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arXiv:cond-mat/9911387 · Physical review. B, Condensed matter

Magnetization plateaus in dimerized spin-ladder arrays

D. C. Cabra, Marcelo D. Grynberg

Published Jul 1, 2000• 15 citations
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Abstract

We investigate the ground-state magnetization plateaus appearing in spin-$\frac{1}{2}$ two-leg ladders built up from dimerized antiferromagnetic Heisenberg chains and dimerized zig-zag interchain couplings. Using both Abelian bosonization and Lanczos methods we find that the system yields rather unusual plateaus and exhibits massive and massless phases for specific choices or ``tuning'' of exchange interactions. The relevance of this behavior in the study of ${\mathrm{NH}}_{4}{\mathrm{CuCl}}_{3}$ is discussed.

DOI
10.1103/physrevb.62.337

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We investigate the ground-state magnetization plateaus appearing in spin-12\frac{1}{2}21​ two-leg ladders built up from dimerized antiferromagnetic Heisenberg chains and dimerized zig-zag interchain couplings. Using both Abelian bosonization and Lanczos methods we find that the system yields rather unusual plateaus and exhibits massive and massless phases for specific choices or ``tuning'' of exchange interactions. The relevance of this behavior in the study of NH4CuCl3{\mathrm{NH}}_{4}{\mathrm{CuCl}}_{3}NH4​CuCl3​ is discussed.
We investigate the conditions under which a gap vanishes in the spectrum of dimerized coupled spin-1/2 chains by means of Abelian bosonization and Lanczos diagonalization techniques. Although both interchain ( ${J}^{\ensuremath{'}}$) and dimerization ( $\ensuremath{\delta}$) couplings favor a gapful phase, it is shown that a suitable choice of these interactions yields massless spin excitations. We also discuss the influence of different arrays of relative dimerization on the appearance of nontrivial magnetization plateaus.
We analyze the phase diagram of a system of spin-1/2 Heisenberg antiferromagnetic chains interacting through a zig-zag coupling, also called zig-zag ladders. Using bosonization techniques we study how a spin-gap or more generally plateaux in magnetization curves arise in different situations. While for coupled XXZ chains, one has to deal with a recently discovered chiral perturbation, the coupling term which is present for normal ladders is restored by an external magnetic field, dimerization or the presence of charge carriers. We then proceed with a numerical investigation of the phase diagram of two coupled Heisenberg chains in the presence of a magnetic field. Unusual behaviour is found for ferromagnetic coupled antiferromagnetic chains. Finally, for three (and more) legs one can choose different inequivalent types of coupling between the chains. We find that the three-leg ladder can exhibit a spin-gap and/or non-trivial plateaux in the magnetization curve whose appearance strongly depends on the choice of coupling.
We study the one-dimensional spin-1/2 model with nearest and next-to-nearest-neighbor couplings exposed to a homogeneous magnetic field h3{h}_{3}h3​ and a dimer field with period q and strength $\ensuremath{\delta}$. The latter generates a magnetization plateau at $M=(1\ensuremath{-}q/\ensuremath{\pi})/2$, which evolves with strength $\ensuremath{\delta}$ of the perturbation as ${\ensuremath{\delta}}^{\ensuremath{\epsilon}}$, where $\ensuremath{\epsilon}=\ensuremath{\epsilon}{(h}_{3},\ensuremath{\alpha})$ is related to the $\ensuremath{\eta}$ exponent which describes the critical behavior of the dimer structure factor, if the perturbation is switched off $(\ensuremath{\delta}=0)$. We also discuss the appearance of magnetization plateaus in ladder systems with l legs.
MAGNETIC PROPERTIES OF THE TWO-LEG ZIG-ZAG LADDER IN QUANTUM SPIN SYSTEM NH 4 CuCl 3 . Numerical analysis of the two-leg zig-zag ladder as a single chain with next-nearest neighbour interactions has been formulated by Cabra (1999) with the following Hamiltonian: Other formulation for two leg zig-zag ladder with dimmerized chains and coupling between the chains is as follow : From these formulations, we study the closing of the gap at zero magnetization by means of the fine—tuning mechanism and disappreance of the 1/2 plateau (gap) at finite by alternating dimerization of the chains along the rungs. We also described NH 4 CuCl 3 under high magnetic fields in a two-leg system.
The experimental realization of various spin ladder systems has prompted their detailed theoretical investigations. Here we study the evolution of ground-state magnetization with an external magnetic field for two different antiferromagnetic systems: a three-legged spin-1/21/21/2 ladder, and a two-legged spin-1/21/21/2 ladder with an additional diagonal interaction. The finite system density-matrix renormalization-group method is employed for numerical studies of the three-chain system, and an effective low-energy Hamiltonian is used in the limit of strong interchain coupling to study the two- and three-chain systems. The three-chain system has a magnetization plateau at one-third of the saturation magnetization. The two-chain system has a plateau at zero magnetization due to a gap above the singlet ground state. It also has a plateau at half of the saturation magnetization for a certain range of values of the couplings. We study the regions of transitions between plateaus numerically and analytically, and find that they are described, at first order in a strong-coupling expansion, by an XXZ\mathrm{XXZ}XXZ spin-1/21/21/2 chain in a magnetic field; the second-order terms give corrections to the XXZ\mathrm{XXZ}XXZ model. We also study numerically some low-temperature properties of the three-chain system, such as the magnetization, magnetic susceptibility and specific heat.
We study numerically the formation of magnetization plateaux with the Lanczos method in two-leg ladders with mixed spins of magnitudes (S1,S2)=(1,1/2){(S}_{1}{,S}_{2})=(1,1/2)(S1​,S2​)=(1,1/2) located at alternating positions along the ladder and with dimerization $\ensuremath{\gamma}.$ For interchain coupling ${J}^{\ensuremath{'}}>0$ and $\ensuremath{\gamma}=0,$ we find normalized plateaux at m=1/3m=1/3m=1/3 starting at zero field and m=1m=1m=1 (saturation), while when $\ensuremath{\gamma}\ensuremath{\ne}0$ is columnar, another extra plateau at m=2/3m=2/3m=2/3 shows up. For ${J}^{\ensuremath{'}}<0,$ when $\ensuremath{\gamma}<{\ensuremath{\gamma}}_{c}{(J}^{\ensuremath{'}})$ we find no plateau while for $\ensuremath{\gamma}>{\ensuremath{\gamma}}_{c}{(J}^{\ensuremath{'}})$ we find four plateaux at m=0,1/3,2/3,1.m=0,1/3,2/3,1.m=0,1/3,2/3,1. We also apply several approximate analytical methods (spin-wave theory, low-energy effective Hamiltonians, and bosonization) to understand these findings and to conjecture the behavior of ferrimagnetic ladders with a larger number of legs.