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 { \^{}C}₄ \^{} model and the \^{} \^{} 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 { \^{}C}₄ \^{}, { \^{}C}₆ \^{}, and \^{} \^{} 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.