Steady-state free precession NMR in solids undergoing magic angle spinning

Although nuclear magnetic resonance (NMR) is well established to study crystalline and amorphous solids, such experiments are often challenged in sensitivity and resolution. A common approach to improve both of these is magic-angle spinning (MAS); another potential sensitivity-enhancing technique is Steady-State Free Precession (SSFP), an experiment that applies a train of pulses spaced by short repetition delay times, TR. It has recently been shown that, under certain conditions, SSFP could be a method of choice to tackle wide-line solids NMR. But can SSFP and MAS coexist in the same experiment? This study investigates this matter by re-examining SSFP's spin dynamics under MAS for an ensemble of isolated spins subject to a time-dependent second-rank interaction. It is found that if SSFP's interpulse time is rotor-synchronized with the sample spinning rate ωR, then the SSFP MAS response will be like that observed in solutions for identical relaxation parameters. However, without rotor synchronization, the SSFP MAS NMR magnetization behaves non-trivially. If the spin anisotropies are much larger than ωR, no steady state is in fact achieved by a single crystal's evolution. However, under similar mis-synchronization conditions, a steady state can still arise when considering spins over a powdered sample. The dependence of the ensuing steady state on the strength of the anisotropy and the degree of mis-synchronization is not monotonic; the former shows oscillations arising from a series of Bessel-derived functions, while the latter reflects a number of "resonant" dips given by the TR=π2n+1/ωRn=1,2… condition. A rationalization for these behaviors, together with supporting experimental data, is provided.