We present a theoretical study of optical electron-spin orientation and spin-dependent ShockleyRead-Hall recombination taking into account the hyperfine coupling between the bound-electron spin and the nuclear spin of a deep paramagnetic center. We show that the number of master rate equations for the components of the electron-nuclear spin-density matrix is considerably reduced due to the restrictions imposed by the axial symmetry of the system under consideration. The rate equations describe the Zeeman splitting of the electron spin sublevels in the longitudinal magnetic field, the spin relaxation of free and bound electrons, and the nuclear spin relaxation in the two defect states, with one and two (singlet) bound electrons. The general theory is developed for an arbitrary value of the nuclear spin I, the magnetic-field and excitation-power dependencies of the electron and nuclear spin polarizations are calculated for the particular value of I = 1/2. The role of the nuclear spin relaxation in each of the both defect states is analyzed. The circular polarization and intensity of the edge photoluminescence as well as the dynamic nuclear spin polarization as functions of the excitation power are shown to have bell-shaped forms.

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 its 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. Based on our model's results we propose an experimental protocol based on time resolved spectroscopy. It consists of a pump-probe photoluminescence scheme that would allow the detection and the tracing of the electron-nucleus flip-flops through time resolved PL measurements.

We demonstrate the detection of coherent electron-nuclear spin oscillations related to the hyperfine interaction and revealed by the band-to-band photoluminescence (PL) in zero external magnetic field. On the base of a pump-probe PL experiment we measure, directly in the temporal domain, the hyperfine constant of an electron coupled to a gallium defect in GaAsN by tracing the dynamical behavior of the conduction electron spin-dependent recombination to the defect site. The hyperfine constants and the relative abundance of the nuclei isotopes involved can be determined without the need of electron spin resonance technique and in the absence of any magnetic field. Information on the nuclear and electron spin relaxation damping parameters can also be estimated from the oscillations damping and the long delay behavior.

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