  Using non-equilibrium molecular dynamics simulations, we study the rheology
of a model hybrid mixture of liquid crystals (LCs) and dipolar soft spheres
(DSS) representing magnetic nanoparticles. The bulk isotropic LC-DSS mixture is
sheared with different shear rates using Lees-Edwards periodic boundary
conditions. The steady-state rheological properties and the effect of the shear
on the microstructure of the mixture are studied for different strengths of the
dipolar coupling, $\lambda$, among the DSS. We find that at large shear rates,
the mixture shows a shear-thinning behavior for all considered values of
$\lambda$. At low and intermediate values of $\lambda$, a crossover from
Newtonian to non-Newtonian behavior is observed as the rate of applied shear is
increased. In contrast, for large values of $\lambda$, such a crossover is not
observed within the range of shear rates considered. Also, the extent of the
non-Newtonian regime increases as $\lambda$ is increased. These features can be
understood via the shear-induced changes of the microstructure. In particular,
the LCs display a shear-induced isotropic-to-nematic transition at large shear
rates with a shear-rate dependent degree of nematic ordering. The DSS show a
shear-induced nematic ordering only for large values of $\lambda$, where the
particles self-assemble into chains. Moreover, at large $\lambda$ and low shear
rates, our simulations indicate that the DSS form ferromagnetic domains.
