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Journal of the Physical Society of Japan

Dynamical Structure Factor ofS=1/2AF–F Alternating Chains

Satoshi Kokado, Naoshi Suzuki

Published Sep 15, 1999• 6 citations
Publisher

Abstract

Dynamical structure factors of S =1/2 antiferromagnetic–ferromagnetic alternating chains are calculated by the numerical method based on the ground state obtained by exact diagonalization procedure and also by the pair dynamical correlated-effective-field approximation. A couple of characteristic natures of neutron scattering intensity due to magnetic excitations are predicted: the intensity of transition to the lowest triplet states takes the maximum value at q =π/2 in the whole range of the exchange ratio, and the continuum states above the second gap could be observable at large q .

DOI
10.1143/jpsj.68.3091

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Dynamical structure factors of the S =1 bond-alternating spin chains in the dimer state are calculated at finite temperature using the pair dynamical correlated-effective-field approximation. At T =0, the delta-function-type peak corresponding to the one-magnon mode appears. When temperature increases, such a sharp peak is broadened and the additional weak peak caused by the excitation from the triplet state to the quintet state emerges in the higher energy region. The results are discussed in comparison with those obtained by the exact diagonalization method.
The dynamical structure factor S(Q,\ensuremath{\omega}) of the S=1 antiferromagnetic Heisenberg chain with length 20 at zero temperature is calculated. The lowest-energy states have the \ensuremath{\delta}-function peak at the region \ensuremath{\pi}\ensuremath{\ge}\ensuremath{\Vert}Q\ensuremath{\Vert}>0.3\ensuremath{\pi}. At \ensuremath{\Vert}Q\ensuremath{\Vert}0.3\ensuremath{\pi} the lowest-energy states are the lower edge of the continuum of the scattering state, the strength of which decreases for large systems. This gives a reasonable explanation for the experimental fact that no clear peak is observed at the region Q0.3\ensuremath{\pi}. This situation is more apparent for the valence-bond solid state. On the contrary for S=1/2 antiferromagnetic Heisenberg chain the lowest-energy states are always the edge of the continuum.
We calculate the dynamical structure factors of the magnetization plateau state in the S=12S=\frac{1}{2}S=21​ bond-alternating spin chain with a next-nearest-neighbor interaction. The results show characteristic behaviors depending on the next-nearest-neighbor interaction $\ensuremath{\alpha}$ and the bond alternation \ensuremath{\delta}. We discuss the lower excited states in comparison with the exact excitation spectrums of an effective Hamiltonian. From the finite size effects, characteristics of the lowest excited states are investigated. The dispersionless mode of the lowest excitation appears in adequate sets of $\ensuremath{\alpha}$ and \ensuremath{\delta}, indicating that the lowest excitation is localized spatially and forms an isolated mode below the excitation continuum. We further calculate the static structure factors. The largest intensity is located at $q=\ensuremath{\pi}$ for small $\ensuremath{\delta}$ in fixed \ensuremath{\alpha}. With increasing \ensuremath{\delta}, the wave number of the largest intensity shifts towards $q=\ensuremath{\pi}/2,$ taking the incommensurate value.
Dynamic spin correlation function of the S=1/2S=1/2S=1/2 antiferromagnetic spin chain with alternating nearest neighbor and competing next nearest neighbor interactions is studied using the numerical diagonalization method. We find characteristics of the correlation function, which are the consequence of the dimer order in the ground state: (1) A typical singlet-triplet gap is observed and such a lowest-energy triplet state is found to form a bound state, showing strong peaks below a continuum band with weak but distinct upper and lower boundaries. (2) The intensity of the bound state shows a quite different wavevector-dependence from that of the corresponding intensity at the lower boundary in the usual antiferromagnet. These features are examined by the variational calculation and are favorably discussed in connection with recent experimental results of neutron inelastic scattering in the inorganic spin-Peierls system, CuGeO3_33​.
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