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Physical review. B, Condensed matter

Spin dynamics in the quantum antiferromagnetic chain compound KCuF3

S. E. Nagler, D. M. Tennant, Roger Arthur Cowley, T. G. Perring, Sushil K. Satija

Published Dec 1, 1991• 119 citations
Publisher

Abstract

The magnetic excitations of a nearly ideal realization of a one-dimensional S=1/2 Heisenberg antiferromagnet, ${\mathrm{KCuF}}_{3}$, have been studied by inelastic neutron scattering. The experimments were performed using the pulsed neutron source ISIS and show that the magnetic scattering occurs at energies well above the top of the linearized spin-wave band. This result shows that it is essential to take account of quantum effects in discussing the excitations. The results are in excellent accord with theoretical predictions for the dynamical correlation function.

DOI
10.1103/physrevb.44.12361

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Physical Review Letters•Mar 20, 1995•30 citations
The magnetic excitations of a nearly ideal realization of a one-dimensional S=1/2 Heisenberg antiferromagnet, KCuF3{\mathrm{KCuF}}_{3}KCuF3​, have been studied by inelastic neutron scattering. The experimments were performed using the pulsed neutron source ISIS and show that the magnetic scattering occurs at energies well above the top of the linearized spin-wave band. This result shows that it is essential to take account of quantum effects in discussing the excitations. The results are in excellent accord with theoretical predictions for the dynamical correlation function.
In this, and the following paper, we present the results of a detailed experimental investigation into the spin dynamics of the quasi-one-dimensional S=1/2 Heisenberg antiferromagnet KCuF3{\mathrm{KCuF}}_{3}KCuF3​. In this paper we report results of inelastic neutron-scattering measurements made using the MARI time-of-flight spectrometer at the Rutherford Appleton Laboratory. Measurement of the magnetic excitation spectrum was made in both the low-temperature phase, where the chains are ordered together, and in the high-temperature phase, where the correlations between chains become unimportant. We compare our measurements with the M\"uller ansatz, which is identified with a two-spinon cross section, and find excellent agreement with this. The effect of temperature on the excitation continuum was also investigated. A series of measurements were made at temperatures ranging from 20 to 200 K. These results are compared to the predictions of field theory for the one-dimensional Heisenberg chain. Again good agreement is found with the theoretical predictions. In the following paper measurements of the low-energy scattering in the ordered phase, made on a triple-axis spectrometer, are presented.
Inelastic neutron scattering has been used to study the temperature dependence of the magnetic response in the one-dimensional S=1/2 Heisenberg antiferromagnet KCuF3{\mathrm{KCuF}}_{3}KCuF3​. The scattering is consistent with that expected for unbound spinon pair excitations.
Investigation of dynamical excitations is difficult but crucial to the understanding of many exotic quantum phenomena discovered in quantum materials. This is particularly true for highly frustrated quantum antiferromagnets whose dynamical properties deviate strongly from theoretical predictions made based on the spin-wave or other approximations. Here, we present a large-scale numerical calculation on the dynamical correlation functions of spin-1/2 triangular Heisenberg model using a state-of-the-art tensor network renormalization group method. The calculated results allow us to gain for the first time a comprehensive picture on the nature of spin excitation spectra in this highly frustrated quantum system. It provides a quantitative account for all the key features of the dynamical spectra disclosed by inelastic neutron scattering measurements for Ba_{3}CoSb_{2}O_{9}, revealing the importance of the interplay between low- and high-energy excitations and its renormalization effect to the low-energy magnon bands and high-energy continuums. We identify the longitudinal Higgs modes in the intermediate-energy scale and predict the energy and momentum dependence of spectral functions along the three principal axes that can be verified by polarized neutron scattering experiments. Furthermore, we find that the spin excitation spectra weakly depend on the anisotropic ratio of the antiferromagnetic interaction.
Many phenomena in magnetism can be described using classical models, yet magnetism is a quantum mechanical effect. In addition to thermal fluctuations, quantum fluctuations arise due to the quantum uncertainty of the ground state. These fluctuations are enhanced by low dimensionality and low spin. Spin chains show interesting excitations associated with quasiparticles. Model materials for spin chains can be realized in compounds where the interchain interactions are weak enough. This thesis presents neutron scattering studies of two model materials for spin chains with different spin symmetry. The spin2 Heisenberg antiferromagnetic chain CuSO4*5D2O has a main exchange of J ∼ 3 K, which permits to study its excitation spectrum up to temperatures of ten times the exchange. The spin2 Heisenberg magnet has been studied widely both theoretically and experimentally. The excitation spectrum of the spin2 Heisenberg antiferromagnet consists of quasiparticles called spinons, and calculations for it exist for T = 0 and as a function of temperature. A quantitative comparison between experimental data and theoretical models across a range of temperatures is presented. The excitation spectrum of CuSO4*5D2O is excellently described by the excitation spectrum of a spin2 Heisenberg antiferromagnetic chain at finite temperatures. Energy-temperature scaling is observed at temperatures up to 2J . For these temperatures the Luttinger liquid description of the spin2 Heisenberg antiferromagnetic chain is valid. A spinon continuum is confirmed at all measured temperatures. Therefore, even at ten times the main exchange (T ≈ 10 J), CuSO4*5D2O shows the behavior of a quantum magnet, and not of a classical system at infinite temperatures, for which one would expect single spin flips. The Ising chain is one of the most studied models in magnetism, one model compound for it is RbCoCl3. Optical spectroscopy measurements suggest a lower gap than for similar compounds, which makes it better suited for high resolution neutron spectroscopy. Magnetic correlations along the chains arise in RbCoCl3 below 80 K. A gapped continuum is observed, which arises from isolated antiferromagnetic Ising chains. Below the first magnetic ordering temperature TN1 ≈ 28 K bound states are observed, which arise due to correlations which form between the chains. Strong diffuse scattering leads to the conclusion that disorder is still present. At the second magnetic ordering transition, at TN2 ≈ 14 K, the bound states split as the correlations between the chains change. Fits indicate that the correlations change continuously as a function of temperature. Above TN2 the excitation spectrum of RbCoCl3 can be described by a spin1 2 Ising chain with an XY-component which is treated as a perturbation. Below TN2 the main features are reproduced correctly, but deviations from the details indicate that additional terms in the Hamiltonian may be necessary. This thesis was carried out at the Institut Laue-Langevin, the Laboratory for Neutron Scattering and Imaging at the Paul Scherrer Institute and ETH Zurich.
Inelastic neutron scattering experiments investigating the spin dynamics along the chain direction of an S = 3 / 2 quasi-one-dimensional Heisenberg antiferromagnet CsVCl 3 were performed up to the zone boundary energy. The authors observed the quantum renormalization in the exchange constant and found that the scattering function cannot be described by either the classical delta -function or the quantum Heisenberg model for S = 1 / 2 . The spin excitations have apparent linewidths and they are compared with the theory of the classical isotropic Heisenberg system at finite temperatures.
Well-defined spin-wave excitations were observed by using pulsed neutrons from CsVCl3{\mathrm{l}}_{3}l3​, an S=3/2S\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}3/2S=3/2 Heisenberg antiferromagnetic chain. The observed spin-wave dispersion relation shows an enhancement of the excitation energy by a factor of 1.26, which must be compared with the quantum renormalization factor of $\ensuremath{\pi}/2$ for an S=1/2S\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}1/2S=1/2 system. The linewidth of the spectrum at 40 K was broad and independent of qqq. The qqq-independent linewidth is the first experimental observation, which was predicted by rigorous theories for a classical chain at sufficiently low temperature.