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Prog. Theor. Phys. Vol. 48 No. 4 (1972) pp. 1133-1149

[ Full Text PDF : FREE ACCESS (1229K) ]

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

Hiroyuki Tomita and Hiroyuki Mashiyama

Department of Physics, Faculty of Science, Kyoto University, Kyoto

(Received April 1, 1972)

Abstract:

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).


URL : http://ptp.ipap.jp/link?PTP/48/1133/
DOI : 10.1143/PTP.48.1133

[ Full Text PDF : FREE ACCESS (1229K) ] Citation:

References:

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Citing Article(s) :

  1. Journal of the Physical Society of Japan 64 (1995) pp. 4142-4155 :
    Universal Finite-Size Scaling Function of the Ferromagnetic Heisenberg Chain in a Magnetic Field. II –Nonlinear Susceptibility–
    Hiroaki Nakamura, Naomichi Hatano and Minoru Takahashi
  2. Progress of Theoretical Physics Vol. 49 No. 3 (1973) pp. 714-730 :
    Role of Anisotropy in Spin Dynamics
    Tatuo Kawasaki
  3. Progress of Theoretical Physics Vol. 49 No. 6 (1973) pp. 1858-1876 :
    Dynamical Properties of One-Dimensional Heisenberg Model
    Kazuhisa Tomita and Kazuko Kawasaki
  4. Progress of Theoretical Physics Vol. 49 No. 6 (1973) pp. 2163-2164 :
    Paramagnetic Resonance Line Width of a Linear Chain
    Hiroyuki Mashiyama
  5. Progress of Theoretical Physics Vol. 51 No. 5 (1974) pp. 1312-1331 :
    Physical Representation of Special Line Shape Based on Moments
    Kazuhisa Tomita and Hiroyuki Mashiyama
  6. Progress of Theoretical Physics Vol. 55 No. 1 (1976) pp. 21-32 :
    Time Correlation Function in the One-Dimensional Heisenberg System at High Temperatures
    Naruichi Nagao and Hiroshi Miyagi
  7. Progress of Theoretical Physics Vol. 56 No. 4 (1976) pp. 1021-1041 :
    New Self-Consistent Approach to Spin Dynamics at High Temperatures
    Naruichi Nagao and Tuto Nakamura
  8. Progress of Theoretical Physics Vol. 64 No. 4 (1980) pp. 1161-1175 :
    Dynamical Properties of the Diluted Heisenberg and XY Magnets at Infinite Temperature. I
    Tsuyoshi Horiguchi and Tohru Morita

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