotations of the spin operators. The resulting Hamiltonian is studied by both perturbation theory and exact numerical diagonalization on a 32-site cluster. We argue that the dispersion is dominated by Dzyaloshinskii-Moriya interactions. We point out which combinations of these anisotropies affect the dispersion to linear order, and extract their magnitudes.

The Shastry-Sutherland model is a two-dimensional frustrated spin model whose ground state is a spin gap state. We study this model doped with one and two holes on a 32-site lattice using exact diagonalization. When tЈϾ0, we find that the diagonal dimer order that exists at half-filling is retained at these moderate doping levels. No other order is found to be favored on doping. The holes are strongly repulsive unless the hopping terms are unrealistically small. Therefore, the existence of a spin gap at half-filling does not guarantee holepairing in the present case. DOI: 10.1103/PhysRevB.69.180403 PACS number͑s͒: 75.40.Mg, 71.10.Fd, 71.27.ϩa The Shastry-Sutherland ͑SS͒ model is an exceptional example of a two-dimensional frustrated spin system that has an exact solution. 1 Remarkably, it is also an excellent theoretical model for the spin gap material Sr Cu 2 (BO 3 ) 2 . 2 The SS model is a Heisenberg model with exchange interaction J on a two-dimensional square lattice frustrated by diagonal bonds JЈ as shown in Fig. 1. When J/JЈ is smaller than a critical value of about 0.677, 3 the ground state is a direct product of orthogonal singlet dimers residing on the JЈ bonds. This is a spin gap state because the lowest spin excitation involves turning a singlet dimer into a triplet. Different experiments have suggested a range of J/JЈ for SrCu 2 (BO 3 ) 2 , out of which 0.635 seems to be the optimal one. A great deal of work has been devoted to studying the excited states of this model as an effort to explain various experimental results. It is found that the almost localized nature of spin excitations leads to superstructures that give rise to plateaux in the magnetization curve. Besides its importance as a theoretical model for Sr Cu 2 (BO 3 ) 2 , the SS model possesses a quantum phase transition. One believes that there is at least one intermediate state between the diagonal dimer state at small J and the Néel state at large J. While the nature of the intermediate state is still controversial, it seems like the plaquette resonating-valence-bond ͑RVB͒ state and the helical state are among the most likely candidates. Although discussions on the quantum phase transition are theoretical, they are not totally irrelevant to SrCu 2 (BO 3 ) 2 . Since its J/JЈ is not too far from the critical value, it may be possible to shift it even closer by applying pressure, substitution, etc. to Sr Cu 2 (BO 3 ) 2 .The relation between disordered spin liquids with a gap in the spin excitation and superconductivity has aroused a lot of interest. It has been suggested that doping a spin gap system may lead to hole-pairing and superconductivity. It is therefore interesting and important to identify spin gap materials that are Mott insulators with no long-range spin order. SrCu 2 (BO 3 ) 2 is one such compound. Although this compound has not been doped, there is no shortage of suggestions that on doping the SS model may exhibit superconductivity. Different types of superconducting states have been suggested at different doping levels...

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