A physical interpretation of the Floquet description of magic angle spinning nuclear magnetic resonance spectroscopy

A physical interpretation of the Floquet description for magic angle spinning (MAS) nuclear magnetic resonance (NMR) is proposed. The effect of the spatial rotation on the spin system in sample spinning is analysed and described in terms of orbital angular momentum operators. The analogy between rotations in real space and in spin space is emphasized. The transformation properties of the irreducible tensors in real space are used to construct a Floquet Hamiltonian for MAS NMR, that is time independent and comprises one term associated with pure sample rotation. The remaining terms are associated with the spin system, and consist of spin-phonon type Floquet operators generating simultaneous transitions between rotational states and spin states. Finally, two different definitions for the Floquet density operator are compared.