Long-lived selective spin echoes in dipolar solids under periodic and aperiodic π -pulse trains

The application of Carr-Purcell-Meiboom-Gill (CPMG) π trains for dynamically decoupling a system from its environment has been extensively studied in a variety of physical systems. When applied to dipolar solids, recent experiments have demonstrated that CPMG pulse trains can generate long-lived spin echoes. In this work, we develop a theory to describe the spin dynamics in a dipolar coupled spin-12 system under a CPMG(φ1,φ2) pulse train, where φ1 and φ2 are the phases of the π pulses. From our theoretical framework, the propagator for the CPMG(φ1,φ2) pulse train is equivalent to an effective "pulsed" spin locking of single-quantum coherences with phase ±φ2-3φ12, which generates a periodic quasiequilibrium that corresponds to the long-lived echoes. Numerical simulations, along with experiments on both magnetically dilute, random spin networks found in C60 and C70 and in nondilute spin systems found in adamantane and ferrocene, were performed and confirm the predictions from the proposed theory.