Spin Correlations in Impure Linear Heisenberg Chains

Abstract

We present calculations of the high-temperature time-dependent two-spin correlation functions in impure one-dimensional Heisenberg chains. The dynamics is assumed to be dominated by diffusion, which is obtained as the continuous time limit of a random walk of spin along the chain. The correlations are calculated in the presence of finite concentrations of both nonmagnetic and strongly spin-lattice-coupled impurities. Application is made to the determination of position-dependent (relative to an impurity) NMR linewidths in the presence of hyperfine or electron-nuclear dipole interactions. In the case of spin-lattice-coupled impurities and for short enough chains, the NMR line shape is found to be Lorentzian with a width significantly less than that found in pure chains. The width is found to depend approximately linearly on distance from the nearest impurity. In the case of nonmagnetic impurities, the line shape is found to be Lorentzian in the wings but Gaussian near the center. No narrowing of the resonance is found above that for the pure chain, and the position dependence is such as to increase the width near an impurity.