Spin-locking of half-integer quadrupolar nuclei in nuclear magnetic resonance of solids: creation and evolution of coherences.

Spin-locking of half-integer quadrupolar nuclei, such as 23Na (I=3/2) and 27Al (I=5/2), is of renewed interest owing to the development of variants of the multiple-quantum and satellite-transition magic angle spinning (MAS) nuclear magnetic resonance experiments that either utilize spin-locking directly or offer the possibility that spin-locked states may arise. However, the large magnitude and, under MAS, the time dependence of the quadrupolar interaction often result in complex spin-locking phenomena that are not widely understood. Here we show that, following the application of a spin-locking pulse, a variety of coherence transfer processes occur on a time scale of approximately 1/omegaQ before the spin system settles down into a spin-locked state which may itself be time dependent if MAS is performed. We show theoretically for both spin I=3/2 and 5/2 nuclei that the spin-locked state created by this initial rapid dephasing typically consists of a variety of single- and multiple-quantum coherences and nonequilibrium population states and we discuss the subsequent evolution of these under MAS. In contrast to previous work, we consider spin-locking using a wide range of radio frequency field strengths, i.e., a range that covers both the "strong-field" (omega1 >> omegaQPAS and "weak-field" (omega1 << omegaQPAS limits. Single- and multiple-quantum filtered spin-locking experiments on NaNO2, NaNO3, and Al(acac)3, under both static and MAS conditions, are used to illustrate and confirm the results of the theoretical discussion.