Magnetization Plateaus in the Shastry-Sutherland Model for SrCu_2(BO_3)_2: Results of Fourth-Order Perturbation Expansion with a Low-Density Approximation

Abstract

Magnetization plateaus in the Shastry-Sutherland model for $\mathrm{SrC}{\mathrm{u}}_2(\mathrm{B}{\mathrm{O}}_3{)}_2$ are studied by the perturbation expansion method. The fourth-order effective Hamiltonian which describes the dynamics of triplet dimers (TD's) with $S_z^{\mathrm{tot}}=1$ 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.

8 pages, 12 figures

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