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Today, searching for materials hosting quantum anomalous Hall effect (QAHE) at high temperature and with long conductivity plateau is an important issue for next generation spintronic applications at nanoscale. In this article, we discuss a quantized spin Hall response in heterostructures composed of a three-dimensional topological insulator (TI) film and a ferromagnetic normal insulator (FMNI). The magnetic proximity effect at the TI/FMNI interface provides exchange splitting of the topological states in the TI film. We predict analytically that the FMNI/TI/FMNI trilayer can be driven into the QAHE state either from the topologically trivial state or the quantum spin Hall state, depending on the TI film thickness and the interface potential. We calculate the corresponding phase diagram of the FMNI/TI/FMNI trilayer. Our results provide a useful guide to realize the QAHE regime in the TI/FMNI heterostructures.

We report analytic investigation of the electronic properties of heterostructures comprised by films of three-dimensional topological insulator (TI) and normal insulator (NI) revealing strong interface and size effects on their spin transport characteristics. Imposing at the TI/NI interfaces the natural boundary conditions within a continual scheme, we show that the intrinsic spin Hall response of the NI/TI/NI trilayer can be controlled by tuning the interface potential (IP) together with the TI film thickness. We predict a series of interface induced quantum transitions between topological insulating phase and trivial band insulator phase. We calculate the phase diagram of the NI/TI/NI trilayer and establish an appropriate range of the IP strength and the TI film thickness to realize the regime of quantum spin Hall effect. Our results can provide a useful guide in choosing the relevant material parameters to facilitate the detection of quantum spin Hall conductivity in the TI/NI heterostructures.

Here we study how interface and edge perturbations as well as a size effect can be used to manipulate the transport properties in semiconductor heterostructures where a thin film of three-dimensional topological insulator (TI) is sandwiched by normal insulator (NI) slabs. Within the framework of the NI/TI/NI trilayer model based on a continual scheme, we argue that characteristics of electron states in the TI film (energy spectrum, envelope function profile, the Berry curvature, etc.) are controlled by the film thickness and TI/NI interface potential whose variation can lead to the modification of topological properties of the system. Calculating a spin Hall response for the NI/TI/NI trilayer infinite in the interface plane, we find that a series of quantum transitions between topological insulating phase and trivial band insulator phase can be induced by tuning both the film thickness and the interface potential. We draw in detail the corresponding phase diagram of the NI/TI/NI trilayer, which is controlled by change of the sign of either the hybridization gap or the dispersion parameter. To quantify the edge effect, we formulate a model of the half-infinite in the interface plane NI/TI/NI trilayer, which describes evanescent edge states and provides the necessary conditions under which they exist. It is found that the presence of the in-gap edge states is ambiguously determined by the phase of the TI film. Our findings provide a useful guide in choosing the relevant material parameters to facilitate the observation of quantum spin Hall effect in the TI/NI heterostructures.

Thin films of MnxSi1-xalloys with different Mn concentration x ≈ 0.44-0.63 grown by the pulsed-laser deposition (PLD) method onto the Al2O3(0001) substrate were investigated in the temperature range 4-300 K using ferromagnetic resonance (FMR) measurements in the wide range of frequencies and magnetic fields . For samples with x ≈ 0.52-0.55, FMR data show clear evidence of ferromagnetism (FM) with high Curie temperatures Tc ∼ 300K. These samples demonstrate the complex and unusual character of magnetic anisotropy described in the frame of phenomenological model as a combination of the essential second-order easy-plane anisotropy contribution and the additional fourth-order anisotropy contribution with the easy direction normal to the film plane. We explain the obtained results by a polycrystalline (mosaic) structure of the films caused by the film-substrate lattice mismatch

In this letter we theoretically demonstrate how an interface perturbation and size effect can be used to manipulate the transport properties of semiconductor heterostructures composed of a thin film of a three-dimensional topological insulator (TI) doped with magnetic impurities and sandwiched between topologically normal insulators. In the framework of a continual scheme, we argue that electron states of the TI film are strongly dominated by its thickness and magnetization as well as by an interface potential whose variation can lead to the modification of topological properties of the heterostructure. This opens diverse possibilities to efficiently tune intrinsic Hall conductivity in the system. We calculate a phase diagram of the heterostructure, which demonstrates a series of quantum transitions between distinct regimes of conductivity. We derive the anomalous Hall conductivity and the spin Hall conductivity dependences on the chemical potential. Applicability conditions of the used approach are also discussed.

We theoretically study how magnetic modulation can be used to manipulate the transport properties of heterostructures formed by a thin film of a three-dimensional topological insulator sandwiched between slabs of a normal insulator. Employing the k ∙ p scheme, in the framework of a continual approach, we argue that electron states of the system are spin-polarized when ultrathin magnetic insertions are incorporated into the film. We demonstrate that (i) the spin-polarization magnitude depends strongly on the magnetic insertion position in the film and (ii) there is the optimal insertion position to realize quantum anomalous Hall effect, which is a function of the material parameters, the film thickness and the topological insulator/normal insulator interface potential. For the heterostructure with a pair of symmetrically placed magnetic insertions, we calculate a phase diagram that shows a series of transitions between distinct quantum regimes of transverse conductivity. We provide consistent interpretation of recent experimental findings in the context of our results.

In the framework of an effective functional approach based on the k · p method, we study the combined effect of an interface potential and a thickness of a three-dimensional (3D) topological insulator (TI) thin film on the spin Hall conductivity in layered heterostructures comprising TI and normal insulator (NI) materials. We derive an effective two-dimensional (2D) Hamiltonian of a 3D TI thin film sandwiched between two NI slabs and define the applicability limits of approximations used. The energy gap and mass dispersion in the 2D Hamiltonian, originated from the hybridization between TI/NI interfacial bound electron states at the opposite boundaries of a TI film, are demonstrated to change sign with the TI film thickness and the interface potential strength. Finally, we argue that the spin Hall conductivity can efficiently be tuned varying the interface potential characteristics and TI film thickness.

In the frame of k⋅p method and variational approach for the effective energy functional of a contact between a three-dimensional topological insulator (TI) and normal insulator (NI), we analytically describe the formation of interfacial bound electron states of two types (ordinary and topological) having different spatial distributions and energy spectra. We show that these states appear as a result of the interplay of two factors: hybridization and band bending of the TI and NI electron states near the TI/NI boundary. These results are corroborated by the density functional theory calculations for the exemplar Bi2Se3/ZnSe system.

By means of relativistic density functional theory (DFT) calculations we study electron band structure of the topological insulator (TI) Bi2Se3 thin films deposited on the ferromagnetic insulator (FMI) EuS substrate. In the Bi2Se3/EuS heterostructure, the gap opened in the spectrum of the topological state has a hybridization character and is shown to be controlled by the Bi2Se3 film thickness, while magnetic contribution to the gap is negligibly small. We also analyzed the effect of Eu doping on the magnetization of the Bi2Se3 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/Bi2Se3 heterostructure are discussed.

We apply both analytical and ab-initio methods to explore heterostructures composed of a 3D topological insulator (3D TI) and an ultrathin normal insulator (NI) overlayer as a proving ground for the principles of topological phase engineering. Using the continual model of a semi-infinite 3D TI we study the surface potential (SP) effect caused by an attached ultrathin layer of 3D NI on the formation of topological bound states at the interface. The results reveal that the spatial profile and spectrum of these near-surface states strongly depend on both the sign and the strength of the SP. Using ab-initio band structure calculations to take the specificity of the materials into account, we investigate the NI/TI heterostructures formed by a single tetradymite-type quintuple or septuple layer block and the 3D TI substrate. The analytical continuum theory results relate the near-surface state evolution with the SP variation and are in good qualitative agreement with those obtained from density-functional theory (DFT) calculations. We also predict the appearance of the quasi-topological bound state on the 3D NI surface caused by a local band gap inversion induced by an overlayer.

Using the continual model of a semi-infinite three dimensional (3D) topological insulator (TI) we study the effect of the surface potential (SP) on the formation of helical topological states near the surface. The results reveal that spatial profile and spectrum of these states strongly depend on the SP type and strength. We pay special attention to the 3D TI substrate/non-magnetic insulating overlayer system to illustrate the principles of the topological near-surface states engineering. © 2013 Pleiades Publishing, Inc.

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 Bi2Se3/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.

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.

We show that, when a three-dimensional (3D) narrow-gap semiconductor with inverted band gap ("topological insulator," TI) is attached to a 3D wide-gap semiconductor with non-inverted band gap ("normal insulator," NI), two types of bound electron states having different spatial distributions and spin textures arise at the TI/NI interface. Namely, the gapless ("topological") bound state can be accompanied by the emergence of the gapped ("ordinary") bound state. We describe these states in the framework of the envelope function method using a variational approach for the energy functional; their existence hinges on the ambivalent character of the constraint for the envelope functions that correspond to the "open" or "natural" boundary conditions at the interface. The properties of the ordinary state strongly depend on the effective interface potential, while the topological state is insensitive to the interface potential variation.

We describe the occurrence of a spin-polarized ferromagnetic state on the surface of a topological insulator with implanted 3d transition-metal atoms, within a model which takes into account the hybridization between the (s,p) orbitals of the insulator and the d orbitals of the metal, entailing the delocalized character of magnetic moments. Depending on the position of the Fermi level, the energy spectrum of this state displays both metallic and semimetallic, or semiconducting characteristics.

We report on theoretical study of the bound electron states induced by a ferromagnetic delta-layer embedded into a narrow-band-gap semiconductor of the Bi2Se3-type which is a three-dimensional topological insulator with large spin-orbit coupling. We make use of an effective Hamiltonian taking into account the inverted band structure of the semiconductor host at the Γ point and describe the properties of the in-gap bound states: energy spectrum, characteristic length and spin polarization. We highlight a role of these states for a magnetic proximity effect in digital magnetic heterostructures based on the Bi2Se3-type semiconductors. © 2012 Pleiades Publishing, Ltd.

We present a first-principles study of the electronic structure and exchange interactions in Si/Mn digital magnetic alloy (DMA) consisting of Mn monolayers embedded in a Si matrix stacking along [001] direction. The main focus of our study is on the dependence of magnetic properties on the morphology of the Mn monolayer. Three different structural models for the Mn monolayer are considered: manganese in substitutional (i), interstitial (ii), and both interstitial and substitutional (iii) positions. The atomic positions in Si/Mn DMA are determined by means of the VASP code and then serve as input for multiple-scattering calculations of the electronic and magnetic structure. The magnetic force theorem is used to evaluate the exchange coupling parameters. A Heisenberg model based on those parameters is used to estimate magnon frequencies and magnetic phase-transition temperatures for different anisotropies. The magnetic properties of Si/Mn DMA are found to be strongly dependent on the underlying crystalline structure. © 2011 American Physical Society.

We study the effect of magnetic doping at the surface of a three dimensional topological insulator (TI) on emergence of ferromagnetic ordering at the TI-surface assuming the exchange coupling between the Dirac fermions and the dilute magnetic ions. We show that this coupling results in an uniaxial magnetic anisotropy with out-of-plane magnetization direction. It is found that the system under consideration is unstable with respect to a spontaneous uniform magnetization along the easy axis, which is accompanied by opening a gap in a spectrum of the Dirac surface states. In the framework of a mean-field approach, we study the possibility of ferromagnetic order on the magnetically doped surface of TI at different temperatures and positions of the chemical potential. © 2011 Pleiades Publishing, Ltd.

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 MnSi2-z precipitate with z≈(0.25–0.30), which are embedded in the Mn-poor silicon matrix. We consider the MnSi2-z precipitate to be the MnSi1.7 silicide host containing a certain amount of magnetic defects associated with unbound Mn 3d orbitals. The MnSi1.7 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.

The ab initio investigation of the magnetic ordering in digital alloys consisting of monolayers of 3d-transition metals Ti, V, Cr, Mn, Fe, Co, and Ni introduced into the Si, Ge, and Si0.5Ge0.5 semiconductor hosts is reported. The calculations of the parameters of the exchange interactions and total-energy calculations indicate that the ferromagnetic order appears only in the manganese monolayers, whereas the antiferromagnetic order is more probable in V, Cr, and Fe monolayers, and Ti, Co, and Ni monolayers are nonmagnetic. The stability of the ferromagnetic phase in digital alloys containing manganese monolayers has been analyzed using the calculations of magnon spectra.

We carry on a theoretical investigation of the conditions for the appearance and/or modification of spin ordering in a dilute magnetic semiconductor that is in contact with a ferromagnetic metal. We show that the magnetic proximity effect has a rather complex physical nature in this system. Allowing for the hybridization between the ferromagnetic metal and semiconductor electron states, we calculate the spin polarization and spin susceptibility of carriers in the semiconductor layer near the contact. The peculiar mechanism of indirect exchange coupling that occurs between local spins dissolved in the semiconductor host when a dilute magnetic semiconductor is in contact with a ferromagnetic metal is analyzed. The structure of the proximity-induced ordering of local moments in a dilute magnetic semiconductor is qualitatively described within a mean-field approach. On the basis of our results, we interpret the experimental data on Fe/(Ga,Mn)As and Py/(Ga,Mn)As layered structures.