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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.

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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.

We theoretically study the magnetic proximity effect in the three-dimensional (3D) topological insulator/ ferromagnetic insulator (TI/FMI) structures in the context of possibility to manage the Dirac helical state in TI. Within a continual approach based on the k · p Hamiltonian, we predict that, when a 3D TI is brought into contact with a 3D FMI, the ordinary bound state arising at the TI/FMI interface becomes spin polarized due to the orbital mixing at the boundary. Whereas the wave function of FMI decays into the TI bulk on the atomic scale, the induced exchange field, which is proportional to the FMI magnetization, builds up at the scale of the penetration depth of the ordinary interface state. Such an exchange field opens the gap at the Dirac point in the energy spectrum of the topological bound state existing on the TI side of the interface. We estimate the dependence of the gap size on the material parameters of the TI/FMI contact.

A possible mechanism for high-temperature ferromagnetic order in Si:Mn alloys is proposed. These materials, which are semiconducting or metallic, depending on the Mn content, are suggested to undergo phase separation. In the phase-separated state, again depending on the Mn content, Mn atoms can be gathered within nanometer-sized particles or micrometer-sized islands composed of the MnSi 2−z precipitate with z ≈ (0.25-0.30), which are embedded in the Mn-poor silicon matrix. We consider the MnSi 2−z precipitate to be the MnSi 1.7 silicide host containing a certain amount of magnetic defects associated with unbound Mn 3d orbitals. The MnSi 1.7 silicide is considered to be a weak itinerant ferromagnet, where sizable spin fluctuations (paramagnons) exist far above its intrinsic Curie temperature, leading to a strong enhancement of the exchange coupling between the local moments of the defects. As a result, a significant enhancement of the temperature of onset of long-range order among the local moments may be achieved. We associate this temperature with the global Curie temperature of the precipitate. A phenomenological model is developed to determine the spatial structures and characteristics of ferromagnetic order for the cases of a bulk precipitate and of precipitate particles of various shapes. Moreover, allowing for the presence of strong quenched disorder in the precipitate, we describe short-range ferromagnetic order in the system. Experimental data on Si:Mn alloys are interpreted on the basis of our theoretical results.

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