We propose a novel two-dimensional (2D) frustrated quantum spin-1/2 anisotropic Heisenberg model with alternating ferromagnetic and antiferromagnetic magnetic chains along one direction and antiferromagnetic interactions along the other. The (mean-field) ground state is ferrimagnetic in certain range of the interaction space. Spin-wave theory analysis of the reduction of ordered moments at inequivalent spin sites and the instability of the spin waves suggest a quantum phase transition which has the characteristics of both the frustrated 2D antiferromagnetic= 1/2 (,) model and 1D= 1,= 1/2 quantum ferrimagnetic model.
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