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arXiv:cond-mat/9911258 · Physical review. B, Condensed matter

Optical absorption of CuO3 antiferromagnetic chains at finite temperatures

Eduardo R. Gagliano, F. Lema, Silvia Bacci, J. J. Vicente Alvarez, J. Lorenzana

Published Jul 1, 2000• 3 citations
arXivHTMLPDF

Abstract

We use a high-statistic quantum Monte Carlo and maximum entropy regularization method to compute the dynamical energy correlation function (DECF) of the one-dimensional (1D) $S=1/2$ antiferromagnetic Heisenberg model at finite temperatures. We also present a finite-temperature analytical ansatz for the DECF that is in very good agreement with the numerical data in the considered temperature range. From these results, and from a finite-temperature generalization of the mechanism proposed by Lorenzana and Sawatsky [Phys. Rev. Lett. $74,$ 1867 (1995)], we compute the line shape for the optical absorption spectra of multimagnon excitations assisted by phonons for quasi-1D compounds. The line shape has two contributions analogous to the Stokes and anti-Stokes process of Raman scattering. Our low-temperature data are in good agreement with optical absorption experiments of ${\mathrm{CuO}}_{3}$ chains in ${\mathrm{Sr}}_{2}{\mathrm{CuO}}_{3}.$ Our finite-temperature results provide a nontrivial prediction on the dynamics of the Heisenberg model at finite temperatures that is easy to verify experimentally.

DOI
10.1103/physrevb.62.1218

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We use a high-statistic quantum Monte Carlo and maximum entropy regularization method to compute the dynamical energy correlation function (DECF) of the one-dimensional (1D) S=1/2S=1/2S=1/2 antiferromagnetic Heisenberg model at finite temperatures. We also present a finite-temperature analytical ansatz for the DECF that is in very good agreement with the numerical data in the considered temperature range. From these results, and from a finite-temperature generalization of the mechanism proposed by Lorenzana and Sawatsky [Phys. Rev. Lett. 74,74,74, 1867 (1995)], we compute the line shape for the optical absorption spectra of multimagnon excitations assisted by phonons for quasi-1D compounds. The line shape has two contributions analogous to the Stokes and anti-Stokes process of Raman scattering. Our low-temperature data are in good agreement with optical absorption experiments of CuO3{\mathrm{CuO}}_{3}CuO3​ chains in Sr2CuO3.{\mathrm{Sr}}_{2}{\mathrm{CuO}}_{3}.Sr2​CuO3​. Our finite-temperature results provide a nontrivial prediction on the dynamics of the Heisenberg model at finite temperatures that is easy to verify experimentally.
We use numerical and analytical results to construct a simple ansatz for the energy dynamical correlation function of the one-dimensional antiferromagnetic Heisenberg model. This is applied to compute the phonon-assisted absorption spectra of magnetic excitations (spinons) in quasi-one-dimensional spin-1/2 insulators and shown to reproduce very well recent infrared measurements in Sr2{\mathrm{Sr}}_{2}Sr2​ CuO3{\mathrm{CuO}}_{3}CuO3​.
Quasi-one-dimensional magnetic materials provide important test beds for rigorous models of interacting many-body systems. Nevertheless, there have been few studies of finite temperature effects on spin correlations in low-spin systems, though these are most likely to exhibit quantum effects. Copper benzoate, Cu(C6D5COO)2⋅3D2O, is a good realization of the S=1/2 Heisenberg antiferromagnetic chain (HAFC). We have performed ac susceptibility and inelastic neutron scattering experiments on this material which establish the Hamiltonian and an excitation spectrum which is consistent with the spinon continuum ansatz of Müller et al. We present inelastic neutron scattering measurements of the temperature evolution of the dynamic spin–spin correlation function Szz(π,ω). Comparison will be made to the classical prediction and to a finite temperature field theory of Schulz as applied to this S=1/2 HAFC.
Unlike most quantum systems which rapidly become incoherent as temperature is raised, strong correlations persist at elevated temperatures in S=12S=\frac{1}{2}S=21​ dimer magnets, as revealed by the unusual asymmetric line shape of their excitations at finite temperatures. Here, we quantitatively explore and parametrize the strongly correlated magnetic excitations at finite temperatures using high-resolution inelastic neutron scattering of the model compound BaCu2V2O8{\mathrm{BaCu}}_{2}{\mathrm{V}}_{2}{\mathrm{O}}_{8}BaCu2​V2​O8​ which we show to be an alternating antiferromagnetic-ferromagnetic $\mathrm{spin}\ensuremath{-}\frac{1}{2}$ chain. Comparison to state of the art computational techniques shows excellent agreement over a wide temperature range. Our findings hence demonstrate the possibility to quantitatively predict coherent behavior at elevated temperatures in quantum magnets.
This thesis is concerned with the numerical study of one-dimensional (1D) spin-1/2 quantum magnets and related method development. Its focus is on the calculation of dynamical spin correlation functions both at zero and finite temperature. This is motivated by the accessibility of dynamical quantities in experiments such as inelastic neutron scattering (INS) and electron spin resonance (ESR). The numerical methods used in this thesis are based on extensions of the density-matrix renormalization group (DMRG) and are formulated in the framework of matrix product states (MPS). While zero-temperature dynamical correlation functions are computed with existing MPS frequency-domain methods, an MPS frequency-domain approach for their calculation at finite temperature is developed in this thesis. The new method combines the Liouville-space formulation of the dynamics with a moment expansion of the dynamical correlation function. The majority of the results are obtained via MPS-based Chebyshev expansions. These numerical techniques are applied to two different model systems describing real materials. The first one is the material copper pyrimidine dinitrate (Cu-PM) which is modeled by a 1D spin-1/2 Heisenberg antiferromagnet with Dzyaloshinskii-Moriya interactions. The spin dynamics of this model is studied in an applied magnetic field and compared to ESR experiments. Zero-temperature calculations for momentum- and frequency-resolved dynamical quantities give direct access to the intensity of the elementary excitations and go beyond the low-energy description by the quantum sine-Gordon model. Thus, a deviation from the Lorentz invariant dispersion for the single-soliton resonance is found. The presence of the strongest boundary bound state previously predicted from a boundary sine-Gordon field theory is confirmed, while composite boundary-bulk excitations have too low intensities to be found in the numerical results. At finite temperature, there is a temperature-induced crossover of the soliton. Moreover, additional temperature effects such as interbreather transitions emerge, which is confirmed by accompanying ESR experiments on Cu-PM over a wide range of the applied field strength. The second system studied in this thesis is the compound BaCu2_22​V2_22​O8_88​. It is shown that the magnetic properties of this quasi-1D material can be described by a strongly alternating antiferromagnetic-ferromagnetic spin-1/2 Heisenberg chain. As found for other dimerized systems, the strong correlations in BaCu2_22​V2_22​O8_88​ persist even at elevated temperatures. Moreover, these correlations lead to an asymmetric lineshape broadening of the magnetic excitations at finite temperature. Upon raising the temperature, an increasingly asymmetric lineshape is observed in high-resolution INS experiments for BaCu2_22​V2_22​O8_88​. In this thesis, the lineshape is calculated by the MPS finite-temperature method developed as a part of this work. Comparing these results to the INS data and the lineshape obtained by a diagrammatic approach, excellent agreement is found over a broad temperature range. This demonstrates that coherent quantum behavior persists at elevated temperatures in BaCu2_22​V2_22​O8_88​ and that it can be predicted quantitatively.
We present a study of the dynamic structure factor of the antiferromagnetic spin-12\frac{1}{2}21​ Heisenberg chain at finite temperatures and finite magnetic fields. Using quantum Monte Carlo based on the stochastic series expansion and maximum entropy methods, we evaluate the longitudinal and the transverse dynamic structure factors from vanishing magnetic fields up to and above the threshold Bc{B}_{c}Bc​ for ferromagnetic saturation, as well as for high and for intermediate temperatures. We study the field-induced redistribution of spectral weight contrasting longitudinal versus transverse excitations. At finite fields below saturation incommensurate low-energy modes are found consistent with zero-temperature Bethe ansatz. The crossover between the field-induced ferromagnet above Bc{B}_{c}Bc​ and the Luttinger liquid below Bc{B}_{c}Bc​ is analyzed in terms of the transverse spin dynamics. Evaluating sum rules we assess the quality of the analytic continuation and demonstrate excellent consistency of the maximum entropy results.
Proton spin-lattice relaxation times have been measured in the quasi-one-dimensional s=12s=\frac{1}{2}s=21​ Heisenberg antiferromagnetic compounds CuSeO4{\mathrm{O}}_{4}O4​\ifmmode\cdot\else\textperiodcentered\fi{}5H2{\mathrm{H}}_{2}H2​O and CuSO4{\mathrm{O}}_{4}O4​\ifmmode\cdot\else\textperiodcentered\fi{}5H2{\mathrm{H}}_{2}H2​O, in order to study the magnetic field dependence of the 1D quantum spin dynamics at various temperatures. Information is obtained on the low-frequency behavior of the spin autocorrelation functions for the linear chains. The transverse component shows at high TTT a marked decrease with magnetic field above the saturation field Bc{B}_{c}Bc​. Towards lower temperatures a pronounced maximum just below Bc{B}_{c}Bc​ develops and the decrease above Bc{B}_{c}Bc​ becomes more abrupt. The longitudinal component behaves more smoothly near and above Bc{B}_{c}Bc​. The field dependence of the relaxation rates is well explained at all nonzero temperatures by finite-chain calculations. For T=0T=0T=0 we present analytical calculations of autocorrelation functions based on the predominance of a two-parameter spin-wave continuum for the quantum spin dynamics yielding a nondivergent behavior at $\ensuremath{\omega}=0$ and B=0B=0B=0. Exact results are obtained for fields above Bc{B}_{c}Bc​. Further, an effective XY\mathrm{XY}XY approach is used for low but finite TTT. Here, good agreement is found with the proton relaxation data for very low temperatures.