  A four-stroke quantum Otto engine can outperform when conducted between two
thermal reservoirs, one at a positive spin temperature and the other one at an
effective negative spin temperature. Along with a magnetic field in the
(x,y)-plane, we introduce an additional magnetic field in the z-direction. We
demonstrate that the efficiency increases with the increase in the strength of
the additional magnetic field although the impact is not monotonic.
Specifically, we report a threshold value of the magnetic field, depending on
the driving time which exhibits a gain in efficiency. We argue that this
benefit may result from the system being more coherent with driving time, which
we assess using the l1-norm coherence measure. Moreover, we find that the
increment obtained in efficiency with an additional magnetic field endures even
in presence of disorder in parameter space.
