Topological magnetic crystalline insulators and corepresentation theory

Gapless surface states of time reversal invariant topological insulators are protected by the antiunitary 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 antiunitary 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 corepresentation theory of magnetic crystalline symmetry groups. We construct two concrete tight-binding models of topological magnetic crystalline insulators, the ɤ4Θ model and the τΘ model, in which topological surface states and topological invariants are calculated explicitly. Moreover, we check different types of antiunitary operators in magnetic systems and find that the systems with ɤ4Θ,ɤ6Θ, and τΘ 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.