Effects of a magnetic field on the dynamics of the one-dimensional Heisenberg model with Dzyaloshinskii-Moriya interactions.

Abstract

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 →∞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.