Frustrated three-leg spin tubes: From spin1∕2with chirality to spin3∕2

Abstract

Motivated by the recent discovery of the spin tube $[{(\mathrm{Cu}{\mathrm{Cl}}_{2}\mathrm{tach}\mathrm{H})}_{3}\mathrm{Cl}]{\mathrm{Cl}}_{2}$, 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 $[{(\mathrm{Cu}{\mathrm{Cl}}_{2}\mathrm{tach}\mathrm{H})}_{3}\mathrm{Cl}]{\mathrm{Cl}}_{2}$ are discussed, with the conclusion that this system behaves essentially as a spin-$3∕2$ chain.