Heteronuclear polarization transfers between spin-locked and anti-longitudinal spin states in the NMR of liquids and spinning solids

Recently, a three-spin rotating-frame nuclear magnetic resonance (NMR) analog of the cross effect, whereby polarization was transferred between two 13Cs and an 15N in a single crystal, was reported. This effect is closely related to the mixed rotational and rotary resonance (MIRROR) experiment, where spin-locked magnetization (e.g., from a 13C) could introduce an “anti-longitudinal” magnetization state in neighboring 1Hs, suitable for examining spin-diffusion under magic angle spinning (MAS). The present work revisits these experiments, as applied to the proton-driven enhancement of rare spins in liquids and in solids under MAS NMR. Average Hamiltonian Theory (AHT) is used to derive the conditions needed for implementing such three-spin transfer in liquids and solids, matching, for the latter case, the conditions derived by MIRROR studies based on triple-mode Floquet theory. AHT was also found in good quantitative agreement with numerical simulations and experiments, which predict that under optimal transfer conditions whereby an I-spin RF irradiation field matches the S1–S2 chemical-shift-difference, a maximum polarization enhancement of γS/γI is achieved. Ca. half of this was effectively obtained for I = 13C in powdered solids, and ca. a quarter in multi-spin solution systems. Such processes are of a reciprocal nature, meaning that the transverse spin-locked polarization of a rare spin can also become “anti-longitudinal” ±(S1z– S2z) magnetization of abundant spins. The roles played by many-body interactions, RF inhomogeneities, fast sample spinning, and interference from other coherences during the execution of these cross-polarization experiments were investigated, and are exemplified with experiments and simulations.