Spin-dependent recombination in GaAs$_{1-x}$N$_{x}$ alloys at oblique magnetic field

We have studied experimentally and theoretically the optical orientation and spin-dependent Shockley–Read–Hall recombination in a semiconductor in a magnetic field at an arbitrary angle $\alpha$ between the field and circularly polarized exciting beam. The experiments are performed at room temperature in GaAs$_{1-x}$N$_{x}$ alloys where deep paramagnetic centers are responsible for the spin-dependent recombination. The observed magnetic-field dependences of the circular polarization $\rho(\mathbf B)$ and intensity $J(\mathbf B)$ of photoluminescence can be approximately presented as a superposition of two Lorentzian contours, normal and inverted, with their half-widths differing by an order of magnitude. The normal, narrow, Lorentzian contour is associated with depolarization of the transverse (to the field) component of spin polarization of the localized electrons, whereas the inverted, broad, Lorentzian is due to suppression of the hyperfine interaction of the localized electron with the own nucleus of the defect. The ratio between the height of one Lorentzian and depth of the other is governed by the field tilt angle $\alpha$. In contrast to the hyperfine interaction of a shallow-donor-bound electron with a large number of nuclei of the crystal lattice, in the optical orientation of the electron-nuclear system under study no additional narrow peak appears in the oblique field. This result demonstrates that in the GaAsN alloys the hyperfine interaction of the localized electron with the single nucleus of the paramagnetic center remains strong even at room temperature. For a theoretical description of the experiment, we have extended the theory of spin-dependent recombination via deep paramagnetic centers with the nuclear angular momentum $I$ = 1/2 developed previously for the particular case of the longitudinal field. The calculated curves $\rho(\mathbf B)$, $J(\mathbf B)$ agree with the approximate description of the experimental dependences as a sum of two Lorentzians, and an additional narrow shifted peak does not appear in the computation as well.