  The ground state and magnetization process of an exactly solved spin-$1/2$
Ising-Heisenberg orthogonal-dimer chain with two different gyromagnetic factors
of the Ising and Heisenberg spins are investigated in detail. It is shown that
the investigated quantum spin chain exhibits up to seven possible ground states
depending on a mutual interplay of the magnetic field, intra- and inter-dimer
coupling constants. More specifically, the frustrated and modulated quantum
antiferromagnetic phases are responsible in zero-temperature magnetization
curves for a zero magnetization plateau. The intermediate 1/11- and
5/11-plateaus emerge due to the frustrated and modulated quantum ferrimagnetic
phases, while the intermediate 9/11- and 10/11-plateaus can be attributed to
the quantum and classical ferrimagnetic phases. It is conjectured that the
magnetization plateau experimentally observed in a high-field magnetization
curve of 3$d$-4$f$ heterobimetallic coordination polymer
[\{Dy(hfac)$_2$(CH$_3$OH)\}$_2$\{Cu(dmg)(Hdmg)\}$_2$]$_n$ (H$_2$dmg $=$
dimethylglyoxime; Hhfac $=$ 1,1,1,5,5,5-hexafluoropentane-2,4-dione) could be
attributed to the classical and quantum ferrimagnetic phases.
