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

Non-conserved magnetization operator and `fire-and-ice' ground states in the Ising-Heisenberg diamond chain