Frustrated three-leg spin tubes: From spin 1/2 with chirality to spin 3/2

Motivated by the recent discovery of the spin tube [(CuCl(2)tachH)(3)Cl]Cl-2, we investigate the properties of a frustrated three-leg spin tube with antiferromagnetic intra- and inter-ring couplings. We pay special attention to the evolution of the properties from weak to strong inter-ring coupling and show on the basis of extensive density matrix renormalization group and exact diagonalization calculations that the system undergoes a first-order phase transition between a dimerized gapped phase at weak coupling that can be described by the usual spin-chirality model and a gapless critical phase at strong coupling that can be described by an effective spin-3/2 model. We also show that there is a magnetization plateau at 1/3 in the whole gapped phase and slightly beyond. The implications for [(CuCl(2)tachH)(3)Cl]Cl-2 are discussed, with the conclusion that this system behaves essentially as a spin-3/2 chain.