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The nature of the magnetism brought about by Fe adatoms on the surface of thetopological insulator Bi2Se3 was examined in terms of density functionalcalculations. The Fe adatoms exhibit strong easy-axis magnetic anisotropy inthe dilute adsorption limit due to the topological surface states (TSS). Thespin 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 bythe TSS, and can be further raised to ~0.6 by an external electric field. Theapparent single-ion anisotropy of a Fe adatom is indispensable in determiningthe spin orientation.

Strong single-ion anisotropy and anisotropic interactions of magnetic adatoms induced by topological surface states