Many-body kinetics of dynamic nuclear polarization by the cross effect

Dynamic nuclear polarization (DNP) is an out-of-equilibrium method for generating nonthermal spin polarization which provides large signal enhancements in modern diagnostic methods based on nuclear magnetic resonance. A particular instance is cross-effect DNP, which involves the interaction of two coupled electrons with the nuclear spin ensemble. Here we develop a theory for this important DNP mechanism and show that the nonequilibrium nuclear polarization buildup is effectively driven by three-body incoherent Markovian dissipative processes involving simultaneous state changes of two electrons and one nucleus. We identify different parameter regimes for effective polarization transfer and discuss under which conditions the polarization dynamics can be simulated by classical kinetic Monte Carlo methods. Our theoretical approach allows simulations of the polarization dynamics on an individual spin level for ensembles consisting of hundreds of nuclear spins. The insight obtained by these simulations can be used to find optimal experimental conditions for cross-effect DNP and to design tailored radical systems that provide optimal DNP efficiency.