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Physical review. B, Condensed matter

Susceptibility behavior of CuGeO3: Comparison between experiment and the quantum transfer-matrix approach

G. Kamieniarz, M. Bieliński, Jean‐Pierre Renard

Published Dec 1, 1999• 11 citations
Publisher

Abstract

Thermodynamical properties of the one-dimensional $S=1/2$ Heisenberg model with dimerized nearest and uniform next-nearest neighbor interactions are studied by the numerically exact quantum transfer-matrix method and the results are applied to ${\mathrm{CuGeO}}_{3}.$ The Suzuki-Trotter formula is used to obtain a classical system with spin $\ensuremath{\sigma}=3/2$ and effective interactions between nearest neighbors only. The magnetic susceptibility curve is calculated and compared with experimental results in a wide temperature range, revealing the presence of frustration in the model proposed for ${\mathrm{CuGeO}}_{3}.$ Temperature dependence of the dimerization parameter below the spin-Peierls transition point is also estimated.

DOI
10.1103/physrevb.60.14521

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Thermodynamical properties of the one-dimensional S=1/2S=1/2S=1/2 Heisenberg model with dimerized nearest and uniform next-nearest neighbor interactions are studied by the numerically exact quantum transfer-matrix method and the results are applied to CuGeO3.{\mathrm{CuGeO}}_{3}.CuGeO3​. The Suzuki-Trotter formula is used to obtain a classical system with spin \ensuremathσ=3/2\ensuremath{\sigma}=3/2\ensuremathσ=3/2 and effective interactions between nearest neighbors only. The magnetic susceptibility curve is calculated and compared with experimental results in a wide temperature range, revealing the presence of frustration in the model proposed for CuGeO3.{\mathrm{CuGeO}}_{3}.CuGeO3​. Temperature dependence of the dimerization parameter below the spin-Peierls transition point is also estimated.
Thermodynamical properties of one-dimensional S = 1/2 Heisenberg model with dimerized nearest-and uniform next-nearest-neighbour interactions are studied by the numerically exact quantum transfer matrix method and the results are applied to CuGeO 3 .Suzuki-Trotter formula is used to obtain a classical system with spin σ = 3/2 and effective interactions between nearest-neigbours only.Magnetic susceptibility curve is calculated and compared with new experimental results performed in a wide temperature range, revealing the presence of frustration in the model proposed for CuGeO 3 .
We present a numerical study of thermodynamical properties of dimerized frustrated Heisenberg chains down to extremely low temperatures with applications to CuGeO3{\mathrm{CuGeO}}_{3}CuGeO3​. A variant of the finite temperature density matrix renormalization group (DMRG) allows the study of the dimerized phase previously unaccessible to ab initio calculations. We investigate static dimerized systems as well as the instability of the quantum chain towards lattice dimerization. The crossover from a quadratic response in the free energy to the distortion field at finite temperature to nonanalytic behavior at zero temperature is studied quantitatively. Various physical quantities are derived and compared with experimental data for CuGeO3{\mathrm{CuGeO}}_{3}CuGeO3​ such as magnetic dimerization, critical temperature, susceptibility, and entropy.
Properties of the zigzag spin chains with various nearest-neighbor and next-nearest-neighbor interactions are studied by making use of the transfer-matrix renormalization group method. Thermodynamic quantities of the systems (temperature dependence of the susceptibility and the specific heat), as well as the field dependence of the magnetization are analyzed numerically with a high accuracy in the thermodynamic limit. The results have been compared with the recent experimental data on Rb2_22​Cu2_{2}2​Mo3_{3}3​O12_{12}12​.
Motivated by recent experiments on low-dimensional frustrated quantum magnets with competing nearest-neighbor exchange coupling J 1 and next nearest-neighbor exchange coupling J 2 we investigate the magnetic susceptibility of two-dimensional J 1 - J 2 Heisenberg models with arbitrary spin quantum number s . We use exact diagonalization and high- temperature expansion up to order 10 to analyze the influence of the frustration strength J 2 / J 1 and the spin quantum number s on the position and the height of the maximum of the susceptibility. The derived theoretical data can be used to get information on the ratio J 2 / J 1 by comparing with susceptibility measurements on corresponding magnetic compounds.
It is widely accepted that the low-energy physics in edge-sharing cuprate materials has one-dimensional (1D) character. The relevant model to study such systems is believed to be the 1D extended Heisenberg model with ferromagnetic nearest-neighbor (NN) interaction and antiferromagnetic next-nearest-neighbor one. Thus far, however, theoretical studies of such materials have been confined to the case of isotropic interactions. In the present work, we compare the spin susceptibility of the 1D extended Heisenberg model with anisotropy in the NN channel, obtained by means of the Transfer Matrix Renormalization Group method, with that of the edge-sharing chain cuprate Li 2 CuO 2 .
In a magnetic substance the gap in the Raman spectrum, ${\mathrm{\ensuremath{\Delta}}}_{\mathrm{R}}$, and the neutron-scattering gap, ${\mathrm{\ensuremath{\Delta}}}_{\mathrm{N}}$, are related by ${\mathrm{\ensuremath{\Delta}}}_{\mathrm{R}}$/${\mathrm{\ensuremath{\Delta}}}_{\mathrm{N}}$\ensuremath{\approx}2 if the the magnetic excitations (magnons) are only weakly interacting. But for CuGeO3{\mathrm{CuGeO}}_{3}CuGeO3​ the experimentally observed ratio is of the order ${\mathrm{\ensuremath{\Delta}}}_{\mathrm{R}}$/${\mathrm{\ensuremath{\Delta}}}_{\mathrm{N}}$\ensuremath{\sim}1.49--1.78, indicating attractive magnon-magnon interactions in the quasi-one-dimensional spin-Peierls compound CuGeO3{\mathrm{CuGeO}}_{3}CuGeO3​. We present numerical estimates of ${\mathrm{\ensuremath{\Delta}}}_{\mathrm{R}}$/${\mathrm{\ensuremath{\Delta}}}_{\mathrm{N}}$ from exact diagonalization studies for finite chains and find agreement with experiment for intermediate values of the frustration parameter \ensuremath{\alpha}. An analysis of the numerical Raman intensity leads us to postulate a continuum of two-magnon bound states in the spin-Peierls phase. We discuss in detail the numerical method used, the dependence of the results on the model parameters, and a matrix-element effect due to the dimerization of the Raman operator in the spin-Peierls phase.