  We present a new type of three-dimensional essential Dirac semimetal with
magnetic ordering. The Dirac points are protected by the magnetic space groups
and cannot be gapped without lowering such symmetries, where the combined
antiunitary symmetry of half-translation operator and time-reversal plays an
essential role. We introduce two explicit tight-binding models for space groups
$16$ and $102$, which possesses Dirac point at time-reversal-invariant momenta
of surface Brillouin zone. In contrast to the time-reversal-invariant essential
Dirac semimetal, the magnetic space groups here can be either symmorphic or
non-symmorphic, and the magnetic DSM is symmetry tuned to the boundary between
weak topologically distinct insulating phases. Interestingly, the
symmetry-breaking perturbations could lead to an ideal Weyl semimetal phase
with only two minimal Weyl points pinned exactly at the Fermi energy for
filling $\nu\in4\mathbb{Z}+2$. By reducing the dimensionality we are able to
access the Dirac and Weyl semimetal phases in two dimensions.
