High-temperature dynamics of one-dimensional magnetic systems

A self-consistent theory is presented which describes the long-wavelength dynamics of one-dimensional Heisenberg systems in the presence of a static magnetic field at high temperatures. The dipole-dipole interaction between the electronic spins (and/or single-ion anisotropy) plays the role of a symmetry-breaking field. Incorporation of interchain coupling is possible within this framework and lowest-order corrections due to this perturbation have been given explicitly. The mode-coupling theory is valid for all orientations of the magnetic field and treats both secular and nonsecular terms of the dipolar interaction. The results can be used to describe magnetic-resonance phenomena (EPR and NMR) in (quasi-)one-dimensional paramagnets. These resonance experiments include the normal EPR transition, the EPR satellites, and the NMR relaxation times including diffusion cutoff effects. The mode-coupling equations generated by the theory have to be solved numerically. Numerical calculations are presented which are relevant to experimental results. A completely new feature of the theory is a "reverse 10/3 effect": at some orientations of the magnetic field the introduction of the nonsecular part of the dipolar interaction produces a decrease in the normal EPR linewidth. This pure one-dimensional effect seems in agreement with experiment. The satellite lines present in the spectral functions of the two-spin correlation functions are a consequence of the very pronounced resonance structure of the self-energies associated with these spectral functions. This resonance structure is very sensitive to interchain Heisenberg exchange. Numerical results demonstrate that a small interchain exchange interaction broadens the resonances of the self-energies substantially. A comparison is made between existing theories and this work.