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Physical Review Letters

Quantum Spin Dynamics of an S=3/2 Heisenberg Antiferromagnetic Chain: Inelastic Pulsed Neutron Scattering from CsVC l3

Shinichi Itoh, Y. Endoh, Kazuhisa Kakurai, Hidekazu Tanaka

Published Mar 20, 1995• 30 citations
Publisher

Abstract

Well-defined spin-wave excitations were observed by using pulsed neutrons from CsVC${\mathrm{l}}_{3}$, an $S\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}3/2$ 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 $S\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}1/2$ system. The linewidth of the spectrum at 40 K was broad and independent of $q$. The $q$-independent linewidth is the first experimental observation, which was predicted by rigorous theories for a classical chain at sufficiently low temperature.

DOI
10.1103/physrevlett.74.2375

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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 \ensuremathπ/2\ensuremath{\pi}/2\ensuremathπ/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.
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.
We used a combination of the quantum Monte Carlo technique and the maximum entropy method to calculate the dynamic structure factor of the quantum Heisenberg antiferromagnet. The dynamics is governed by renormalized damped spin waves and we calculate their frequencies and linewidths. The computed spin-wave dispersion is in quantitative agreement with inelastic-neutron-scattering experiments on La2{\mathrm{La}}_{2}La2​CuO4{\mathrm{CuO}}_{4}CuO4​. The low-energy sector exhibits scaling behavior with the characteristic frequency scale, which is inversely proportional to the correlation length.
We have mapped from the quantum to the classical limit the spin excitation spectrum of the antiferromagnetic spin-1 Heisenberg chain system CsNiCl3{\mathrm{CsNiCl}}_{3}CsNiCl3​ in its paramagnetic phase from T=5T=5T=5 to 200K.200\mathrm{K}.200K. Neutron scattering shows that the excitations are resonant and dispersive up to at least $T=70\mathrm{K}\ensuremath{\simeq}2.7J,$ but broaden considerably with increasing temperature. The dispersion flattens out with increasing temperature as the resonance energy $\ensuremath{\Delta}$ at the antiferromagnetic wave vector increases and the maximum in the dispersion decreases. The correlation length $\ensuremath{\xi}$ between T=12T=12T=12 and 50K50\mathrm{K}50K is in agreement with quantum Monte Carlo calculations for the spin-1 chain. $\ensuremath{\xi}$ is also consistent with the single mode approximation, suggesting that the excitations are short-lived single particle excitations. Below T=12KT=12\mathrm{K}T=12K where three-dimensional spin correlations are important, $\ensuremath{\xi}$ is shorter than predicted and the experiment is not consistent with the random phase approximation for coupled quantum chains. At T=200K,T=200\mathrm{K},T=200K, the structure factor and second energy moment of the excitation spectrum are in excellent agreement with the high-temperature series expansion.
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.
Exact diagonalization calculations of finite antiferromagnetic spin-1 Heisenberg chains at finite temperatures are presented and compared to a recent inelastic neutron scattering experiment for temperatures T up to 7.57.57.5 times the intrachain exchange constant J. The calculations show that the excitations at the antiferromagnetic point q=1q=1q=1 and at q=0.5q=0.5q=0.5 remain resonant up to at least T=2J,T=2J,T=2J, confirming the recent experimental observation of resonant high-temperature domain wall excitations. The predicted first and second moments are in good agreement with experiment, except at temperatures where three-dimensional spin correlations are most important. The ratio of the structure factors at q=1q=1q=1 and 0.5 is well predicted for the paramagnetic infinite-temperature limit. For T< 2J,T<~2J,T< 2J, however, we found that the experimentally observed intensity is considerably less than predicted. This suggests that domain wall excitations on different chains interact up to temperatures of the order of the spin band width.
We report a detailed neutron-scattering study of the spin dynamics in CuCl2{\mathrm{Cl}}_{2}Cl2​\ifmmode\cdot\else\textperiodcentered\fi{}2N(C5{\mathrm{C}}_{5}C5​D5{\mathrm{D}}_{5}D5​), a physical realization of the one-dimensional S=12S=\frac{1}{2}S=21​ Heisenberg antiferromagnet. At T=1.3T=1.3T=1.3 K well-defined excitations are observed over the whole zone with energies given by $E(q)=\ensuremath{\pi}{J}_{\mathrm{nn}}sin(\mathrm{qc})$, the celebrated des Cloizeaux-Pearson exact solution for the spectrum of first excited states, but with intensities approximately those expected from classical spin-wave theory. At T=8T=8T=8 K the excitations are broad and ill defined.