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Physical Review Letters

Nonlinear Effects in the Dynamic Structure Factor of the Classical Antiferromagnetic Heisenberg Chain in an External Field at Low Temperatures

Bart De Raedt, Hans A. De Raedt, Jan Fivez

Published Mar 23, 1981• 7 citations
Publisher

Abstract

Is is found that nonlinear effects give rise to anomalies in the spectrum of the antiferromagnetic Heisenberg chain in an external field, even at low temperatures. Divergences in the two-magnon density of states are responsible for additional resonances, besides the usual spin-wave peak, in the dynamic structure factor.
DOI
10.1103/physrevlett.46.786

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The influence of the nonlinearity of the spin equations of motion on the dynamic structure factor of the antiferromagnetic Heisenberg chain in an external field is calculated in the low-temperature limit. The memory functions for the longitudinal and transverse spin component are calculated rigorously to lowest nonvanishing order in the temperature. In this limit, only two-magnon processes contribute to the memory functions. Divergencies in the two-magnon density of states give rise to resonances in addition to the usual spin-wave peak in the dynamic structure factor.
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The author calculates the dynamical structure factors of a two-dimensional Heisenberg antiferromagnet at T=0, to order 1/(2S) 2 , taking careful account of the umklapp processes. It is shown that, for the transverse spin part, the terms of order 1/(2S) 2 give rise to a broad sideband peak of three-magnon excitations, whose intensity is small but not negligible. For the longitudinal spin part, the terms of order 1/(2S) 2 modify noticeably the spectral shape of the continuum of two-magnon excitations as a function of frequency. These results could be observed in future neutron scattering experiments.
We present results for the dynamic structure factor of the S=1∕2S=1∕2S=1∕2 bond alternating Heisenberg chain over a large range of frequencies and temperatures. Data are obtained from a numerical evaluation of thermal averages based on the calculation of all eigenvalues and eigenfunctions for chains of up to 20 spins. Interpretation is guided by the exact temperature dependence in the noninteracting dimer limit which remains qualitatively valid up to an interdimer exchange $\ensuremath{\lambda}\ensuremath{\approx}0.5$. The temperature induced central peak around zero frequency is clearly identified and aspects of the crossover to spin diffusion in its variation from low to high temperatures are discussed. The one-magnon peak acquires an asymmetric shape with increasing temperature. The two-magnon peak is dominated by the S=1S=1S=1 bound state which remains well defined up to temperatures of the order of JJJ. The variation with temperature and wave vector of the integrated intensity for one-magnon and two-magnon scattering and of the central peak are discussed.
Dynamical structure factors of the S =1 bond-alternating spin chains in the dimer state are calculated at finite temperature using the pair dynamical correlated-effective-field approximation. At T =0, the delta-function-type peak corresponding to the one-magnon mode appears. When temperature increases, such a sharp peak is broadened and the additional weak peak caused by the excitation from the triplet state to the quintet state emerges in the higher energy region. The results are discussed in comparison with those obtained by the exact diagonalization method.
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