Magnetization plateaus in weakly coupled dimer spin system

I study a spin system consisting of strongly coupled dimers which are, in turn, weakly coupled in a plane by zigzag interactions. The model can be viewed as the strong-coupling limit of a two-dimensional zigzag chain structure typical, e.g., for the (ac) planes of KCuCl₃. It is shown that the magnetization curve in this model has plateaus at 1/3 and 2/3 of the saturation magnetization, and an additional plateau at 1/2; the critical fields are calculated perturbatively. It is argued that for the three-dimensional lattice structure of the KCuCl₃ family the plateaus at 1/4 and 3/4 of the saturation can be favored in a similar way, which might be relevant to the recent experiments on NH₄CuCl₃ by Shiramura et al., J. Phys. Soc. Jpn. 67, 1548 (1998).