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arXiv:cond-mat/0304244 · Physical review. B, Condensed matter

Dynamical structure factor in copper benzoate and other spin-1/2 antiferromagnetic chains

Fabian H. L. Eßler, Akira Furusaki, Takashi Hikihara

Published Aug 8, 2003• 49 citations
arXivHTMLPDF

Abstract

Recent experiments of the quasi-one-dimensional spin-$\frac{1}{2}$ antiferromagnet copper benzoate established the existence of a magnetic field induced gap. The observed neutron scattering intensity exhibits resolution limited peaks at both the antiferromagnetic wave number and at incommensurate wave numbers related to the applied magnetic field. We determine the ratio of spectral weights of these peaks within the framework of a low-energy effective field theory description of the problem.

DOI
10.1103/physrevb.68.064410

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Recent experiments of the quasi-one-dimensional spin-12\frac{1}{2}21​ antiferromagnet copper benzoate established the existence of a magnetic field induced gap. The observed neutron scattering intensity exhibits resolution limited peaks at both the antiferromagnetic wave number and at incommensurate wave numbers related to the applied magnetic field. We determine the ratio of spectral weights of these peaks within the framework of a low-energy effective field theory description of the problem.
Recent experiments on the S=12S=\frac{1}{2}S=21​ antiferromagnetic chain compound, Cu benzoate, discovered an unexpected gap scaling as approximately the 23\frac{2}{3}32​ power of an applied magnetic field. A theory of this gap, based on an effective staggered field, orthogonal to the applied uniform field, resulting from a staggered gyromagnetic tensor and a Dzyaloshinskii-Moriya interaction, leading to a sine-Gordon quantum field theory, has been developed. Here we discuss many aspects of this subject in considerable detail, including a review of the S=12S=\frac{1}{2}S=21​ chain in a uniform field, a spin-wave theory analysis of the uniform plus staggered field problem, exact amplitudes for the scaling of gap, staggered susceptibility and staggered magnetization with field or temperature, intensities of soliton and breather peaks in the structure function, and field and temperature dependence of the total susceptibility.
We study the spin-12\frac{1}{2}21​ antiferromagnetic Heisenberg chain in both uniform and (perpendicular) staggered magnetic fields using the density-matrix renormalization-group method. This model has been shown earlier to describe the physics of the copper benzoate materials in magnetic field. In the present work, we extend the study to more general case for a systematic investigation of the field-induced gap and related properties of the spin-12\frac{1}{2}21​ antiferromagnetic Heisenberg chain. In particular, we explore the high magnetic field regime where interesting behaviors in the field-induced gap, magnetization, and spin correlation functions are found. Careful examination of the low energy properties and magnetization reveals interesting competing effects of the staggered and uniform fields. The incommensurate behavior in the spin correlation functions is demonstrated and discussed in detail. The present work reproduces earlier results in good agreement with experimental data on copper benzoate and predicts new interesting field-induced features at very high magnetic field.
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.
Various forms of antiferromagnetic exchange interaction among quantized spins in one-dimensional and quasi-one-dimensional lattices are examined. Primary results are reported in two real compounds, the sodium vanadate NaV2O5 and the copper germanate CuGeO3, and in a class of compounds of real materials modeled as dimerized antiferromagnetically coupled spin-1/2 chains susceptible to spin-1 impurity doping and that include such examples as the strontium cuprate Sr14Cu24O41 and vanadium pyrophosphate (VO)2P2O7. Sodium vanadate, NaV2O5, a quarter-filled two-leg ladder compound that was originally thought to be composed of magnetic legs and nonmagnetic legs was subsequently shown to be a charge ordered system below room temperature. Initial models of the material as isolated antiferromagnetically coupled spin-1/2 chains can be mapped to the subsequently resolved magnetic system of the charge ordered state with the spins on molecular orbitals of V-O-V rungs antiferromagentically coupled between neighboring rungs either on the same ladder or on neighboring ladders. Comparing the model's dynamic structure factor to inelastic neutron scattering data could distinguish between the proposed spin coupling schemes and consequently reveal the details of the interaction between the lattice and the "zig-zag" charge density as well as the magnetic stabilization of the low temperature phase. Copper germanate, the first and only known inorganic spin-Peierls compound, exhibits a strong temperature dependent exchange coupling pattern among the spin-1/2 Cu2+ chains. Above the spin-Peierls transition temperature an unmodulated antiferromagnetic nearest neighbor exchange interaction J1 competes with an antiferromagnetic next nearest neighbor interaction J2. The next nearest neighbor exchange represents an effective coupling equivalent to the net effect of all longer range exchange interactions. This frustration to the nearest neighbor spin exchange produces a distinctive magnetic susceptibility χ (T) much different from the Bonner-Fisher susceptibility of the spin-1/2 Heisenberg chain with nearest neighbor antiferromagnetic exchange only. The ratio of the second to first nearest neighbor couplings α = J2/J1 ≈ 0.36 is sufficient to open a spontaneous gap in the spin-wave excitation spectrum at low temperatures. Below TSP = 14K, the dynamical structure factor is used to fit the dimerization δ and the exchange interactions J1 and J2 to the inelastic neutron scattering data of CuGeO3 at T = 10K. It is found that both δ and α increase significantly at lower temperatures, relative to the values obtained in the high temperature phase and at the onset of dimeration at 14 K. Static structure factor calculations how Scattering inconsistent with the δ−J1−J2 model and can be attributed primarily to the phonon degrees of freedom but possibly also to the couplings between chains in the b and a directions of the crystal lattice. Structurally dimerized compounds of antiferromagnetic spin-1/2 chains possess dynamic structure factor and magnetic susceptibility features that are very sensitive to doping with magnetic and nonmagnetic impurities. It is shown that the effects of spin-1 impurities are very similar to those of nonmagnetic (S = 0) impurities if the coupling between impurity and native spin is about the same magnitude as or larger than between native S = 1/2 spins. The microscopic origins of the similarity can be appreciated with the consideration that neighboring spins to the impurity find it more energetically favorable to couple to the impurity than the other spins of the lattice. Thus the spin-1 impurity and its neighboring S = 1/2 spins decouple from the lattice, creating a nonmagnetic break in the chain. The spins that now observe a nonmagnetic cluster on one side can couple to the S = 1/2 spins on the other side with a higher AF correlation than in the pure compound since they do not have to have a fluctuating dimer resonating between two neighbors. Such enhancements to the local correlations can stabilize the global AF order in one dimensional compounds as shown in theoretical and experimental studies of CuGeO3. ED calculations of the dynamic structure factor show that S(q, ω) developes states with ω = 0 in the gap at q = π. Magnetic susceptibilites in the presense of spin-1 impurities were obtained for 80 site chains by QMC simulations and for 16 site chains by ED calculations. An impurity concentration-dependent second peak in the low temperature region reveals an increasing second maximum with T as observed in doped copper germanates and suggests that the results of the study are applicable even to phonon mediated dimerization. This is not immediately apparent because spin-phonon coupling could distort the dimerization patterns. However, experimental and theoretical results show that elastic coupling between chains can stabilize the dimerization pattern due to the impurities and the results will still apply.
We consider quasi-one-dimensional spin-1 Heisenberg chains with crystal field anisotropy in a uniform magnetic field. We determine the dynamical structure factor in various limits and obtain a fairly complete qualitative picture of how it changes with the applied field. In particular, we discuss how the width of the higher energy single magnon modes depends on the field. We consider the effects of a weak interchain coupling. We discuss the relevance of our results for recent neutron scattering experiments on the quasi-1D Haldane-gap compound NDMAP.
We measured the magnetization processes of the S = 1/2 antiferromagnetic chain compound, Cu benzoate. From the inelastic neutron scattering and the specific heat measurements it was recently discovered that the substance exhibits an unexpected gap which varies approximately as the 2/3 power of an applied magnetic field. The primary mechanism of the gap formation is produced by an effective staggered field due to both the alternating g-tensor and the Dzyaloshinskii-Moriya interaction. We observed the effect of the effective staggered field on the magnetization process of Cu benzoate as a rounding behavior near the saturation field as well as an initial nonlinear increment near zero field. The experimental results are well reproduced by the numerical calculation on the Hamiltonian which includes the appropriate term of the staggered field, using the finite temperature density matrix renormalization group method.