Two-dimensional spin-echo nuclear magnetic resonance in rotating solids

Two-dimensional spin-echo nuclear magnetic resonance (NMR) experiments on rotating powders are presented. A single π pulse in the center of the evolution period of a two-dimensional experiment produces an effective reduction of the spinning speed in an orthogonal frequency dimension. Sets of two-dimensional rotational sidebands are produced from which shielding tensors may be derived by comparison with numerical simulations. A skew projection of the 2D spectrum corresponds rigorously to the normal magic angle spinning NMR spectrum obtained at one-half the spinning speed. For small shielding tensors this corresponds to a considerable enhancement in sideband intensity, assisting the estimation of shift anisotropies without the loss in resolution associated with low actual spinning speeds. Symmetries in the intensities and phases of the 2D sidebands are shown to result from a time-domain symmetry in the powder-averaged signal. Cases where the evolution period includes two or more π pulses, and where a heteronuclear dipolar interaction is introduced, are also examined.