  Gapless surface states of time reversal invariant topological insulators are
protected by the anti-unitary nature of the time reversal operation. Very
recently, this idea was generalized to magnetic structures, in which time
reversal symmetry is explicitly broken, but there is still an anti-unitary
symmetry operation combining time reversal symmetry and crystalline symmetry.
These topological phases in magnetic structures are dubbed "topological
magnetic crystalline insulators". In this work, we present a general theory of
topological magnetic crystalline insulators in different types of magnetic
crystals based on the co-representation theory of magnetic crystalline symmetry
groups. We construct two concrete tight-binding models of topological magnetic
crystalline insulators, the $\hat{C}_4\Theta$ model and the $\hat{\bf
\tau}\Theta$ model, in which topological surface states and topological
invariants are calculated explicitly. Moreover, we check different types of
anti-unitary operators in magnetic systems and find that the systems with
$\hat{C}_4\Theta$, $\hat{C}_6\Theta$ and $\hat{\bf \tau}\Theta$ symmetry are
able to protect gapless surface states. Our work will pave the way to search
for topological magnetic crystalline insulators in realistic magnetic
materials.
