Spectral Diffusion Decay in Spin Resonance Experiments

Abstract

In spin resonance experiments random flipping by $T_1$ or $T_2$ processes of nearby, nonresonant spins introduces fluctuations into the precessional frequency of the observed spins. These fluctuations may be described by means of a stochastic model, and for wide classes of both Markoffian and non-Markoffian distributions we make predictions for the line shape, for the free induction decay, and for various spin-echo signals. If the homogeneous broadening of the line is due to a dipolar interaction term, then we find that the conditional distribution for the precessional frequency has the shape of a Lorentzian with a cutoff on the wings, rather than a Gaussian shape as commonly assumed. The causes and consequences of Lorentzian diffusion are analyzed in detail for samples in which $T_1$ processes control the source of local frequency fluctuations and for samples in which $T_2$ processes dominate. Recent two- and three-pulse spin-echo experiments of Mims et al. dramatically confirm the predictions of Lorentzian diffusion for electron paramagnetic resonances in samples with temperature-dependent diffusion, as well as with temperature-independent diffusion. "Instantaneous" diffusion caused by the action of the applied pulses is predicted by our model and explains features of Mims' data. The generality of our principal results still permits the outcome of various resonance experiments to be predicted, even when a simple dipolar interaction is no longer an adequate model.