The magnetic proximity effect is a fundamental feature of heterostructures composed of layers of topological insulators and magnetic materials since it underlies many potential applications in devices with novel quantum functionality. Within density functional theory we study magnetic proximity effect at the three-dimensional topological insulator/magnetic insulator (TI/MI) interface in the Bi 2 Se 3 /MnSe(111) system as an example. We demonstrate that a gapped ordinary bound state caused by the interface potential arises in the immediate region of the interface. The gapped topological Dirac state also arises in the system owing to relocation to deeper atomic layers of topological insulator. The gap in the Dirac cone originates from an overlapping of the topological and ordinary interfacial states. This result being also corroborated by the analytic model, is a key aspect of the magnetic proximity effect mechanism in the TI/MI structures.

By means of relativistic density functional theory (DFT) calculations we study electron band structure of the topological insulator (TI) Bi 2 Se 3 thin films deposited on the ferromagnetic insulator (FMI) EuS substrate. In the Bi 2 Se 3 /EuS heterostructure, the gap opened in the spectrum of the topological state has a hybridization character and is shown to be controlled by the Bi 2 Se 3 film thickness, while magnetic contribution to the gap is negligibly small. We also analyzed the effect of Eu doping on the magnetization of the Bi 2 Se 3 film and demonstrated that the Eu impurity induces magnetic moments on neighboring Se and Bi atoms an order of magnitude larger than the substrate-induced moments. Recent magnetic and magneto-transport measurements in EuS/Bi 2 Se 3 heterostructure are discussed.