Gaussian to exponential crossover in the attenuation of polarization echoes in NMR

Abstract

An ingenious pulse sequence devised by Zhang, S., Meier, B. H., and Ernst, R. R., 1992, Phys. Rev. Lett., 69, 2149 reverses the time evolution (‘spin diffusion’) of the local polarization in a dipolar coupled ¹H spin system. This refocusing originates a polarization echo, whose amplitude attenuates by increasing the time t _R elapsed until the dynamics are reversed. Different functional attenuations are found for a set of dipolar coupled systems: ferrocene, (C₅H₅)₂Fe, cymantrene, (C₅H₅)Mn(CO)₃, and cobaltocene, (C₅H₅)₂Co. To control a relevant variable involved in this attenuation a pulse sequence has been devised to progressively reduce the dipolar dynamics. Since it reduces the evolution of the polarization echo it is referred to as the REPE sequence. Two extreme behaviours were found while characterizing the materials. In systems with a strong source of relaxation and slow dynamics the attenuation follows an exponential law (cymantrene). In systems with strong dipolar dynamics the attenuation is mainly Gaussian. By the application of the REPE sequence the characteristic time of the Gaussian decay is increased until the presence of an underlying dissipative mechanism is revealed (cobaltocene). For ferrocene, however, the attenuation remains Gaussian within the experimental timescale. These two types of behaviour suggest that the many-body quantum dynamics present an extreme intrinsic instability which, in the presence of small perturbations, leads to the onset of irreversibility. This experimental conclusion is consistent with the tendencies displayed by the numerical solutions of model systems.