Septuple Layers Research Articles

Layer-polarized anomalous Hall effect in the MnBi[formula omitted]Te[formula omitted]/In[formula omitted]Se[formula omitted] (In[formula omitted]Te[formula omitted]) heterostructures

The layer-polarized anomalous Hall effect has emerged as a novel phenomenon in the field of condensed matter physics, holding significant promise for future applications in designing low-dissipation devices. Currently, the layer-polarized anomalous Hall effect has been theoretically predicted or experimentally demonstrated through the application of external electric fields or the utilization of sliding ferroelectricity in diverse systems. Here, through first-principles calculations, we propose a pathway to realize the layer-polarized anomalous Hall effect by constructing A-type antiferromagnetic topological insulator MnBi2Te4 based heterostructures with ferroelectric materials In2Se3/In2Te3. Our results firstly show that the sizeable band splitting (larger than 20 meV) appears in the antiferromagnetic 4 septuple layers MnBi2Te4/In2Se3 system due to broken inversion symmetry. Further calculations approve that the layer-polarized anomalous Hall conductivity with reversal signs can be observed in the antiferromagnetic 4 septuple layers MnBi2Te4/In2Se3 (In2Te3) systems by shifting the Fermi energy level. Additionally, it is also found that ferrimagnetic 4 septuple layers MnBi2Te4/In2Se3 (In2Te3) can be realized by controlling the direction of ferroelectric polarization of ferroelectric materials. Thus, the resulting layer-polarized anomalous Hall effect may be switchable in our suggested systems. This work provides feasible systems for the further experimental realization of the layer-polarized anomalous Hall effect.

Even-Odd Layer-Dependent Exchange Bias Effect in MnBi2Te4 Chern Insulator Devices.

Magnetic topological materials with coexisting magnetism and nontrivial band structures exhibit many novel quantum phenomena, including the quantum anomalous Hall effect, the axion insulator state, and the Weyl semimetal phase. As a stoichiometric layered antiferromagnetic topological insulator, thin films of MnBi2Te4 show fascinating even-odd layer-dependent physics. In this work, we fabricate a series of thin-flake MnBi2Te4 devices using stencil masks and observe the Chern insulator state at high magnetic fields. Upon magnetic field training, a large exchange bias effect is observed in odd but not in even septuple layer (SL) devices. Through theoretical calculations, we attribute the even-odd layer-dependent exchange bias effect to the contrasting surface and bulk magnetic properties of MnBi2Te4 devices. Our findings reveal the microscopic magnetic configuration of MnBi2Te4 thin flakes and highlight the challenges in replicating the zero magnetic field quantum anomalous Hall effect in odd SL MnBi2Te4 devices.

Topology-Engineered Orbital Hall Effect in Two-Dimensional Ferromagnets.

Recent advances in the manipulation of the orbital angular momentum (OAM) within the paradigm of orbitronics presents a promising avenue for the design of future electronic devices. In this context, the recently observed orbital Hall effect (OHE) occupies a special place. Here, focusing on both the second-order topological and quantum anomalous Hall insulators in two-dimensional ferromagnets, we demonstrate that topological phase transitions present an efficient and straightforward way to engineer the OHE, where the OAM distribution can be controlled by the nature of the band inversion. Using first-principles calculations, we identify Janus RuBrCl and three septuple layers of MnBi2Te4 as experimentally feasible examples of the proposed mechanism of OHE engineering by topology. With our work, we open up new possibilities for innovative applications in topological spintronics and orbitronics.

Unveiling the Anomalous Hall Response of the Magnetic Structure Changes in the Epitaxial MnBi2Te4 Films.

Recently discovered as an intrinsic antiferromagnetic topological insulator, MnBi2Te4 has attracted tremendous research interest, as it provides an ideal platform to explore the interplay between topological and magnetic orders. MnBi2Te4 displays distinct exotic topological phases that are inextricably linked to the different magnetic structures of the material. In this study, we conducted electrical transport measurements and systematically investigated the anomalous Hall response of epitaxial MnBi2Te4 films when subjected to an external magnetic field sweep, revealing the different magnetic structures stemming from the interplay of applied fields and the material's intrinsic antiferromagnetic (AFM) ordering. Our results demonstrate that the nonsquare anomalous Hall loop is a consequence of the distinct reversal processes within individual septuple layers. These findings shed light on the intricate magnetic structures in MnBi2Te4 and related materials, offering insights into understanding their transport properties and facilitating the implementation of AFM topological electronics.

Electrically Controlled Anomalous Hall Effect and Orbital Magnetization in Topological Magnet MnBi_{2}Te_{4}.

We propose an intrinsic mechanism to understand the even-odd effect, namely, opposite signs of anomalous Hall resistance and different shapes of hysteresis loops for even and odd septuple layers (SLs), of MBE-grown MnBi_{2}Te_{4} thin films with electron doping. The nonzero hysteresis loops in the anomalous Hall effect and magnetic circular dichroism for even-SLs MnBi_{2}Te_{4} films originate from two different antiferromagnetic (AFM) configurations with different zeroth Landau level energies of surface states. The complex form of the anomalous Hall hysteresis loop can be understood from two magnetic transitions, a transition between two AFM states followed by a second transition to the ferromagnetic state. Our model also clarifies the relationship and distinction between axion parameter and magnetoelectric coefficient, and shows an even-odd oscillation behavior of magnetoelectric coefficients in MnBi_{2}Te_{4} films.

CoX2Y4: a family of two-dimensional magnets with versatile magnetic order.

Two-dimensional (2D) magnetic materials offer a promising platform for nanoscale spintronics and for exploration of novel physical phenomena. Here, we predict a diverse range of magnetic orders in cobalt-based 2D single septuple layers CoX2Y4, namely, CoBi2Te4, CoBi2Se2Te2, CoBi2Se4, and CoSb2Te4. Notably, CoBi2Te4 presents intrinsic non-collinear antiferromagnetism (AFM), while the others display collinear AFM. The emergence of AFM in all CoX2Y4 materials is attributed to the antiferromagnetic 90° Co-Te(Se)-Co superexchange coupling. The origin of non-collinear/collinear orders lies in competing Heisenberg exchange interactions within the Co triangular lattice. A pivotal factor governing the non-collinear order of CoBi2Te4 is the vanishingly small ratio of exchange coupling between next-nearest neighbour Co and the nearest neighbour Co (J2/J1 ∼ 0.01). Furthermore, our investigation into strain effects on CoX2Y4 lattices demonstrates the tunability of the magnetic state of CoSb2Te4 from collinear to non-collinear. Our prediction of the unique non-collinear AFM in 2D suggests the potential for observing extraordinary magnetic phenomena in 2D, including non-collinear scattering and magnetic domain walls.

Structural and topological phase transitions in Se doping-controlled intrinsic magnetic topological material FeBi2Te4

Defects profoundly affect the magnetic, electronic structure and topological behaviour of intrinsic magnetic topological insulators. Here, we investigate the magnetic, structural stability and topological properties of different Te atomic sites in the intrinsic magnetic topological insulator FeBi2Te4 with Se substitution of the FM-z magnetic order. When Se replaces the outermost site of the septuple layer (the Te atomic layer connected by van der Waals bonds), the Se–Bi bond length formed with its nearest neighbour Bi is drastically shortened and the lattice constant and volume contract accordingly. We speculate that this defect-induced chemical bond enhancement is related to the strong electronegativity of Se over Te. In contrast, the system has lower formation energy, a more stable structure, and enhanced magnetic moment when Se replaces the Te atomic layer inside the septuple layer. Also, we reveal a variety of topological phase transitions due to substitution defects. FeBi2Te4 is considered to belong to the topological classification of higher-order topological insulators with z 4 = 2. The system after Se substitution can be transformed into Weyl semimetals, strong 3D topological insulators, and unknown topological materials without symmetry-base indicators, respectively.

Theoretical investigation of the electronic structure and thermoelectric performance of 2D GeSb2Te4 and GeBi2Te4

Thermoelectric technology is attractive for waste heat recovery and clean energy; it is highly desired as a potential power supply. In this paper, we investigated the stability, elastic, electronic structures and thermoelectric properties of unexplored 2D materials, GeSb2Te4 and GeBi2Te4, which deliver high stability, acceptable cleavage energies (0.32–0.33 J/m2), and narrow band gaps of 0.80 and 0.69 eV. We also revealed that the septuple layers possess anisotropic electron and hole mobilities of about 1593.71/791.50 and 522.04/240.52 cm2/Vs, which result in high conductivities of 107–108 S/m, as well as desirable thermoelectric power factors of 28.08–70.382 mW/Km2. Besides, owing to the low group velocities and strong dissipative scattering for low-lying phonons, the materials inherit the low lattice thermal conductivities of 1.51 and 0.41 W/mK. As a result, their thermoelectric figure of merit reaches 1.60 and 1.70 at 300 K, and rises further to 3.80 and 4.16 at 700 K. Together, 2D GeSb2Te4 and GeBi2Te4 are suitable candidates for low-medium temperature thermoelectric application.

Evolution of Mn1-xGexBi2Te4 Electronic Structure under Variation of Ge Content.

One of the approaches to manipulate MnBi2Te4 properties is the magnetic dilution, which inevitably affects the interplay of magnetism and band topology in the system. In this work, we carried out angle-resolved photoemission spectroscopy (ARPES) measurements and density functional theory (DFT) calculations for analysing changes in the electronic structure of Mn1-xGexBi2Te4 that occur under parameter x variation. We consider two ways of Mn/Ge substitution: (i) bulk doping of the whole system; (ii) surface doping of the first septuple layer. For the case (i), the experimental results reveal a decrease in the value of the bulk band gap, which should be reversed by an increase when the Ge concentration reaches a certain value. Ab-initio calculations show that at Ge concentrations above 50%, there is an absence of the bulk band inversion of the Te pz and Bi pz contributions at the Γ-point with significant spatial redistribution of the states at the band gap edges into the bulk, suggesting topological phase transition in the system. For case (ii) of the vertical heterostructure Mn1-xGexBi2Te4/MnBi2Te4, it was shown that an increase of Ge concentration in the first septuple layer leads to effective modulation of the Dirac gap in the absence of significant topological surface states of spatial redistribution. The results obtained indicate that surface doping compares favorably compared to bulk doping as a method for the Dirac gap value modulation.

Fermi-level dependence of magnetism and magnetotransport in the magnetic topological insulators Bi2Te3 and BiSbTe3 containing self-organized MnBi2Te4 septuple layers

The magnetic coupling mechanisms underlying ferromagnetism and magnetotransport in magnetically doped topological insulators (TIs) have been a central issue to gain controlled access to the magnetotopological phenomena such as the quantum anomalous Hall effect (AHE) and the topological axion insulating state. Here, we focus on the role of bulk carriers in magnetism of the family of magnetic TIs, in which the host material is either ${\mathrm{Bi}}_{2}{\mathrm{Te}}_{3}$ or $\mathrm{BiSb}{\mathrm{Te}}_{3}$, containing Mn self-organized in $\mathrm{Mn}{\mathrm{Bi}}_{2}{\mathrm{Te}}_{4}$ septuple layers. We tune the Fermi level using the electron irradiation technique and study how magnetic properties vary through the change in carrier density; the role of the irradiation defects is also discussed. Ferromagnetic resonance spectroscopy and magnetotransport measurements show no effect of the Fermi-level position on the magnetic anisotropy field and the Curie temperature, respectively, excluding bulk magnetism based on a carrier-mediated process. Furthermore, the magnetotransport measurements show that the AHE is dominated by the intrinsic and dissipationless Berry-phase-driven mechanism, with the Hall resistivity enhanced near the bottom/top of the conduction/valence band, due to the Berry curvature which is concentrated near the avoided band crossings. These results demonstrate that the AHE can be effectively managed, maximized, or turned off by adjusting the Fermi level.

High Curie temperature ferromagnetic structures of (Sb2Te3)1−x(MnSb2Te4)x with x = 0.7–0.8

Magnetic topological materials are promising for realizing novel quantum physical phenomena. Among these, bulk Mn-rich MnSb2Te4 is ferromagnetic due to MnSb antisites and has relatively high Curie temperatures (TC), which is attractive for technological applications. We have previously reported the growth of materials with the formula (Sb2Te3)1−x(MnSb2Te4)x, where x varies between 0 and 1. Here we report on their magnetic and transport properties. We show that the samples are divided into three groups based on the value of x (or the percent septuple layers within the crystals) and their corresponding TC values. Samples that contain x < 0.7 or x > 0.9 have a single TC value of 15–20 K and 20–30 K, respectively, while samples with 0.7 < x < 0.8 exhibit two TC values, one (TC1) at ~ 25 K and the second (TC2) reaching values above 80 K, almost twice as high as any reported value to date for these types of materials. Structural analysis shows that samples with 0.7 < x < 0.8 have large regions of only SLs, while other regions have isolated QLs embedded within the SL lattice. We propose that the SL regions give rise to a TC1 of ~ 20 to 30 K, and regions with isolated QLs are responsible for the higher TC2 values. Our results have important implications for the design of magnetic topological materials having enhanced properties.

Intermixing-Driven Surface and Bulk Ferromagnetism in the Quantum Anomalous Hall Candidate MnBi6 Te10.

The recent realizations of the quantum anomalous Hall effect (QAHE) in MnBi2 Te4 and MnBi4 Te7 benchmark the (MnBi2 Te4 )(Bi2 Te3 )n family as a promising hotbed for further QAHE improvements. The family owes its potential to its ferromagnetically (FM) ordered MnBi2 Te4 septuple layers (SLs). However, the QAHE realization is complicated in MnBi2 Te4 and MnBi4 Te7 due to the substantial antiferromagnetic (AFM) coupling between the SLs. An FM state, advantageous for the QAHE, can be stabilized by interlacing the SLs with an increasing number n of Bi2 Te3 quintuple layers (QLs). However, the mechanisms driving the FM state and the number of necessary QLs are not understood, and the surface magnetism remains obscure. Here, robust FM properties in MnBi6 Te10 (n = 2) with Tc ≈ 12 K are demonstrated and their origin is established in the Mn/Bi intermixing phenomenon by a combined experimental and theoretical study. The measurements reveal a magnetically intact surface with a large magnetic moment, and with FM properties similar to the bulk. This investigation thus consolidates the MnBi6 Te10 system as perspective for the QAHE at elevatedtemperatures.

Direct observation of cation diffusion driven surface reconstruction at van der Waals gaps

Weak interlayer van der Waals (vdW) bonding has significant impact on the surface/interface structure, electronic properties, and transport properties of vdW layered materials. Unraveling the complex atomistic dynamics and structural evolution at vdW surfaces is therefore critical for the design and synthesis of the next-generation vdW layered materials. Here, we show that Ge/Bi cation diffusion along the vdW gap in layered GeBi2Te4 (GBT) can be directly observed using in situ heating scanning transmission electron microscopy (STEM). The cation concentration variation during diffusion was correlated with the local Te6 octahedron distortion based on a quantitative analysis of the atomic column intensity and position in time-elapsed STEM images. The in-plane cation diffusion leads to out-of-plane surface etching through complex structural evolutions involving the formation and propagation of a non-centrosymmetric GeTe2 triple layer surface reconstruction on fresh vdW surfaces, and GBT subsurface reconstruction from a septuple layer to a quintuple layer. Our results provide atomistic insight into the cation diffusion and surface reconstruction in vdW layered materials.

Van der Waals Engineering of Ultrafast Carrier Dynamics in Magnetic Heterostructures

Heterostructures composed of the intrinsic magnetic topological insulator MnBi2Te4 and its nonmagnetic counterpart Bi2Te3 host distinct surface electronic band structures depending on the stacking order and exposed termination. Here, we probe the ultrafast dynamical response of MnBi2Te4 and MnBi4Te7 following near-infrared optical excitation using time- and angle-resolved photoemission spectroscopy and disentangle surface from bulk dynamics based on density functional theory slab calculations of the surface-projected electronic structure. We gain access to the out-of-equilibrium charge carrier populations of both MnBi2Te4 and Bi2Te3 surface terminations of MnBi4Te7, revealing an instantaneous occupation of states associated with the Bi2Te3 surface layer followed by carrier extraction into the adjacent MnBi2Te4 layers with a laser fluence-tunable delay of up to 350 fs. The ensuing thermal relaxation processes are driven by phonon scattering with significantly slower relaxation times in the magnetic MnBi2Te4 septuple layers. The observed competition between interlayer charge transfer and intralayer phonon scattering demonstrates a method to control ultrafast charge transfer processes in MnBi2Te4-based van der Waals compounds.

Magnetic proximity enabled bulk photovoltaic effects in van der Waals heterostructures

The bulk photovoltaic (BPV) effect, a second-order nonlinear process that generates static current under light irradiation, requires centrosymmetric broken systems as its application platform. To realize measurable BPV photocurrent in spatially centrosymmetric materials, various schemes such as chemical doping, structural deformation, or electric bias have been developed. In this paper, we suggest that the magnetic proximity effect via van der Waals (vdW) interfacial interaction, a contact-free strategy, also breaks the centrosymmetry and generates large BPV currents. Using the ${\mathrm{Bi}}_{2}{\mathrm{Te}}_{3}$ quintuple layer as an exemplary material, we show that magnetic proximity effect from $\mathrm{Mn}{\mathrm{Bi}}_{2}{\mathrm{Te}}_{4}$ septuple layers yields a finite and tunable shift and injection photocurrents. We apply group theory and first-principles calculations to evaluate the layer-specific shift and injection current generations under linearly polarized light irradiation. We find that the magnetic injection photoconductivity that localized on the ${\mathrm{Bi}}_{2}{\mathrm{Te}}_{3}$ layer can reach $&gt;70\ifmmode\times\else\texttimes\fi{}{10}^{8}\phantom{\rule{0.16em}{0ex}}\mathrm{A}/({\mathrm{V}}^{2}\phantom{\rule{0.16em}{0ex}}\mathrm{s})$, so that a one-dimensional linear current density on the order of 0.1 mA/nm can be achieved under an intermediate intensity light. In addition to charge current, we also extend our discussions into spin BPV current, giving pure photogenerated spin current. The vertical propagation direction between the charge and spin photocurrents suggests that they can be used individually in a single material. Compared with previously reported methods, the magnetic proximity effect via vdW interface does not significantly alter the intrinsic feature of the centrosymmetric material (e.g., ${\mathrm{Bi}}_{2}{\mathrm{Te}}_{3}$), and its manipulation can be easily achieved by the proximate magnetic configurations (of $\mathrm{Mn}{\mathrm{Bi}}_{2}{\mathrm{Te}}_{4}$), interlayer distance, and light polarization.

Ferromagnetic Layers in a Topological Insulator (Bi,Sb)2Te3 Crystal Doped with Mn.

Magnetic topological insulators (MTIs) have recently become a subject of poignant interest; among them, Z2 topological insulators with magnetic moment ordering caused by embedded magnetic atoms attract special attention. In such systems, the case of magnetic anisotropy perpendicular to the surface that holds a topologically nontrivial surface state is the most intriguing one. Such materials demonstrate the quantum anomalous Hall effect, which manifests itself as chiral edge conduction channels that can be manipulated by switching the polarization of magnetic domains. In the present paper, we uncover the atomic structure of the bulk and the surface of Mn0.06Sb1.22Bi0.78Te3.06 in conjunction with its electronic and magnetic properties; this material is characterized by naturally formed ferromagnetic layers inside the insulating matrix, where the Fermi level is tuned to the bulk band gap. We found that in such mixed crystals septuple layers (SLs) of Mn(Bi,Sb)2Te4 form structures that feature three SLs, each of which is separated by two or three (Bi,Sb)2Te3 quintuple layers (QLs); such a structure possesses ferromagnetic properties. The surface obtained by cleavage includes terraces with different terminations. Manganese atoms preferentially occupy the central positions in the SLs and in a very small proportion can appear in the QLs, as indirectly indicated by a reshaped Dirac cone.

Routes for the topological surface state energy gap modulation in antiferromagnetic MnBi2Te4

We have analyzed different factors responsible for changes in the Dirac gap in MnBi2Te4 and the routes that determine the possibilities of the purposeful gap modulation. It was shown that upon changing the surface van der Waals interval and surface spin–orbit coupling strength the topological surface states localization shifts between the surface septuple layers with opposite magnetizations, which leads to a nonmonotonic change in the Dirac gap size. The minimum in the Dirac gap corresponds to the point of changing the sign of the emerging exchange field. Moreover, we have shown that the Dirac gap can be effectively modulated by replacing magnetic Mn atoms in the surface layer with nonmagnetic ones or Bi and Te atoms with atoms of elements with a lower spin–orbit coupling that makes it possible to create synthetic layered topological systems with purposeful modification of the surface properties.

Electronic and Spin Structure of Topological Surface States in MnBi4Te7 and MnBi6Te10 and Their Modification by an Applied Electric Field

The electronic and spin structure of topological surface states in antiferromagnetic topological insulators MnBi4Te7 and MnBi6Te10 consisting of a sequence of magnetic MnBi2Te4 septuple layers separated by nonmagnetic Bi2Te3 quintuple layers has been calculated within the density functional theory. Features characteristic of systems with different terminations of the surface (both septuple and quintuple layers) have been analyzed and theoretical calculations have been compared with the measured dispersions of electronic states. It has been shown that a band gap of about 35–45 meV, as in MnBi2Te4, opens at the Dirac point in the structure of topological surface states in the case of the surface terminated by a magnetic septuple layer. In the case of the surface terminated by a nonmagnetic quintuple layer, the structure of topological surface states is closer to the form characteristic of Bi2Te3 with different energy shifts of the Dirac point and the formation of hybridized band gaps caused by the interaction with the lower-lying septuple layer. The performed calculations demonstrate that the band gap at the Dirac point can be changed by varying the distance between layers on the surface without a noticeable change in the electronic structure. The application of an electric field perpendicular to the surface changes the electronic and spin structure of topological surface states and can modulate the band gap at the Dirac point depending on the magnitude and direction of the applied field, which can be used in applications.

Lattice Dynamics of Bi2Те3 and Vibrational Modes in Raman Scattering of Topological Insulators MnBi2Te4·n(Bi2Te3)

This work is devoted to the experimental study and symmetry analysis of the Raman-active vibration modes in MnBi2Te4·n(Bi2Te3) van der Waals topological insulators, where n is the number of Te–Bi–Te–Bi–Te quintuple layers between two neighboring Te–Bi–Te–Mn–Te–Bi–Te septuple layers. Confocal Raman spectroscopy is applied to study Raman spectra of crystal structures with n = 0,1,2,3,4,5,6, and ∞. The experimental frequencies of vibration modes of the same symmetry in the structures with different n are compared. The lattice dynamics of free-standing one, three, and four quintuple layers, as well as of bulk Bi2Те3(n = infty ) and MnBi2Te4(n = 0), is considered theoretically. Vibrational modes of the last two systems have the same symmetry, but different displacement fields. These fields in the case of a Raman-active mode do not contain displacements of manganese atoms for any finite n. It is shown that two vibrational modes in the low-frequency region of the spectrum (35–70 cm–1) of structures with n = 1,;2,;3,;4,;5, and 6 practically correspond to the lattice dynamics of n free quintuple Bi2Те3 layers. For this reason, the remaining two vibration modes, which are observed in the high-frequency region of the spectrum (100–140 cm–1) and are experimentally indistinguishable in the sense of belonging to quintuple or septuple layer or to both layers simultaneously, should also be assigned to vibrations in quintuple layers under immobile atoms of septuple layers.

High Chern number quantum anomalous Hall effect tunable by stacking order in van der Waals topological insulators

The discovery of van der Waals (vdW) ${\mathrm{MnBi}}_{2}{\mathrm{Te}}_{4}$ provides a platform for investigating the quantum anomalous Hall effect (QAHE), which is a candidate for quantum computation without dissipation. However, because of the topological requirement, the High Chern number QAHE with extended dissipation-free channels is hard to achieve in atomically thin samples, which can take full advantage of two-dimensional (2D) materials. In this work, by first-principles calculations, the variable stacking order (inherent to vdW materials) was proposed as a means of regulating the Chern number of the QAHE in ${\mathrm{MnBi}}_{2}{\mathrm{Te}}_{4}$ (MBT). The interlayer stacking order in the 2D limit dominates the orbital hybridization, resulting in a tunable topological property. Furthermore, the High Chern number QAHE with $C=N$ was achieved in ultrathin MBT ($2N$ septuple layers) with alternate stacking orders, which have different topological states. This scenario was extended to the vdW heterostructure of MBT-family materials for achieving a stable, zero-field, High Chern number QAHE. Our work reveals stacking tunable topological properties in vdW magnetic topological insulators and provides an effective means of regulating the QAHE.