Manifestations of the absence of spin diffusion in multipulse NMR experiments on diluted dipolar solids

Puzzling anomalies previously observed in multipulse NMR experiments in natural abundance ^29Si A. E. Dementyev, D. Li, K. MacLean, and S. E. Barrett, Phys. Rev. B 68, 153302 (2003), such as long-lived spin echoes and even-odd asymmetries, are also found in polycrystalline C₆₀. Further experiments controlling the phases and tilting angles of the pulse trains, as well as analytical and numerical calculations, allowed us to explain the origin of these anomalies. We prove that the observation of long magnetization tails requires two conditions: (i) an rf field inhomogeneity or a highly inhomogeneous line able to produce different tilting angles in different sites of the sample and (ii) the absence of spin diffusion (noneffective flip-flop interactions). The last requirement is easily satisfied in diluted dipolar solids, where the frequency differences between sites, caused by disorder or other sources, are usually at least one order of magnitude larger than the dipolar couplings. Both conditions lead to the generation of stimulated echoes in Carr-Purcell (CP) and Carr-Purcell-Meiboom-Gill (CPMG) pulse trains. We show, both experimentally and theoretically, that the stimulated echoes interfere constructively or destructively with the normal (Hahn) echoes depending on the alternation or not of the pulse phases in the CP and CPMG sequences. Constructive interferences occur for the CP and CPMG sequences with and without phase alternation, respectively, which are the cases where long magnetization tails are observed. Sequences with two, three, and four pulses after the ∕2 pulse allow us to disentangle the contributions of the different echoes and show how the stimulated echoes originate the even-odd asymmetry observed in both ^29Si and C₆₀ polycrystalline samples.