  Precession frequencies measured by optically pumped scalar magnetometers are
dependent on the relative angle between the sensor and the external magnetic
field. This dependence is known to be induced mainly by the nonlinear Zeeman
effect and the orientation-dependent light shift, resulting in the so-called
heading errors if the magnetic field orientation is not well known or is not
stable. In this work, we find that the linear nuclear Zeeman effect has also a
significant impact on the heading errors. It not only shifts the precession
frequency but causes asymmetry: the heading error for sensors orienting in the
upper-half plane with respect to the external field is different from the case
when the sensors work in the lower-half plane. This heading error also depends
on the relative direction of the probe laser to the driving magnetic field.
With a left-handed circularly-polarized pump laser, when the probe laser is
parallel to the driving field, the angular dependence of the precession
frequency is smaller when the sensor is in the upper plane. Otherwise, when
they are perpendicular to each other, the heading error is smaller when the
sensor is in the lower plane. Furthermore, to suppress the heading error, we
propose to utilize a small magnetic field along the propagation direction of
the pump laser. By tuning the magnitude of this auxiliary field, the
heading-error curve is flattened around different angles, which can increase
the accuracy in practice when the magnetometer works around a certain
orientation angle.
