Longitudinal rotational resonance echoes in solid state nuclear magnetic resonance: Investigation of zero quantum spin dynamics

In the magic angle spinning NMR of rotating solids, it is possible to drive nuclear spin transitions by the macroscopic sample rotation. This rotational resonance phenomenon arises when the chemical shift frequency difference between two neighboring spin sites matches a small integer multiple of the sample rotation frequency. The mechanically driven spin evolution may be reversed by applying a radio-frequency pulse cycle, leading to the formation of rotational resonance echoes. A detailed theory based on a Liouville space formalism is developed. Experimental demonstrations are given for a polycrystalline sample of zinc ${}^{\mathrm{13}}{\mathrm{C}}_{\mathrm{2}}$ acetate. The decay of zero quantum coherence is examined at two different magnetic fields.