Cross-Effect Dynamic Nuclear Polarization Explained: Polarization, Depolarization and Oversaturation.

The scope of this perspective is to analytically describe NMR hyper-polarization by the three-spin cross effect (CE) dynamic nuclear polarization (DNP) using an effectiveHamiltonian concept. We apply, for the first time, the bimodal operator-based Floquet theory in the Zeeman-interaction frame for two and three coupled spins to derive the known interaction Hamiltonian for CE-DNP. With a unified understanding of CE-DNP, and supported by empirical observation of the state of electron spin polarization under the given experimental conditions, we explain diverse manifestations of CE from oversaturation, enhanced hyper-polarization by broad-band saturation to nuclear spin depolarization under magic-angle spinning.