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MAGNETIC PROPERTIES OF THE TWO-LEG ZIG-ZAG LADDER IN QUANTUM SPIN SYSTEM NH4CuCl3

Teguh Yoga Raksa, Robi Kurniawan

Published Jan 1, 2002• 0 citations
Publisher

Abstract

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.

DOI
10.17146/jusami.2002.3.2.5252

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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.
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 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.
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.
A one-dimensional spin-1∕2 model in which the alternation of the exchange interactions between neighboring spins is accompanied by the next-nearest-neighbor (NNN) spin exchange (zig-zag spin ladder with alternation) is studied. The thermodynamic characteristics of the model quantum spin chain are obtained in the mean-field-like approximation. Depending on the strength of the NNN interactions, the model manifests either the spin-gapped behavior of low-lying excitations at low magnetic fields, or ferrimagnetic ordering in the ground state with gapless low-lying excitations. The system undergoes second-order or first-order quantum phase transitions, governed by the external magnetic field, NNN coupling strength, and the degree of the alternation. Hence, NNN spin–spin interactions in a dimerized quantum spin chain can produce a spontaneous magnetization. On the other hand, for quantum spin chains with a spontaneous magnetization, caused by NNN spin–spin couplings, the alternation of nearest-neighbor (NN) exchange interactions can cause destruction of that magnetization and the onset of a spin gap for low-lying excitations. Alternating NN interactions produce a spin gap between two branches of low-energy excitations, and the NNN interactions yield asymmetry of the dispersion laws of those excitations, with possible minima corresponding to incommensurate structures in the spin chain.
The energy spectra and low-temperature magnetic properties of two one-dimensional Heisenberg mixed spin (s = 1, 1/2) systems, namely decorated two-leg mixed spin ladders with the lattice topology of polyacene, are studied. The gapless character of the exact excitation energy spectra for both ladder models has been determined. We found numerically that the model with macroscopic ground state spin S0 has gapped excitations with the spin S > S0. This leads to the appearance of an intermediate plateau in field dependence of magnetization at low temperatures. We have shown that the ladder with equal coupling in legs has the maximal size of this plateau at the same coupling in rungs. For a mixed spin ladder model with Ising interactions in legs, the appearance of two intermediate magnetization plateaus at low temperatures and some values of coupling parameters was shown.
Thermodynamic properties of spin=1/2 two-leg ladders with alternating chains including ferromagnetic and antiferromagnetic interactions are discussed on the basis of the numerical results obtained by quantum Monte Carlo simulations. As well as the role of exchange interaction of rungs, the essential role of the bond alternation in the chain on ladder systems is investigated in connection with the appearance of characteristic properties in magnetic susceptibilities and heat capacities. Furthermore, quantum effects on the ground-state energy are obtained. On the basis of calculated results, the relationship between singlet dimer phases and Haldane states is discussed.