Spin-Wave Modes in a Heisenberg Linear Chain of Classical Spins

The second, fourth and sixth moments of the time-dependent correlation functions are calculated rigorously for a classical Heisenberg linear chain with the nearest-neighbour interactions. With use of these moments the spectral-line shape of the time-dependent correlation functions is reproduced by a Gaussian assumption at the second step in a continued fraction expansion. At the low temperatures, well-defined spin-wave peaks are obtained. From this result it may be considered that there exist propagating modes in the highly developed local order instead of the long-range order that is required in the simple spin-wave theory. At finite temperatures the calculated spectrum is compared with the inelastic neutron scattering data of (CD3)4NMnCl3 (TMMC) and there can be found a good agreement. The conspicuous discrepancy is found only in the line-width and intensity at the lowest temperature. At the high-temperature limit we reproduce a spectrum which is very similar to the rigorous solution calculated by Carboni and Richards for a finite chain of quantum spin (S=1/2).