Combined analytical and numerical approach to magnetization plateaux in one-dimensional spin tube antiferromagnets

Abstract

In this paper, we investigate the properties of frustrated three-leg spin-$S$ tubes under a magnetic field. We concentrate on two kind of geometries for these tubes, one of which is relevant for the compound $[{({\mathrm{CuCl}}_{2}\mathrm{tachH})}_{3}\mathrm{Cl}]{\mathrm{Cl}}_{2}$. We perform an analytical large-$S$ path-integral approach to determine the phase diagrams, which exhibit several magnetization plateaux. Moreover, by combining the field-theory approach with a strong-coupling one, we also investigate the issue of gapless nonmagnetic excitations on some plateaux, dubbed chirality degrees of freedom for both tubes: on increasing the intertriangle exchange couplings, a gapless chiral phase transforms into a gapped ``ferrochiral'' state, possibly through intermediate ``spin-imbalanced'' states. All these predictions are confirmed numerically using large-scale density-matrix renormalization-group simulations for the $S=3/2$ case.