Magnetization Plateaus in the Shastry-Sutherland Model for SrCu2(BO3)2: Results of Fourth-Order Perturbation Expansion with a Low-Density Approximation

Magnetization plateaus in the Shastry-Sutherland model for SrCu₂(BO₃)₂ are studied by the perturbation expansion method. The fourth-order effective Hamiltonian which describes the dynamics of triplet dimers (TD's) with S^tot_z=1 in the singlet sea is derived and then partially diagonalized for the space that consists of the TD configurations with the lowest second-order energy. The fourth-order terms are treated within a low-density approximation. Our procedure makes clear how TD interactions are responsible for the formation of magnetization plateaus. Particularly, the 1/4-plateau is obtained by the fourth-neighbor TD repulsion in the fourth-order perturbation, and a diagonal stripe arrangement of TD's appears at this plateau.