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Journal of Physics Condensed Matter

Schwinger-boson mean-field method for an alternating-spin (1/2, 1) two-leg ladder

X Y Chen, Qing Jiang, Wen Zhong Shen

Published Feb 3, 2003• 2 citations
Publisher

Abstract

We study the low-lying excitations and thermodynamic properties of a ferrimagnetic Heisenberg two-leg ladder, which is composed of alternating-spin (1/2, 1) double chains with antiferromagnetic coupling between the chains. The spin excitation spectra as well as the corresponding energy gaps are calculated by means of the Schwinger-boson mean-field theory. The two interactions between the chains and along the chains play an important role in determining the two branches of the spectrum, not only regarding the size of the low-lying excitation energy gap but also the bandgap between the optical spectrum and the acoustic spectrum. In addition, the two energy gaps and the specific heat have also been calculated at low temperatures.

DOI
10.1088/0953-8984/15/6/318

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We study the low-lying excitations and thermodynamic properties of a ferrimagnetic Heisenberg two-leg ladder, which is composed of alternating-spin (1/2, 1) double chains with antiferromagnetic coupling between the chains. The spin excitation spectra as well as the corresponding energy gaps are calculated by means of the Schwinger-boson mean-field theory. The two interactions between the chains and along the chains play an important role in determining the two branches of the spectrum, not only regarding the size of the low-lying excitation energy gap but also the bandgap between the optical spectrum and the acoustic spectrum. In addition, the two energy gaps and the specific heat have also been calculated at low temperatures.
We study ground-state properties and the low-lying excitations of Heisenberg spin ladders composed of two ferrimagnetic chains with alternating site spins (S1>S2){(S}_{1}>{S}_{2})(S1​>S2​) by using the bosonic Dyson-Maleev formalism and Lanczos numerical techniques. The emphasis is on properties of the ferrimagnetic phase, which is stable for antiferromagnetic interchain couplings ${J}_{\ensuremath{\perp}}>~0$. There are two basic implications of the underlying lattice structure: (i) the spin-wave excitations form folded acoustic and optical branches in the extended Brillouin zone and (ii) the ground-state parameters (such as the on-site magnetizations and spin-stiffness constant) show a crossover behavior in the weak-coupling region $0<{J}_{\ensuremath{\perp}}<1$. The above peculiarities of the ladder ferrimagnetic state are studied up to second order in the quasiparticle interaction and by a numerical diagonalization of ladders containing up to N=12N=12N=12 rungs. The presented results for the ground-state parameters and the excitation spectrum can be used in studies on the low-temperature thermodynamics of ferrimagnetic ladders.
The Schwinger-boson mean-field theory is applied to the quantum ferrimagnetic Heisenberg chain. There is a ferrimagnetic long-range order in the ground state. We observe two branches of the low-lying excitation and calculate the spin reduction, the gap of the antiferromagnetic branch, and the spin fluctuation at T=0K.T=0 \mathrm{K}.T=0K. These results agree with the established numerical results quite well. At finite temperatures, the long-range order is destroyed because of the disappearance of the Bose condensation. The thermodynamic observables, such as the free energy, magnetic susceptibility, specific heat, and the spin correlation at T>0K,T>0 \mathrm{K},T>0K, are calculated. The $T{\ensuremath{\chi}}_{\mathrm{uni}}$ has a minimum at intermediate temperatures and the spin-correlation length behaves as ${T}^{\ensuremath{-}1}$ at low temperatures. These qualitatively agree with the numerical results and the difference is small at low temperatures.
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.
We investigate the zero-temperature and the finite-temperature properties of the two-dimensional antiferromagnetic quantum spin system composed of the s=1/2s=1/2s=1/2 and s=1s=1s=1 spins. The spin excitation spectrum as well as the thermodynamic quantities are computed by means of the Schwinger-boson mean-field theory. We discuss how the magnetic double structure with the gapful and the gapless excitations is generated, and apply the results systematically to the Haldane gap system in a staggered magnetic field and also to the weakly coupled ferrimagnetic mixed-spin chains. It is confirmed that the results obtained are consistent with the experiments for the quasi-one-dimensional Haldane compounds R2BaNiO5.{R}_{2}{\mathrm{BaNiO}}_{5}.R2​BaNiO5​.
The Schwinger-boson mean-field theory (SBMFT) and the linearized tensor renormalization group (LTRG) methods are complementarily applied to explore the thermodynamics of the quantum ferromagnetic mixed spin (S, σ) chains. It is found that the system has double excitations, i.e. a gapless and a gapped excitation; the low-lying spectrum can be approximated by ωk∼Sσ2(S+σ)Jk2 with J the ferromagnetic coupling; and the gap between the two branches is estimated to be △ ∼ J. The Bose-Einstein condensation indicates a ferromagnetic ground state with magnetization mtotz=N(S+σ). At low temperature, the spin correlation length is inversely proportional to temperature (T), the susceptibility behaviors as χ=a1∗1T2+a2∗1T, and the specific heat has the form of C=c1∗T−c2∗T+c3∗T32, with ai (i = 1, 2) and ci (i = 1, 2, 3) the temperature independent constants. The SBMFT results are shown to be in qualitatively agreement with those by the LTRG numerical calculations for S = 1 and σ = 1/2. A comparison of the LTRG results with the experimental data of the model material MnIINiII(NO2)4(en)2(en = ethylenediamine), is made, in which the coupling parameters of the compound are obtained. This study provides useful information for deeply understanding the physical properties of quantum ferromagnetic mixed spin chain materials.
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.