Spontaneous ferromagnetism and finite surface energy gap in the topological insulator Bi${}_2$Se${}_3$ from surface Bi${}_{\mathrm{S}\mathrm{e}}$ antisite defects

We perform ab-initio calculations on Bi${}_{\mathrm{S}\mathrm{e}}$ antisite defects in the surface of Bi${}_2$Se${}_3$, finding strong low-energy defect resonances with a spontaneous ferromagnetism, fixed to an out-of-plane orientation due to an exceptional large magnetic anisotropy energy. For antisite defects in the surface layer, we find semi-itinerant ferromagnetism and strong hybridization with the Dirac surface state, generating a finite energy gap. For deeper lying defects, such hybridization is largely absent, the magnetic moments becomes more localized, and no energy gap is present.