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

The application of Carr-Purcell-Meiboom-Gill (CPMG) 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 (₁, ₂) pulse train, where ₁ and ₂ are the phases of the pulses. From our theoretical framework, the propagator for the CPMG (₁, ₂) pulse train is equivalent to an effective ``pulsed'' spin locking of single-quantum coherences with phase {₂-3₁}2, 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.