We use the method of recurrence relations to investigate the dynamics of the one-dimensional spin-
1/2 Heisenberg model with Dzyaloshinskii-Moriya (DM) interaction in a magnetic field perpendicular to the DM axis. Our results are valid in the high-temperature limit. We determine exactly the first four recurrants, which produce the time-dependent correlation functions. In order to extend our results to longer times, we introduce a new extrapolation procedure for obtaining higher-order recurrants. Our extrapolation mechanism produces good results when compared to the well-known behavior of the relaxation function in the limit of the
XY and isotropic Heisenberg models. The relaxation function and the spectral density function are then analyzed for several values of the external field
B for the Heisenberg model with DM interactions in one dimension, in the $T\ensuremath{\rightarrow}\ensuremath{\infty}$ limit. We find that the external field produces stronger and faster oscillations in relaxation functions and a suppression of the central peak in the spectral density. That is accompanied by the appearance of a peak centered at a finite frequency, due to enhancement of the collective mode of spins precessing about the external field.
Abstract Motivated by recent experimental progress on the quasi-one-dimensional quantum magnet NiNb2O6, we study the spin dynamics of an S = 1 ferromagnetic Heisenberg chain with single-ion anisotropy by using a semiclassical molecular dynamics approach. This system undergoes a quantum phase transition from a ferromagnetic to a paramagnetic state under a transverse magnetic field, and the magnetic response reflecting this transition is well described by our semiclassical method. We show that at low temperature the transverse component of the dynamical structure factor depicts clearly the magnon dispersion, and the longitudinal component exhibits two continua associated with single- and two-magnon excitations, respectively. These spin excitation spectra show interesting temperature dependence as effects of magnon interactions. Our findings shed light on the experimental detection of spin excitations in a large class of quasi-one-dimensional magnets.
Proton spin-lattice relaxation times have been measured in the quasi-one-dimensional
s=21 Heisenberg antiferromagnetic compounds CuSe
O4\ifmmode\cdot\else\textperiodcentered\fi{}5
H2O and CuS
O4\ifmmode\cdot\else\textperiodcentered\fi{}5
H2O, in order to study the magnetic field dependence of the 1D quantum spin dynamics at various temperatures. Information is obtained on the low-frequency behavior of the spin autocorrelation functions for the linear chains. The transverse component shows at high
T a marked decrease with magnetic field above the saturation field
Bc. Towards lower temperatures a pronounced maximum just below
Bc develops and the decrease above
Bc becomes more abrupt. The longitudinal component behaves more smoothly near and above
Bc. The field dependence of the relaxation rates is well explained at all nonzero temperatures by finite-chain calculations. For
T=0 we present analytical calculations of autocorrelation functions based on the predominance of a two-parameter spin-wave continuum for the quantum spin dynamics yielding a nondivergent behavior at $\ensuremath{\omega}=0$ and
B=0. Exact results are obtained for fields above
Bc. Further, an effective
XY approach is used for low but finite
T. Here, good agreement is found with the proton relaxation data for very low temperatures.