  We consider the diamond chain with S=1/2 XYZ vertical dimers which interact
with the intermediate sites via the interaction of the Ising type. We also
suppose all four spins form the diamond-shaped plaquette to have different
g-factors. The non-uniform g-factors within the quantum spin dimer as well as
the XY-anisotropy of the exchange interaction lead to the non-conserving
magnetization for the chain. We analyze the effects of non-conserving
magnetization as well as the effects of the appearance of negative g-factors
among the spins from the unit cell. A number of unusual frustrated states for
ferromagnetic couplings and g-factors with non-uniform signs are found out.
These frustrated states generalize the "half-fire-half-ice" state introduced in
Ref. [8]. The corresponding zero-temperature ground state phase diagrams are
presented.
