  We study topological crystalline insulators 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 ground states 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
twofold symmetry, sixfold symmetry, or eightfold 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.
