The spin dynamics of an Ising-like S =1/2 antiferromagnet with a weak next-nearest-neighbor interaction on a linear chain is studied by a perturbation method. Bound states of two domain walls, i.e., 2-soliton bound states, are found in addition to soliton-pair states. When the next-nearest-neighbor interaction is ferromagnetic, the dynamical structure factor S x x ( k , ω) exhibits a sharp peak at a lower energy and a tail at higher energies. Our results are in good agreement with experimental observations of S x x ( k , ω) on CsCoCl 3 and CsCoBr 3 at low temperatures.
The dynamics of quantum solitons in an Ising-like S=(1/2 antiferromagnet on finite linear chains with spins N (\ensuremath{\le}15) is studied by integrating the Schr\"odinger equation of motion. Space-time correlation functions
Szz(r,t) and their Fourier transforms, i.e., dynamical structure factor
Szz(q,\ensuremath{\omega}), are calculated for both even and odd N. A slow but large oscillation of
Szz(r,t) is seen, which gives a direct evidence of the occurrence of propagating domain walls, i.e., solitons. The oscillation leads to a low-energy component of
Szz(q,\ensuremath{\omega}) whose line shape greatly depends on whether N is even or odd and on the temperature. We analyze in detail the dependence of soliton number in the line shape and give a plausible conjecture that
Szz(q,\ensuremath{\omega}) for N=\ensuremath{\infty} should exhibit a very broad double maximum at low temperatures. We estimate
Szz(q,\ensuremath{\omega}) at various temperatures. Our results reproduce experimental observations of
Szz(q,\ensuremath{\omega}) on
CsCoCl3 and
CsCoBr3 very well over a wide temperature range.
The lowest-lying excited states in the S=1/2 one-dimensional Ising-like antiferromagnet
CsCoCl3 consist of domain-wall (soliton) pair states. Although the dynamical response function S(Q,\ensuremath{\omega}) has been calculated for these states, it has not proved possible to explain the results of neutron scattering and Raman experiments without recourse to the introduction of extra terms in the spin Hamiltonian. We argue against the two modifications to the Hamiltonian of
CsCoCl3 proposed in previous papers, a staggered field term arising from a mean field approach to exchange mixing, and next-nearest-neighbor intrachain coupling, as being unphysical. Instead we derive a nearest-neighbor effective Hamiltonian, which takes account of the mixing of higher
Co2+ ion crystal-field levels in a self-consistent manner. We also present a high-resolution inelastic neutron scattering experiment on
CsCoCl3, which has allowed the dispersion of the excited states across the Brillouin zone to be studied more carefully than before. These results give a direct measure of S(Q,\ensuremath{\omega}) in the one-dimensional phase where there is a continuum of excited states, and in the three-dimensionally ordered phases, where weak interchain interactions split the continuum into a ``Zeeman ladder'' of discrete states. The predictions of our theory are found to be in quantitative agreement with experiment.
The dynamical properties of the S=1/2 antiferromagnetic XXZ chain are studied by the exact diagonalization and the recursion method of finite systems up to 24 sites. Two types of the exchange interaction are considered: one is the nearest-neighbor type, and the other is the inverse-square one. As the Ising anisotropy becomes larger, there appears a noticeable difference in the transverse component S^{xx}(q,ω) between the two types of the exchange. For the nearest-neighbor type, the peak frequency of S^{xx}(q,ω) for each q approaches the center of the continuum spectrum. On the contrary, the peak frequency for the inverse-square type moves to the upper edge of the continuum, and separates from the continuum for the anisotropy larger than the threshold value. Whether the interaction between domain walls (solitons) is absent or repulsive in the Ising limit leads to this difference in the behavior of S^{xx}(q,ω). In the longitudinal component S^{zz}(q,ω), on the other hand, the feature of the dynamics is scarcely different between the two types. The energy gap and the static properties are also discussed.
Neutron inelastic-scattering experiments on an Ising-like quantum antiferromagnetic chain with nonmagnetic impurities, CsCo c Mg 1- c Cl 3 (c=1, 0.95, 0.9, 0.85, 0.6 and 0.4), were performed. The concentration dependence of the spin dynamics showed that although the solitons and the spin-wave continuum state were stable for a small amount of nonmagnetic impurities, they vanished at c=0.8. We also observed the coexistence of Ising-cluster excitations and intra-cluster excitations at low temperatures. These results can be well interpreted by a theory incorporated with next-nearest-neighbor interactions in the chain.
Dynamic spin correlation function of the
S=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, CuGeO
3.
Dynamics of one-dimensional Ising-like (strongly anisotropic) antiferromagnets is studied by the perturbation theory from the pure Ising limit and by an exact calculation for finite chains. Both calculations show that the des Cloizeaux-Gaudin (dC-G) “spin-wave” spectrum corresponds neither to a lower bound of excitation continuum nor to the peak position of the transverse response Sxx(Q, ω). A new interpretation is given of the spin-wave spectrum of CsCoCl3 without relying on the dC-G theory. It is also shown that at elevated temperatures Sxx(Q, ω) has a three-peak structure. The longitudinal response Sxx(Q, ω) at low temperatures has a weak peak at the position of spin wave peak, while with increasing temperature Sxx(Q, ω) is dominated by the central peak due to thermally activated solitons, which was predicted by Villain.