  We have found that intensity $I$ and circular polarization degree $\rho$ of
the edge photoluminescence, excited in GaAsN alloys by circularly polarized
light at room temperature, grow substantially in the longitudinal magnetic
field $B$ of the order of 1\,kG. This increase depends on the intensity of
pumping and, in the region of weak or moderate intensities, may reach a twofold
value. In two-charge-state model, which considers spin-dependent recombination
of spin-oriented free electrons on deep paramagnetic centers, we included the
magnetic-field suppression of spin relaxation of the electrons bound on
centers. The model describes qualitatively the rise of $\rho$ and $I$ in a
magnetic field under different pump intensities. Experimental dependences
$\rho(B)$ and $I(B)$ are shifted with respect to zero of the magnetic field by
a value of $\sim$170\,Gauss, while the direction of the shift reverses with
change of the sign of circular polarization of pumping. As a possible cause of
the discovered shift we consider the Overhauser field, arising due to the
hyperfine interaction of an electron bound on a center with nuclei of the
crystal lattice in the vicinity of the center.
