Surface Magnetism in Topological Crystalline Insulators

Topological crystalline insulators (TCI's) are a class of materials in which the energy bands can host non-trivial topology protected by a crystalline symmetry rather than by time reversal symmetry as in the case of usual topological insulators. By deriving an analytic surface theory and numerical simulations, we study TCT's doped with magnetic impurities, in which ferromagnetism at the surface lowers the electronic energy by spontaneous breaking of a crystalline symmetry. The number of energetically equivalent groundstates is sensitive to the crystalline symmetry of the surface, as well as the precise density of electrons at the surface. We show that for a SnTe model in the topological state, magnetic states can have two-fold, six-fold symmetry, or eight-fold degenerate minima. We compute spin stiffnesses within the model to demonstrate the stability of ferromagnetic states, and consider their ramifications for thermal disordering. Possible experimental consequences of the surface magnetism are discussed.