  Spin dependent recombination in GaAsN offers many interesting possibilities
in the design of spintronic devices mostly due to its astounding capability to
reach conduction band electron spin polarizations close to 100% at room
temperature. The mechanism behind the spin selective capture of electrons in
Ga$^{2+}$ paramagnetic centers is revisited in this paper to address
inconsistencies common to most previously presented models. Primarily, these
errors manifest themselves as major disagreements with the experimental
observations of two key characteristics of this phenomenon: the effective
Overhauser-like magnetic field and the width of the photoluminescence
Lorentzian-like curves as a function of the illumination power. These features
are not only essential to understand the spin dependent recombination in GaAsN,
but are also key to the design of novel spintronic devices. Here we demonstrate
that the particular structure of the electron capture expressions introduces
spurious electron-nucleus correlations that artificially alter the balance
between the hyperfine and the Zeeman contributions. This imbalance strongly
distorts the effective magnetic field and width characteristics. In this work
we propose an alternative recombination mechanism that preserves the
electron-nucleus correlations and, at the same time, keeps the essential
properties of the spin selective capture of electrons. This mechanism yields a
significant improvement to the agreement between experimental and theoretical
results. In particular, our model gives results in very good accord with the
experimental effective Overhauser-like magnetic field and width data, and with
the degree of circular polarization under oblique magnetic fields.
