Dynamic nuclear polarization and spin-diffusion in non-conducting solids

Microwave irradiation of a coupled electron-nuclear spin system can facilitate a transfer of polarization from the electron to the nuclear spin. In dielectric materials dynamic nuclear polarization (DNP) typically occurs via the solid effect,thermal mixing or the cross effect. In these systems the electron spins are localized and the non-equilibrium polarization of the bulk nuclei is generated via a two-stage process: a polarization exchange local to the defect; and spin transport to distribute the polarization throughout the sample. Here the DNP process is essentially the inverse of the standard T1 relaxation mechanism in dielectric solids. While much attention is paid to improving the local polarization transfer efficiency from the electron to the neighboring nuclear spins, usually by incorporating the appropriate electron spins in the sample, the ratelimiting step in efficiently polarizing bulk samples is frequently the spin transport from the defect sites to the bulk. As we attempt to use DNP to enhance nuclear magnetization in an ever-increasing number of systems, it is important to understand the many-spin dynamics that underly the process. As we improve our system model for describing DNP dynamics, we will eventually be able to incorporate recent developments in the theory and practice of optimal control of quantum systems to further improve our techniques. The purpose of this paper is to clarify our understanding of the spin dynamics in light of recent experiments in our laboratory. The paper begins with a description of the Bloembergen model and examines the different steps of the transport processes involved in dynamic nuclear polarization, before concluding with a review of recent experimental results. In a strong magnetic field, the Hamiltonian of a nuclear spin system, doped with electron spins is given by