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arXiv:1203.3084 · Physical Review B

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

Xavier Plat, Sylvain Capponi, Pierre Pujol

Published May 16, 2012• 14 citations
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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.

DOI
10.1103/physrevb.85.174423

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In this paper, we investigate the properties of frustrated three-leg spin-SSS tubes under a magnetic field. We concentrate on two kind of geometries for these tubes, one of which is relevant for the compound [(CuCl2tachH)3Cl]Cl2[{({\mathrm{CuCl}}_{2}\mathrm{tachH})}_{3}\mathrm{Cl}]{\mathrm{Cl}}_{2}[(CuCl2​tachH)3​Cl]Cl2​. We perform an analytical large-SSS 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=3/2S=3/2S=3/2 case.
We study the ground state phase diagram of a frustrated spin-1/2 four-leg tube in an external magnetic field. We explore the parameter space of this model in the regime of all-antiferromagnetic exchange couplings by means of three different approaches: density matrix renormalization group (DMRG), a low-energy effective Hamiltonian (LEH) and a Hartree variational approach (HVA). We find that in the limit of weakly interacting plaquettes, singlet and triplet states play an important role in the formation of magnetization plateaux. We study the transition regions numerically and analytically, and find that they are described, at first order in a strong- coupling expansion, by an XXZ spin-1/2 chain in a magnetic field. These results are consistent with the DMRG and HVA calculations.
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We study the magnetization plateau state of the three-leg spin-12\frac{1}{2}21​ tube in the strong rung coupling region, where S3{S}_{3}S3​ symmetry breaking and the low-energy chirality degree of freedom play crucial roles. On the basis of the effective chirality model and density matrix renormalization group, we clarify that, as the leg coupling increases, the chirality liquid with gapless nonmagnetic excitations, the spin-imbalance phase, and the vector-spin-chirality ordered phase emerge without closing the plateau spin gap. The relevance of these results to experiments is also discussed.
We use a combination of numerical density matrix renormalization group calculations and several analytical approaches to comprehensively study a simplified model for a spatially anisotropic spin-12\frac{1}{2}21​ triangular lattice Heisenberg antiferromagnet: the three-leg triangular spin tube (TST). The model is described by three Heisenberg chains, with exchange constant JJJ, coupled antiferromagnetically with exchange constant ${J}^{\ensuremath{'}}$ along the diagonals of the ladder system, with periodic boundary conditions in the shorter direction. Here, we determine the full phase diagram of this model as a function of both spatial anisotropy (between the isotropic and decoupled chain limits) and magnetic field. We find a rich phase diagram, which is remarkably dominated by quantum states: the phase corresponding to the classical ground state appears only in an exceedingly small region. Among the dominant phases generated by quantum effects are commensurate and incommensurate coplanar quasiordered states, which appear in the vicinity of the isotropic region for most fields, and in the high-field region for most anisotropies. The coplanar states, while not classical ground states, can at least be understood semiclassically. Even more strikingly, the largest region of phase space is occupied by a spin density wave phase, which has incommensurate collinear correlations along the field. This phase has no semiclassical analog, and may be ascribed to enhanced one-dimensional fluctuations due to frustration. Cutting across the phase diagram is a magnetization plateau, with a gap to all excitations and ``up-up-down'' spin order, with a quantized magnetization equal to 13\frac{1}{3}31​ of the saturation value. In the TST, this plateau extends almost but not quite to the decoupled chains limit. Most of the above features are expected to carry over to the two-dimensional system, which we also discuss. At low field, a dimerized phase appears, which is particular to the one-dimensional nature of the TST, and which can be understood from quantum Berry phase arguments.
Recent developments of theoretical studies on spin nanotubes are reviewed, especially focusing on the S = 1/2 three-leg spin tube. In contrast to the three-leg spin ladder, the tube has a spin gap in the case of the regular-triangle unit cell when the rung interaction is sufficiently large. The effective theory based on the Hubbard Hamiltonian indicates a quantum phase transition to a gapless spin liquid due to the lattice distortion to an isosceles triangle. This is also supported by the numerical diagonalization and the density matrix renormalization group analyses. Furthermore, combining analytical and numerical approaches, we reveal several novel magnetic-field-induced phenomena: Néel, dimer, chiral and/or inhomogeneous orders, a new mechanism for the magnetization plateau formation, and others. The recently synthesized spin tube materials are also briefly introduced.