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Magnetic Properties of Zig-Zag Ladders ∗

D. C. Cabra, A. Honecker, Pierre Pujol

Published Jan 1, 1999• 51 citations
OpenAlex

Abstract

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.

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Progress of Theoretical Physics Supplement•Jan 1, 2005•1 citation
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.
In this paper we continue and extend a systematic study of plateaux in magnetization curves of antiferromagnetic Heisenberg spin-1/2 ladders. We first review a bosonic field-theoretical formulation of a single XXZ\mathrm{XXZ}XXZ chain in the presence of a magnetic field, which is then used for an Abelian bosonization analysis of NNN weakly coupled chains. Predictions for the universality classes of the phase transitions at the plateaux boundaries are obtained in addition to a quantization condition for the value of the magnetization on a plateau. These results are complemented by and checked against strong-coupling expansions. Finally, we analyze the strong-coupling effective Hamiltonian for an odd number NNN of cylindrically coupled chains numerically. For N=3N=3N=3 we explicitly observe a spin gap with a massive spinon-type fundamental excitation and obtain indications that this gap probably survives the limit $\stackrel{\ensuremath{\rightarrow}}{N}\ensuremath{\infty}$.
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.
Magnetization processes of spin- 12\frac{1}{2}21​ Heisenberg ladders are studied using strong-coupling expansions, numerical diagonalization of finite systems, and a bosonization approach. We find that the magnetization exhibits plateaux as a function of the applied field at certain rational fractions of the saturation value. Our main focus is on ladders with three legs where plateaux with magnetization one third of the saturation value are shown to exist.
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.
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.