  We calculate the frequency-dependent longitudinal and Hall conductivities and
the Faraday and Kerr rotation angles for a single sheet of anisotropic Dirac
semimetal protected by nonsymmorphic symmetry in the presence of a Zeeman term
coupling to the out-of-plane component of the spin. While the Zeeman term
causes a rotation of the plane of polarization of the light, the anisotropy
causes the appearance of an elliptically polarized component in an initially
linearly polarized beam. The two effects can be combined in a single complex
Faraday rotation angle. At the zero-frequency limit, we find a finite value of
the Faraday rotation angle, which is given by $2\alpha_F$, where $\alpha_F$ is
the effective fine structure constant associated with the velocity of the
linearly dispersing Dirac fermions. We also find a logarithmic enhancement of
the Faraday (and Kerr) rotation angles as the frequency of the light approaches
the absorption edge associated with the Zeeman-induced gap. While the
enhancement is reduced by impurity scattering, it remains significant for an
attainable level of material purity. These results indicate that
two-dimensional Dirac materials protected by nonsymmorphic symmetry are
responsive to Zeeman couplings and can be used as platforms for magneto-optic
applications, such as the realization of polarization-rotating devices.
