  We report the microscopic magnetic model for the spin-1/2 Heisenberg system
CdCu2(BO3)2, one of the few quantum magnets showing the 1/2-magnetization
plateau. Recent neutron diffraction experiments on this compound [M. Hase et
al., Phys. Rev. B 80, 104405 (2009)] evidenced long-range magnetic order,
inconsistent with the previously suggested phenomenological magnetic model of
isolated dimers and spin chains. Based on extensive density-functional theory
band structure calculations, exact diagonalizations, quantum Monte Carlo
simulations, third-order perturbation theory, as well as high-field
magnetization measurements, we find that the magnetic properties of CdCu2(BO3)2
are accounted for by a frustrated quasi-2D magnetic model featuring four
inequivalent exchange couplings: the leading antiferromagnetic coupling J_d
within the structural Cu2O6 dimers, two interdimer couplings J_t1 and J_t2,
forming magnetic tetramers, and a ferromagnetic coupling J_it between the
tetramers. Based on comparison to the experimental data, we evaluate the ratios
of the leading couplings J_d : J_t1 : J_t2 : J_it = 1 : 0.20 : 0.45 : -0.30,
with J_d of about 178 K. The inequivalence of J_t1 and J_t2 largely lifts the
frustration and triggers long-range antiferromagnetic ordering. The proposed
model accounts correctly for the different magnetic moments localized on
structurally inequivalent Cu atoms in the ground-state magnetic configuration.
We extensively analyze the magnetic properties of this model, including a
detailed description of the magnetically ordered ground state and its evolution
in magnetic field with particular emphasis on the 1/2-magnetization plateau.
Our results establish remarkable analogies to the Shastry-Sutherland model of
SrCu2(BO3)2, and characterize the closely related CdCu2(BO3)2 as a material
realization for the spin-1/2 decorated anisotropic Shastry-Sutherland lattice.
