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

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Abstract
Spin-locking of half-integer quadrupolar nuclei, such as 23 Na (I=3/2) and 27 Al (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 ∼1/ω Q 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” (ω 1 ≫ω Q PAS ) and “weak-field” (ω 1 ≪ω Q PAS ) limits. Single- and multiple-quantum filtered spin-locking experiments on NaNO 2 , NaNO 3 , and Al(acac ) 3 , under both static and MAS conditions, are used to illustrate and confirm the results of the theoretical discussion.