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arXiv:cond-mat/9904291 · Physical review. B, Condensed matter

Schwinger-boson mean-field theory of the Heisenberg ferrimagnetic spin chain

Congjun Wu, Bin Chen, Xi Dai, Yue Yu, Zhao-Bin Su

Published Jul 1, 1999• 65 citations
arXivHTMLPDF

Abstract

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 $T=0 \mathrm{K}.$ 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 $T>0 \mathrm{K},$ 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.

DOI
10.1103/physrevb.60.1057

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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\ensuremathχuniT{\ensuremath{\chi}}_{\mathrm{uni}}T\ensuremathχuni​ has a minimum at intermediate temperatures and the spin-correlation length behaves as T\ensuremath−1{T}^{\ensuremath{-}1}T\ensuremath−1 at low temperatures. These qualitatively agree with the numerical results and the difference is small at low temperatures.
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.
We study the low-temperature properties of a spin-1 Heisenberg antiferromagnetic chain in an external magnetic field by an extended self-consistent mean-field approach developed earlier based on Anderson's spin-wave theory. At fixed magnetic field, the excitation energies increase, while the correlation length decreases with the increasing temperatures. The magnetic field leads to the Zeeman splitting of the excitations with the upper branch going up and the lower branch going down with the increasing fields. At zero temperature the correlation length is a constant and the gap closes at a critical magnetic field, while at finite temperature the correlation length decreases and a small gap seems to survive at the critical magnetic field. These results are consistent with those of other theoretical studies and agree with the experiments quite well. Also, we show that the system shares very similar properties with the valence-bond-solid state even at finite temperatures. The magnetization is studied and the coexistence of the hidden long-range order and the field-induced ferromagnetic order is discussed.
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.
By using the Villain transformation, the Heisenberg ferrimagnetic spin chain is calculated. Two branches of the low-lying excitation in both the absence and presence of magnetic field are obtained. The thermodynamic quantities (such as free energy, magnetization, specific heat and static magnetic susceptibility) are also evaluated at finite temperature. This is the first time to calculate the Ferrimagnetic spin chain by using Villain's method, and we find that the results at a low temperature are quite similar to the previous calculation. The results of free energy and magnetization in zero temperature suggest that the Villain transformation has a good efficiency.
We investigate the thermodynamic properties of Heisenberg ferrimagnetic mixed-spin chains both numerically and analytically with particular emphasis on the combination of ferromagnetic and antiferromagnetic features. Employing a new density-matrix renormalization-group technique as well as a quantum Monte Carlo method, we reveal the overall thermal behaviour: at very low temperatures, the specific heat and the magnetic susceptibility multiplied by the temperature behave like and , respectively, whereas at intermediate temperatures, they exhibit a Schottky-like peak and a minimum, respectively. Developing the modified spin-wave theory, we complement the numerical findings and give precise estimates for the low-temperature behaviour.
The magnetization process, the susceptibility, and the specific heat of the spin-1∕21∕21∕2 antiferromagnet (AF)-AF-ferromagnet (F) and F-F-AF trimerized quantum Heisenberg chains have been investigated by means of the transfer matrix renormalization group (TMRG) technique as well as the modified spin-wave (MSW) theory. A magnetization plateau at m=1∕6m=1∕6m=1∕6 for both trimerized chains is observed at low temperature. The susceptibility and the specific heat show various behaviors for different ferromagnetic and antiferromagnetic interactions and in different magnetic fields. The TMRG results of susceptibility and the specific heat can be nicely fitted by a linear superposition of double two-level systems, where two fitting equations are proposed. Three branch excitations, one gapless excitation and two gapful excitations, for both systems are found within the MSW theory. It is observed that the MSW theory captures the main characteristics of the thermodynamic behaviors at low temperatures. The TMRG results are also compared with the possible experimental data.