  The quantum spin-1/2 orthogonal-dimer chain with the Heisenberg intra-dimer
and Ising inter-dimer interactions in a magnetic field is considered by a
rigorous approach. The model conserves the z-component of total spin on
vertical Heisenberg bonds and this property is used to calculate exactly the
partition function using the transfer-matrix method. We have found the
ground-state phase diagram of the given model in a magnetic field as well as
the macroscopic degeneracy along field-induced transitions accompanied with the
magnetization jumps. The model exhibits two intermediate fractional plateaux at
one-quarter and one-half of the saturation magnetization. We have examined the
effect of the exchange anisotropy in the XXZ Heisenberg intra-dimer interaction
on the ground state. It is shown that the one-quarter and one-half plateaux may
disappear from the magnetization curve for the ferromagnetic Heisenberg
intra-dimer interaction. We have also rigorously studied the effect of
frustrated interactions on the thermodynamic and magnetic properties of the
model and show how the macroscopic degeneracy of the ground state is reflected
in the low-temperature behavior of the magnetization, entropy and specific
heat. A possibility of observing enhanced magnetocaloric effect during the
adiabatic demagnetization is discussed in detail.
