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Journal of Physics Condensed Matter

1/S expansion for dynamical structure factors in a two-dimensional Heisenberg antiferromagnet at zero temperature

J Igarashi

Published Dec 14, 1992• 12 citations
Publisher

Abstract

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.

DOI
10.1088/0953-8984/4/50/015

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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 an approximate analytic expression for the dynamical spin correlation function of the S=1/2 linear Heisenberg antiferromagnet at T=0. The basis for our approach is that in zero field the spectrum is dominated by a double continuum [in (q,ω) -space] of triplet spin wave excitations. The S=1/2 integrated intensity agrees very well with recent neutron scattering results on CPC, unlike the corresponding classical intensity. Moreover, the S=1/2 spectral weight function shows increasing asymmetry as q→π, a quantum effect, observable in more recent neutron scattering data. In non-zero magnetic field, there exist two, partly overlapping, double continua, each giving rise to a peak situated at the lower boundary. The (zz component of) spectral weight function therefore has a double-peaked structure, as observed experimentally. Theory and experiment are in apparent agreement concerning the energy difference between the peaks.
We present an analytical expression for the dynamical spin-correlation function of the S=12S=\frac{1}{2}S=21​ linear Heisenberg antiferromagnet based on the fact that the spectrum is dominated by a double continuum of spin-wave excitations. Our expression is not exact, but exact sum rules show that the degree of approximation is small. We predict that in a uniform magnetic field the spectral weight function will display a double-peaked structure. Such a feature is observed in recent neutron-scattering experiments.
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.
The authors have evaluated an expression obtained previously for the dynamical spin correlation function of a linear Heisenberg antiferromagnet. The authors discuss the results in relation to both recent neutron scattering experiments and recent computations for finite chains with S= 1 / 2 . It is concluded that contributions to the dynamical structure factor from many accumulating low-frequency excitations provide the high-frequency strength required from sum rule arguments for small wavevectors.
The exact expression derived by Bougourzi, Couture, and Kacir for the two-spinon contribution to the dynamic spin structure factor S(q,\ensuremath{\omega}) of the one-dimensional s=1/2 Heisenberg antiferromagnet at T=0 is evaluated for direct comparison with finite-chain transition rates (N\ensuremath{\leqslant}28) and an approximate analytical result previously inferred from finite-N data, sum rules, and Bethe ansatz calculations. The two-spinon excitations account for 72.89% of the total intensity in S(q,\ensuremath{\omega}). The singularity structure of the exact result is determined analytically and its spectral-weight distribution evaluated numerically over the entire range of the two-spinon continuum. The leading singularities of the frequency-dependent spin autocorrelation function, static spin structure factor, and q dependent susceptibility are determined via sum rules. The impact of the non-two-spinon excitations on the integrated intensity, the susceptibility, the frequency moments, and the Euclidian time representation of S(q,\ensuremath{\omega}) is studied on the basis of finite-size data.
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.