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 excitations of the Heisenberg antiferromagnetic spin chain in zero field are known as spinons. As pairwise-created fractionalized excitations, spinons are important in the understanding of inelastic neutron scattering experiments in (quasi-)one-dimensional materials. In the present paper, we consider the real space-time dynamics of spinons originating from a local spin flip on the antiferromagnetic ground state of the (an)isotropic Heisenberg spin-1/2 model and the Babujan-Takhtajan spin-1 model. By utilizing algebraic Bethe ansatz methods at finite system size to compute the expectation value of the local magnetization and spin-spin correlations, spinons are visualized as propagating domain walls in the antiferromagnetic spin ordering with anisotropy dependent behavior. The spin-spin correlation after the spin flip displays a light cone, satisfying the Lieb-Robinson bound for the propagation of correlations at the spinon velocity.
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.
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.
The effect of the transverse magnetic field h x on the spin dynamics of a one dimensional Ising-like S =1/2 antiferromagnet is discussed. Based on a picture of the propagating domain walls, we obtain dynamical spin correlation functions along the magnetic field S x x ( k ,ω) and perpendicular to it S y y ( k ,ω). A remarkable effect is seen in S y y ( k ,ω) for π/2 ≤ k ≤π, where the spectral weight moves toward the low energy side with the increase of h x . The theory is applied to the analysis of the spin dynamics of CsCoCl 3 , taking into account weak interchain interactions. Zeeman ladders occur and S y y ( k , ω) for k ∼π exhibits a novel feature under the existence of h x .
Many phenomena in magnetism can be described using classical models, yet magnetism is a quantum mechanical effect. In addition to thermal fluctuations, quantum fluctuations arise due to the quantum uncertainty of the ground state. These fluctuations are enhanced by low dimensionality and low spin. Spin chains show interesting excitations associated with quasiparticles. Model materials for spin chains can be realized in compounds where the interchain interactions are weak enough. This thesis presents neutron scattering studies of two model materials for spin chains with different spin symmetry. The spin2 Heisenberg antiferromagnetic chain CuSO4*5D2O has a main exchange of J ∼ 3 K, which permits to study its excitation spectrum up to temperatures of ten times the exchange. The spin2 Heisenberg magnet has been studied widely both theoretically and experimentally. The excitation spectrum of the spin2 Heisenberg antiferromagnet consists of quasiparticles called spinons, and calculations for it exist for T = 0 and as a function of temperature. A quantitative comparison between experimental data and theoretical models across a range of temperatures is presented. The excitation spectrum of CuSO4*5D2O is excellently described by the excitation spectrum of a spin2 Heisenberg antiferromagnetic chain at finite temperatures. Energy-temperature scaling is observed at temperatures up to 2J . For these temperatures the Luttinger liquid description of the spin2 Heisenberg antiferromagnetic chain is valid. A spinon continuum is confirmed at all measured temperatures. Therefore, even at ten times the main exchange (T ≈ 10 J), CuSO4*5D2O shows the behavior of a quantum magnet, and not of a classical system at infinite temperatures, for which one would expect single spin flips. The Ising chain is one of the most studied models in magnetism, one model compound for it is RbCoCl3. Optical spectroscopy measurements suggest a lower gap than for similar compounds, which makes it better suited for high resolution neutron spectroscopy. Magnetic correlations along the chains arise in RbCoCl3 below 80 K. A gapped continuum is observed, which arises from isolated antiferromagnetic Ising chains. Below the first magnetic ordering temperature TN1 ≈ 28 K bound states are observed, which arise due to correlations which form between the chains. Strong diffuse scattering leads to the conclusion that disorder is still present. At the second magnetic ordering transition, at TN2 ≈ 14 K, the bound states split as the correlations between the chains change. Fits indicate that the correlations change continuously as a function of temperature. Above TN2 the excitation spectrum of RbCoCl3 can be described by a spin1 2 Ising chain with an XY-component which is treated as a perturbation. Below TN2 the main features are reproduced correctly, but deviations from the details indicate that additional terms in the Hamiltonian may be necessary. This thesis was carried out at the Institut Laue-Langevin, the Laboratory for Neutron Scattering and Imaging at the Paul Scherrer Institute and ETH Zurich.