The Role of the Interaction Frame in the Theoretical Description of Solid Effect Dynamic Nuclear Polarization

The enhancement of the nuclear spin polarization generated by dynamic nuclear polarization depends on two competing processes: the perturbation of the thermal equilibrium by the applied microwave field and the tendency of relaxation processes to re‐establish the thermal state. Hence, it is important to correctly incorporate relaxation processes in the theoretical description of dynamic nuclear polarization to obtain meaningful simulations. A difficulty arises in the choice of the correct interaction frame when building an appropriate relaxation superoperator. In the Zeeman frame, the rate constants introduced to define longitudinal and transverse relaxation can become mixed if the non‐secular part of the hyperfine interaction between an electron in a paramagnetic centre and the nuclear spins is strong. Deriving the relaxation superoperator in the interaction frame that is defined by the eigenbasis of the stationary Hamiltonian eliminates this issue. However, when using this strategy, not all the non‐secular terms arising in a relaxation model based on local magnetic field fluctuations are taken properly into account if dipolar interactions between nuclear spins dominate over hyperfine interactions. An analytical treatment of this problem is presented that is corroborated by a set of numerical simulations focussing on the case of solid effect dynamic nuclear polarization. The advantage and possible errors arising when using either of the two strategies are briefly summarised and discussed.