  The heading error has been known to be caused mainly by the nonlinear Zeeman
effect and the orientation-dependent light shift. In this work, we find that
the nuclear Zeeman effect can also have a significant impact on the heading
errors, especially for continuously-driving magnetometers with unresolved
magnetic transitions. It not only shifts the precession frequency but deforms
the heading errors and causes asymmetry: the heading errors for pump lasers
with opposite helicities are different. The heading error also depends on the
relative direction (parallel or vertical) of the probe laser to the RF driving
magnetic field. Thus, one can design the configuration of the magnetometer and
make it work in the smaller-heading-error regime. To suppress the heading
error, our studies suggest to sum up the output precession frequencies from
atomic cells pumped by two lasers with opposite helicities and probed by lasers
propagating in orthogonal directions (one parallel and another perpendicular to
the RF field), instead of utilizing probe lasers propagating in the same
directions. Due to the nuclear Zeeman effect, the average precession
frequencies in the latter case can have a non-negligible angular dependence,
while in the former case the nuclear-Zeeman-effect induced heading error can be
largely compensated and the residue is within 1Hz. Furthermore, for practical
use, we propose to simply utilize a small magnetic field parallel/antiparallel
to the pump laser. By tuning the magnitude of this auxiliary field, the heading
error can be flattened around different angles, which can improve the accuracy
when the magnetometer works around a certain orientation angle.
