Magnetization of coupled spin clusters in ladder geometry

We construct a class of spin-1/2 antiferromagnetic two-chain ladder models consisting of blocks of n-spin tetrahedral clusters alternating with two-spin rungs. For n=4 and 6 and in extended parameter regimes, the exact ground state of the ladder is shown to be a product of the ground states of the rungs and the n-spin blocks, in both zero and finite magnetic fields. In the latter case, magnetization/site m versus magenetic field h plot exhibits well-defined magnetization plateaus.