Abstract
Dynamical spin correlation functions in (q, omega )-space are calculated numerically for linear quantum-mechanical Heisenberg systems containing up to ten spins with s=1/2 and s=1. The authors consider ferro- and antiferromagnets including single-site and exchange anisotropies. They compare their results with various other theoretical treatments and draw conclusions for the dynamics of infinite chains. In the case of the s=1 planar Heisenberg ferromagnet direct comparison is made with inelastic neutron scattering cross sections of CsNiF3. The theoretical and experimental results are in good agreement.
Highlights
The one-dimensional magnetic chain has been the object of various theoretical treatments in the past (Bethe 1931, Lieb et al 1961, Des Cloizeaux and Pearson 1962, Fisher 1964, Bonner and Fisher 1964)
We are interested in the dynamics, i.e. in time-dependent quantities, especially in the dynamical two-spin correlation functions
We have calculated these correlation functions for systems of N = 8 spins in order to determine to what extent it is possible to draw conclusions concerning the behaviour of infinite chains from the results for such small systems
Summary
The one-dimensional magnetic chain has been the object of various theoretical treatments in the past (Bethe 1931, Lieb et al 1961, Des Cloizeaux and Pearson 1962, Fisher 1964, Bonner and Fisher 1964). Our motivation to do this work originates mainly from the recently available neutron scattering data for CsNiF3 (Steiner et al 1975), which represents an anisotropic s = 1 Heisenberg ferromagnet. The experimental results of Steiner et al (1975) exhibit some quite particular features, different from those of isotropic Heisenberg systems These facts have already been accounted for in the framework of classical (Loveluck and Lovesey 1975) and semiclassical (Villain 1974) calculations. We characterise those eigenstates which are most important for the correlation functions at low temperatures.
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