  We study a spin-1/2 model with triangular XXZ-clusters on the
orthogonal-dimer chain in the presence of an external magnetic field. First, we
discuss the case where the triangular clusters are coupled via intermediate
"classical" Ising spins. Diagonalization of the triangular XXZ-clusters yields
the exact ground states; finite-temperature properties are computed exactly by
an additional transfer-matrix step. A detailed analysis reveals a large variety
of ground states at magnetization M equal to fractions 0, 1/4, and 1/2 of the
saturation magnetization M=1. Some of these ground states break translational
symmetry spontaneously and give rise to doubling of the unit cell. In a second
part we present complementary numerical data for the spin-1/2 Heisenberg model
on the orthogonal-dimer chain. We analyze several examples of T=0 magnetization
curves, entropy as a function of temperature T and magnetic field, and the
associated magnetic cooling rate. Comparison of the two models shows that in
certain situations the simplified exactly solvable model yields a qualitatively
or sometimes even quantitatively accurate description of the more challenging
quantum model, including a case which may be relevant to experimental
observations of an enhanced magnetocaloric effect in the two-dimensional
compound SrCu2(BO3)2.
