Surface magnetic ordering in topological insulators with bulk magnetic dopants

We show that a three-dimensional topological insulator doped with magnetic impurities in the bulk can have a regime where the surface is magnetically ordered but the bulk is not. This is in contrast to conventional materials where bulk ordered phases are typically more robust than surface ordered phases. The difference originates from the topologically protected gapless surface states characteristic of topological insulators. We study the problem using a mean-field approach in two concrete models that give the same qualitative result, with some interesting differences. Our findings could help explain recent experimental results showing the emergence of a spectral gap in the surface state of Bi₂Se₃ doped with Mn or Fe atoms, but with no measurable bulk magnetism.