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Europhysics Letters (EPL)

Fractionally quantized magnetization plateaus of a spin-(1/2) ladder with different chain exchange

S Sarkar

Published Aug 23, 2005• 10 citations
Publisher

Abstract

We study a system with spin-Peierls dimerization in next-nearest-neighbor (NNN) interaction and also the presence of nearest-neighbor (NN) interaction under a magnetic field. We predict the existence of different fractionally quantized magnetization plateaus with many interesting physical properties. The effect of the frustrating NNN interaction and the role of quantum fluctuations are also explored for different magnetization plateaus. We explain more physically the gapless state of spin spectrum for small values of the frustrating NNN interaction. The transition from commensurate gapped phase to incommensurate Luttinger liquid phase is of Mott-δ type.

DOI
10.1209/epl/i2005-10183-2

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We study a system with spin-Peierls dimerization in next-nearest-neighbor (NNN) interaction and also the presence of nearest-neighbor (NN) interaction under a magnetic field. We predict the existence of different fractionally quantized magnetization plateaus with many interesting physical properties. The effect of the frustrating NNN interaction and the role of quantum fluctuations are also explored for different magnetization plateaus. We explain more physically the gapless state of spin spectrum for small values of the frustrating NNN interaction. The transition from commensurate gapped phase to incommensurate Luttinger liquid phase is of Mott-δ type.
Here we study the dimerized spin ladder with nearest-neighbor (J1) and next-nearest-neighbor (J2) anti-ferromagnetic interaction under a magnetic field. We predict the existence of different magnetization plateaus for the presence of spin-Peierls interaction on both J1 and J2. Magnetization plateau at m = 0 for J1 dimerization is spontaneous due to XY interaction, but it is absent for J2 dimerization, only intrinsic umklapp term leads to plateau (spin gap) state for some specific values of XXZ anisotropy (Δ) and J2. Here we predict a saturation plateau which is the classical phase of the system. There are some numerical support of our analytical approach already existing in the literature. The transition from commensurate gapped phase to incommensurate Luttinger liquid phase is the Mott-δ type of transition.
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 spin ladder systems have attracted a lot of interest in the field of low-dimensional physics. It is well known that the S = 1/2 two-leg spin ladder has a spin gap, while the three-leg one has a gapless spin liquid ground state. Some spin liquid behaviors were observed in the recent experiments of some frustrated systems; the distorted triangular lattice and kagome lattice antiferromagnets etc. Thus we consider the S = 1/2 three-leg spin ladder system with the next-nearest-neighbor interaction to investigate the effect of frustration on the spin liquids. Using the exact numerical diagonalization of finite-cluster systems, we study the ground state of this system. The phase diagram with respect to some exchange interaction constants is presented. It is revealed that sufficiently large next-nearest-neighbor coupling leads to a ferrimagnetic phase, which has a frustration-induced spontaneous magnetization. In addition we find two spin liquid phases, one of which corresponds to a Néel-like spin configuration and the other a collinear spin configuration. As a result of the numerical study, we find a new phase which is different from three phases.
Using the density matrix renormalization group technique, we investigate the quantum phase diagram of a ferromagnetic frustrated two-leg spin-1/2 ladder with diagonal and in-chain next-nearest-neighbor (NNN) interactions. By analyzing the correlation function and four-site entropy, we obtain the quantum phase diagram of the system. We find that the system possesses a tetramer phase, a ferromagnetic phase and states I and II. Spin arrangements for states I and II are also determined. In addition, the influence of the in-chain NNN interaction J 2 on the phase transitions of the anti-ferromagnetic case is studied. We show the phase diagram and find that the stagger dimer phase exists only in a narrow parameter region. Meanwhile, the existence of the controversial columnar dimer phase at J 2 = 0 is carefully analyzed.
The magnetization plateaus of frustrated Kondo necklace model have been studied with use of the bosonization technique and level spectroscopy method. It is shown that the model may show three phases (dimer plateau, Néel plateau and Tomonaga-Luttinger liquid phases) due to competitions among Ising anisotropy Δ, the nearest and next nearest neighbor exchange interactions J1, J2. It is shown from bosonization technique that quantum transition between the dimer and Néel plateaus is Gaussian type, while the transition from one of these plateau phases to Tomonaga-Luttinger phase is Brezinskii-Kosterlitz-Thouless type. The phase diagram is constructed on the Δ-J2/J1 plane with use of level spectroscopy method, under the condition that the system has a half of the saturation magnetization.
We study the S =1/2 and S =1 alternating spin Heisenberg chain with the next-nearest neighbor (NNN) interaction J 2 between neighboring S =1/2 spins, by using the numerical diagonalization method of a finite size system. It is found that a fractional plateau appears at magnetization m =1/2 in the magnetization curve for J 2 > J 2 c =0.106±0.001. The phase transition at J 2 c is characterized by the exponent σ=1, which controls the critical behavior of the spin gap Δ as Δ∼ exp(- a /( J 2 - J 2 c ) 1+σ ). For J 2 < J 2 c , the model at m =1/2 is described by the conformal field theory with central charge c =1 and exponent η for the spin correlation function of the transverse component to a magnetic field is calculated.