  Exact ground states of a spin-1/2 Ising-Heisenberg model on the
Shastry-Sutherland lattice with Heisenberg intra-dimer and Ising inter-dimer
couplings are found by two independent rigorous procedures. The first method
uses a unitary transformation to establish a mapping correspondence with an
effective classical spin model, while the second method relies on the
derivation of an effective hard-core boson model by continuous unitary
transformations. Both methods lead to equivalent effective Hamiltonians
providing a convincing proof that the spin-1/2 Ising-Heisenberg model on the
Shastry-Sutherland lattice exhibits a zero-temperature magnetization curve with
just two intermediate plateaus at one-third and one-half of the saturation
magnetization, which correspond to stripe and checkerboard orderings of
singlets and polarized triplets, respectively. The nature of the remarkable
stripe order relevant to the one-third plateau is thoroughly investigated with
the help of the corresponding exact eigenvector. The rigorous results for the
spin-1/2 Ising-Heisenberg model on the Shastry-Sutherland lattice are compared
with the analogous results for the purely classical Ising and fully quantum
Heisenberg models. Finally, we discuss to what extent the critical fields of
SrCu2(BO3)2 and (CuCl)Ca2Nb3O10 can be described within the suggested
Ising-Heisenberg model.
