  Altermagnets feature vanishing net magnetization, like antiferromagnets, but
exhibit time-reversal symmetry breaking and momentum-dependent spin-split band
structures. Motivated by the prevalence of altermagnetic materials with
non-symmorphic symmetry-dictated band degeneracies, we provide realistic
minimal models for altermagnetism by constructing tight-binding models for
nonsymmorphic space groups with a sublattice defined by two magnetic atoms.
These models can be applied to monoclinic, orthorhombic, tetragonal,
rhombohedral, hexagonal, and cubic materials and can describe d-wave, g-wave,
and i-wave altermagnetism. By examining the altermagnetic susceptibility and
mean field instabilities within a Hubbard model we reveal that these models
have altermagnetic ground states and yield a Berry curvature that is linear in
the spin-orbit coupling. We apply our models to RuO$_2$, MnF$_2$, FeSb$_2$,
$\kappa$-Cl, CrSb, and MnTe.
