  Magnetization plateaus in the Shastry-Sutherland model for ${\rm
SrCu_2(BO_3)_2}$ are studied by the perturbation expansion method. The
fourth-order effective Hamiltonian which describes the dynamics of triplet
dimers (TD's) with $S^{\rm tot}_z=1$ 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.
