  Topological crystalline insulators (TCIs) can host anomalous surface states
which inherits the characteristics of crystalline symmetry that protects the
bulk topology. Especially, the diversity of magnetic crystalline symmetries
indicates the potential for novel magnetic TCIs with distinct surface
characteristics. Here, we propose a topological magnetic Dirac insulator
(TMDI), whose two-dimensional surface hosts fourfold-degenerate Dirac fermions
protected by either the $p'_c4mm$ or $p4'g'm$ magnetic wallpaper group. The
bulk topology of TMDIs is protected by diagonal mirror symmetries, which give
chiral dispersion of surface Dirac fermions and mirror-protected hinge modes.
We propose candidate materials for TMDIs including Nd$_4$Te$_8$Cl$_4$O$_{20}$
and DyB$_4$ based on first-principles calculations, and construct a general
scheme for searching TMDIs using the space group of paramagnetic parent states.
Our theoretical discovery of TMDIs will facilitate future research on magnetic
TCIs and illustrate a distinct way to achieve anomalous surface states in
magnetic crystals.

Mesoscale and Nanoscale Physics