The nature of the magnetism brought about by Fe adatoms on the surface of the topological insulator Bi2Se3 was examined in terms of density functional calculations. The Fe adatoms exhibit strong easy-axis magnetic anisotropy in the dilute adsorption
limit due to the topological surface states (TSS). The spin exchange J between the Fe adatoms follows a Ruderman-Kittel-Kasuya-Yosida (RKKY) behavior with substantial anisotropy, and the Dzyaloshinskii-Moriya (DM) interaction between them is quite strong with |D/J|~0.3 under the mediation by the TSS, and can be further raised to ~0.6 by an external electric field. The apparent single-ion anisotropy of a Fe adatom is indispensable in determining the spin orientation.
