Electron-nuclear spin dynamics of Ga2+ paramagnetic centers probed by spin-dependent recombination: A master equation approach

Similar to nitrogen-vacancy centers in diamond and impurity atoms in silicon, interstitial gallium deep paramagnetic centers in GaAsN have been proven to have useful characteristics for the development of spintronic devices. Among other interesting properties, under circularly polarized light, gallium centers act as spin filters that dynamically polarize free and bound electrons reaching record spin polarizations (close to 100%). Furthermore, the recent observation of the amplification of the spin filtering effect under a Faraday configuration magnetic field has suggested that the hyperfine interaction that couples bound electrons and nuclei permits the optical manipulation of the nuclear spin polarization. Even though the mechanisms behind the nuclear spin polarization in gallium centers are fairly well understood, the origin of nuclear spin relaxation and the formation of an Overhauser-like magnetic field remain elusive. In this work we develop a model based on the master equation approach to describe the evolution of electronic and nuclear spin polarizations of gallium centers interacting with free electrons and holes. Our results are in good agreement with existing experimental observations. In particular, we are able to reproduce the amplification of the spin filtering effect under a circularly polarized excitation in a Faraday configuration magnetic field. In regard to the nuclear spin relaxation, the roles of nuclear dipolar and quadrupolar interactions are discussed. Our findings show that, besides the hyperfine interaction, the spin relaxation mechanisms are key to understand the amplification of the spin filtering effect and the appearance of the Overhauser-like magnetic field. To gain a deeper insight in the interplay of the hyperfine interaction and the relaxation mechanisms, we have also performed calculations in the pulsed excitation regime. Our model's results allow us to propose an experimental protocol based on time-resolved spectroscopy. It consists of a pump-probe photoluminescence scheme with the detection and the tracing of the electron-nucleus flip-flops through photoluminescence measurements.