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Physical review. B, Condensed matter

Excitation spectrum and T=0 dynamics of the one-dimensional anisotropic antiferromagnet

Mahalingam Mohan, Gerhard H. Muller

Published Feb 1, 1983• 14 citations
Publisher

Abstract

Recent low-temperature inelastic neutron scattering data on the quasi-one-dimensional (1D) Heisenberg-Ising antiferromagnet (AFM) CsCo${\mathrm{Cl}}_{3}$ call for new theoretical efforts, for the available theories fail to explain the observed line shapes. In this paper we initiate a detailed study of the dynamical properties of the 1D spin-\textonehalf{} anisotropic $\mathrm{XYZ}$ AFM with emphasis on the dynamic structure factor ${S}_{\ensuremath{\mu}\ensuremath{\mu}}(q,\ensuremath{\omega})$ at $T=0$. The structure of ${S}_{\ensuremath{\mu}\ensuremath{\mu}}(q,\ensuremath{\omega})$ is determined by the combined effects of the density of states and the matrix elements. Both effects are discussed for selected cases: the $\mathrm{XY}$-Heisenberg AFM (planar system), the Heisenberg-Ising AFM (uniaxial system), and the $\mathrm{XY}$-Ising AFM (biaxial system). The exact solution for ${S}_{\mathrm{zz}}(q,\ensuremath{\omega})$ of the $\mathrm{XY}$-Ising AFM has already many features in common with the experimental data on CsCo${\mathrm{Cl}}_{3}$. It is an ideal starting point for a perturbation approach to the Heisenberg-Ising AFM.

DOI
10.1103/physrevb.27.1776

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Spin-dynamical calculations on one-dimensional systems have relied heavily on classical ($s=\ensuremath{\infty}$) theories, despite abundant evidence that quantum effects can be extremely important at low temperatures. We present a new approach to the spin dynamics of the one-dimensional isotropic s=12s=\frac{1}{2}s=21​ Heisenberg antiferromagnetic (HB AF) which does not involve the many-body techniques usually employed. It is based on analytic Bethe ansatz calculations of excitation energies and densities of states combined with finite-chain calculations of matrix elements. An important feature of our method is the use of rigorous selection rules and the introduction of new selection rules, which are valid for macroscopic systems in a magnetic field. We show that in zero field the dynamical two-spin correlation function ${S}_{\ensuremath{\mu}\ensuremath{\mu}}(q,\ensuremath{\omega})$ at T=0T=0T=0 is governed by a two-parameter continuum of spin-wave-type excitations. In nonzero field, the longitudinal component ${S}_{\mathrm{zz}}(q,\ensuremath{\omega})$ and the transverse components ${S}_{\mathrm{xx}}(q,\ensuremath{\omega})\ensuremath{\equiv}{S}_{\mathrm{yy}}(q,\ensuremath{\omega})$ behave quite differently because they are dominated by different continua of excitations. The former is characterized by a lowest excitation branch with a zero-frequency mode moving from the zone boundary ($q=\ensuremath{\pi}$) towards the zone center (q=0q=0q=0) as the field increases, whereas the latter is characterized by a lowest branch with a zero frequency mode moving from $q=0 \mathrm{to} \ensuremath{\pi}$ with increasing field. The first part of our work features an approximate analytic expression for ${S}_{\ensuremath{\mu}\ensuremath{\mu}}(q,\ensuremath{\omega})$ at zero temperature and in zero field. Although our expression is not rigorous, exact sum rules are violated only by a small amount, and good agreement exists with the few known exact results. Our studies are extended to nonzero temperatures by placing major reliance on exact finite-chain calculations. Our work was stimulated by recent neutron scattering experiments and is oriented towards experimental comparisons. Our result for the s=12s=\frac{1}{2}s=21​ integrated intensity is in much better agreement with neutron scattering data on CuCl2{\mathrm{Cl}}_{2}Cl2​\ifmmode\cdot\else\textperiodcentered\fi{}2N(C5{\mathrm{C}}_{5}C5​D5{\mathrm{D}}_{5}D5​) (CPC) than the corresponding semiclassical result. Moreover, the spectral-weight distribution in ${S}_{\ensuremath{\mu}\ensuremath{\mu}}(q,\ensuremath{\omega})$ shows increasing asymmetry as $q\ensuremath{\rightarrow}\ensuremath{\pi}$, a quantum effect, again in agreement with more recent neutron scattering data. The second part of our work deals with the effects of an applied magnetic field. We extend the analytic work of Ishimura and Shiba to obtain expressions for the energies and densities of states of the various excitation continua. It is shown that these continua are expected to give rise to multiple structures in the scattering intensity. Our results appear to be in quantitative agreement with preliminary results of a neutron study in CPC in a field of 70 kOe, revealing anomalous scattering intensity peaks. Our results repeatedly demonstrate the inadequacy of classical spin-wave theory for this problem. They call for additional experimental studies on quasi-one-dimensional antiferromagnets to examine other unusual and interesting phenomena predicted by our approach.
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