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International Journal of Modern Physics B

DYNAMICAL STRUCTURE FACTORS OF THE S = 1/2 SPIN LADDER SYSTEMS WITH A DIAGONAL INTERACTION IN THE MAGNETIZATION-PLATEAU STATE

Nobuyasu Haga, Sei-ichiro Suga

Published Aug 30, 2002• 0 citations
Publisher

Abstract

We investigate the dynamical structure factors of the S = 1/2 spin ladder systems with a diagonal interaction in the magnetization-plateau state. The results show characteristic behaviors depending on the chain interaction α, the ladder interaction 1 + δ and the diagonal interaction 1 - δ. The large weights are located at q = π, when δ is small. With increasing δ, the wavenumber of the large weights shifts towards q = π/2 taking the incommensurate value. The almost dispersionless behavior comes out at several combinations of α and δ, indicating that the elementary excitation is localized spatially. We discuss our results in comparison with the exact excitation spectrums of the S = 1/2 XXZ model which is an effective Hamiltonian of the present system in α ~ 0 and δ ~ 1. Dynamical structure factors of some S = 1/2 one-dimensional quantum spin systems in the magnetic fields were measured by inelastic neutron-scattering experiments1,2 and it has been shown the theoretical results from the numerical diagonalization of finite systems can explain them.3–5

DOI
10.1142/s0217979202014310

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We investigate the dynamical structure factors of the S = 1/2 spin ladder systems with a diagonal interaction in the magnetization-plateau state. The results show characteristic behaviors depending on the chain interaction α, the ladder interaction 1 + δ and the diagonal interaction 1 - δ. The large weights are located at q = π, when δ is small. With increasing δ, the wavenumber of the large weights shifts towards q = π/2 taking the incommensurate value. The almost dispersionless behavior comes out at several combinations of α and δ, indicating that the elementary excitation is localized spatially. We discuss our results in comparison with the exact excitation spectrums of the S = 1/2 XXZ model which is an effective Hamiltonian of the present system in α ~ 0 and δ ~ 1. Dynamical structure factors of some S = 1/2 one-dimensional quantum spin systems in the magnetic fields were measured by inelastic neutron-scattering experiments1,2 and it has been shown the theoretical results from the numerical diagonalization of finite systems can explain them.3–5
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.
The dynamical structure factor of the S=1/2 bond-alternating spin chain with a next-nearest-neighbor interaction in magnetic field is investigated using the continued fraction method based on the Lanczos algorithm. When the plateau exists on the magnetization curve, the longitudinal dynamical structure factor shows a large intensity with a periodic dispersion relation, while the transverse one shows a large intensity with an almost dispersionless mode. The periodicity and the amplitude of the dispersion relation in the longitudinal dynamical structure factor are sensitive to the coupling constants. The dynamical structure factor of the S=1/2 two-leg ladder in magnetic field is also calculated in the strong interchain-coupling regime. The dynamical structure factor shows gapless or gapful behavior depending on the wave vector along the rung.
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 .