Using angle-resolved photoemission spectroscopy (ARPES) and density functional theory (DFT), an experimental and theoretical study of changes in the electronic structure (dispersion dependencies) and corresponding modification of the energy band gap at the Dirac point (DP) for topological insulator (TI) $$\textrm{Mn}_{1-x} \textrm{Ge}_x \textrm{Bi}_2 \textrm{Te}_4$$ have been carried out with gradual replacement of magnetic Mn atoms by non-magnetic Ge atoms when concentration of the latter was varied from 10% to 75%. It was shown that when Ge concentration increases, the bulk band gap decreases and reaches zero plateau in the concentration range of 45–60% while trivial surface states (TrSS) are present and exhibit an energy splitting of 100 and 70 meV in different types of measurements. It was also shown that TSS disappear from the measured band dispersions at a Ge concentration of about 40%. DFT calculations of $$\textrm{Mn}_{1-x} \textrm{Ge}_x \textrm{Bi}_2 \textrm{Te}_4$$ band structure were carried out to identify the nature of observed band dispersion features and to analyze the possibility of magnetic Weyl semimetal state formation in this system. These calculations were performed for both antiferromagnetic (AFM) and ferromagnetic (FM) ordering types while the spin-orbit coupling (SOC) strength was varied or a strain (compression or tension) along the c-axis was applied. Calculations show that two different series of topological phase transitions (TPTs) may be implemented in this system, depending on the magnetic ordering. In the case of AFM ordering, the transition between TI and the trivial insulator phase passes through the Dirac semimetal state, whereas for FM phase such route admits three intermediate states instead of one (TI—Dirac semimetal—Weyl semimetal—Dirac semimetal—trivial insulator). Weyl points that form in the FM system along the $$\varGamma \!Z$$ direction annihilate when either the SOC strength decreases or a sufficient tensile strain is applied, which is accompanied by the corresponding TPTs. Model calculations of the influence of local magnetic ordering in AFM $$\textrm{Mn}_{1-x} \textrm{Ge}_x \textrm{Bi}_2 \textrm{Te}_4$$ were carried out by alternating Mn layers with Ge-doped layers and showed that the magnetic Weyl semimetal state in this system is reachable at a Ge concentration of approximately 40% without application of any external magnetic fields.

The presence of Rashba-like surface states (RSS) in the electronic structure of topological insulators (TIs) has been a longstanding topic of interest due to their significant impact on electronic and spin structures. In this study, we investigate the interaction between topological and Rashba-like surface states (TSS and RSS) in Mn_1-xSn_xBi_2Te_4 systems using density functional theory (DFT) calculations and high-resolution ARPES. Our findings reveal that increasing Sn concentration shifts RSS downward in energy, enhancing their influence on the electronic structure near the Fermi level. ARPES validates these predictions, capturing the evolution of RSS and their hybridization with TSS. Orbital analysis shows RSS are localized within the first three Te-Bi-Te trilayers, dominated by Bi p-orbitals, with evidence of the orbital Rashba effect enhancing spin-momentum locking. At higher Sn concentrations, RSS penetrate deeper into the crystal, driven by Sn p-orbital contributions. These results position Mn_1-xSn_xBi_2Te_4 as a tunable platform for tailoring electronic properties in spintronic and quantum technologies.

Using angle-resolved photoemission spectroscopy (ARPES) and density functional theory (DFT), an experimental and theoretical study of changes in the electronic structure (dispersion dependencies) and corresponding modification of the energy band gap at the Dirac point (DP) for topological insulator (TI) Mn_1-xGe_x Bi_2 Te_4 have been carried out with gradual replacement of magnetic Mn atoms by non-magnetic Ge atoms when concentration of the latter was varied from 10% to 75%. It was shown that when Ge concentration increases then the bulk band gap decreases and reaches zero plateau in the concentration range of 45%-60% while non-topological surface states (TSS) are present and exhibit an energy splitting of 100 and 70 meV in different types of measurements. It was also shown that TSS disappear from the measured band dispersions at a Ge concentration of about 40%. DFT calculations of Mn_1-xGe_x Bi_2 Te_4 band structure were carried out to identify the nature of observed band dispersion features and to analyze a possibility of magnetic Weyl semimetal state formation in this system. These calculations were performed for both antiferromagnetic (AFM) and ferromagnetic (FM) ordering types while the spin-orbit coupling (SOC) strength was varied or a strain (compression or tension) along the c-axis was applied. Calculations show that two different series of topological phase transitions (TPTs) may be implemented in this system depending on the magnetic ordering. At AFM ordering transition between TI and trivial insulator phase goes through the Dirac semimetal state, whereas for FM phase such route admits three intermediate states instead of one (TI - Dirac semimetal - Weyl semimetal - Dirac semimetal - trivial insulator).

The utilization of graphene on silicon carbide (SiC) substrates holds substantial promise for advancements in spintronics and nanoelectronics. Furthermore, incorporating magnetic metals provides an optimal framework for probing fundamental physical phenomena. The approach to developing such systems is in situ intercalation of graphene with magnetic metals. Herein, the electronic structure is analyzed and the magnetic properties of the system are synthesized by the thermal decomposition of 6H‐SiC(0001) surface and subsequent intercalation of graphene with cobalt (Co) and iron (Fe) atoms. X‐ray photoemission spectroscopy and low‐energy electron diffraction are employed to control the synthesis and metal intercalation processes. The morphological characteristics of the synthesized system are studied by means of atomic force microscopy. The findings derived from magneto‐optic Kerr effect measurements reveal a homogeneous ferromagnetic ordering at room temperature. Angle‐resolved photoemission spectroscopy is used to ascertain the impact of intercalation on graphene's electronic structure. The results of this study are essential for the development of graphene‐based spintronics and nanoelectronic devices as well as for fundamental studies in magnetic graphene systems.

Using angle-resolved photoemission spectroscopy (ARPES) and density functional theory (DFT), an experimental andtheoretical study of changes in the electronic structure (dispersion dependencies) and corresponding modification of the energyband gap at the Dirac point (DP) for topological insulator (TI) Mn1−xGexBi2Te4 have been carried out with gradual replacementof magnetic Mn atoms by non-magnetic Ge atoms when concentration of the latter was varied from 10% to 75%. It was shownthat when Ge concentration increases then the bulk band gap decreases and reaches zero plateau in the concentration range of45%–60% while non-topological surface states (TSS) are present and exhibit an energy splitting of 100 and 70 meV in differenttypes of measurements. It was also shown that TSS disappear from the measured band dispersions at a Ge concentrationof about 40%. DFT calculations of Mn1−xGexBi2Te4 band structure were carried out to identify the nature of observed banddispersion features and to analyze a possibility of magnetic Weyl semimetal state formation in this system. These calculationswere performed for both antiferromagnetic (AFM) and ferromagnetic (FM) ordering types while the spin-orbit coupling (SOC)strength was varied or a strain (compression or tension) along the c-axis was applied. Calculations show that two differentseries of topological phase transitions (TPTs) may be implemented in this system depending on the magnetic ordering. At AFMordering transition between TI and trivial insulator phase goes through the Dirac semimetal state, whereas for FM phase suchroute admits three intermediate states instead of one (TI — Dirac semimetal — Weyl semimetal — Dirac semimetal — trivialinsulator). Weyl points that form in FM system along the ΓZ direction annihilate when either the SOC strength decreases or asufficient tensile strain is applied, which is accompanied by the corresponding TPTs. Model calculations of local magneticordering influence in AFM Mn1−xGexBi2Te4 was carried out by alternating Mn layers and Ge-doped layers and showed that themagnetic Weyl semimetal state in this system is reachable at a Ge concentration of approximately 40% without application ofany external magnetic fields

This study investigates methods for controlling the physical properties of the intrinsic magnetic topological insulator MnBi_2Te_4 (MBT) by substituting Mn with Pb in Mn_1-xPb_xBi_2Te_4 (MPBT) solid solutions. This substitution enables tunable magnetic and electronic properties. Using various angle-resolved photoemission spectroscopy (ARPES) techniques, including spin-resolved and circular dichroism (CD) measurements, we analyzed the evolution of the electronic structure across different Pb concentrations, with a focus on topological phase transitions (TPT) near x = 50 TPT include the presence or absence of topological surface states (TSS) and bulk band gap closure. The results show a gradual decrease of the bulk band gap in the electronic structure of MPBT up to x = 40 followed by a constant gap value between 40 - 60 a PbBi_2Te_4-like electronic structure. TSS were observed at x less than 30 were absent near x = 55 semi-metallic or a trivial insulator with a narrow gap phase. These findings demonstrate the tunability of the electronic structure of MPBT, making it a promising candidate for topological and spintronic applications.

We report on in si tu investigation of Au intercalation of differ ent zero -layer graphene surface reconstructions of V V V V V V V V 6 H -SiC(0001): ( 3x 3) R 30 degrees +(6 3x6 3) R 30 degrees , (6 3x6 3) R 30 degrees +(5x5) R 0 degrees , (6 3x6 3) R 30 degrees +(5x5) R 0 degrees +Gr. We show that the most appropriate reconstruction for graphene formation via Au intercalation is a one with some fraction of initial graphene monolayer. A well -ordered epitaxial Au(111) islands on the zero -layer graphene were revealed with the same crystallographic orientation as the SiC surface. Ab initio calculations approve that the value of Rashba splitting in graphene increases with the density of Au atoms per unit cell and with the reduction of average distance between Au and graphene.

Using angle-resolved photoemission spectroscopy (ARPES) and density functional theory (DFT), an experimental and theoretical study of changes in the electronic structure (dispersion dependencies) and corresponding modification of the energy band gap at the Dirac point (DP) for topological insulator (TI) $\mathrm{Mn}_{1-x} \mathrm{Ge}_x \mathrm{Bi}_2 \mathrm{Te}_4$ have been carried out with gradual replacement of magnetic Mn atoms by non-magnetic Ge atoms when concentration of the latter was varied from 10$\%$ to 75$\%$. It was shown that when Ge concentration increases then the bulk band gap decreases and reaches zero plateau in the concentration range of 45$\%$-60$\%$ while non-topological surface states (TSS) are present and exhibit an energy splitting of 100 and 70 meV in different types of measurements. It was also shown that TSS disappear from the measured band dispersions at a Ge concentration of about 40$\%$. DFT calculations of $\mathrm{Mn}_{1-x} \mathrm{Ge}_x \mathrm{Bi}_2 \mathrm{Te}_4$ band structure were carried out to identify the nature of observed band dispersion features and to analyze a possibility of magnetic Weyl semimetal state formation in this system. These calculations were performed for both antiferromagnetic (AFM) and ferromagnetic (FM) ordering types while the spin-orbit coupling (SOC) strength was varied or a strain (compression or tension) along the $c$-axis was applied. Calculations show that two different series of topological phase transitions (TPTs) may be implemented in this system depending on the magnetic ordering. At AFM ordering transition between TI and trivial insulator phase goes through the Dirac semimetal state, whereas for FM phase such route admits three intermediate states instead of one (TI - Dirac semimetal - Weyl semimetal - Dirac semimetal - trivial insulator).

The spin-resolved dispersion dependencies for the topological insulator Mn_1-xGe_xBi_2Te_4 in the K̅Γ̅K̅' path of the Brillouin zone were studied by spin- and angle-resolved photoemission spectroscopy using laser radiation (Laser Spin-ARPES) with variation of the concentration of substitutional Ge atoms (x from 0.1 to 0.8) for in-plane (s_x) and out-of-plane (s_z) spin orientation. The formation of Rashba-like states is shown, which shift to lower energies with increasing Ge concentration. In the region of Ge concentrations from 50 contribution of these states to the formed spin-dependent dispersions becomes predominant. A pronounced in-plane (s_y) spin polarization, asymmetric for opposite ± k_∥ directions, is revealed for the Dirac cone states, while the Rashba-like states exhibit a pronounced asymmetry in both in-plane (s_y) and out-of-plane (s_z) spin polarizations. Theoretical calculations confirmed the asymmetric polarization of the Rashba-like states formed in the K̅Γ̅K̅' path of the BZ, simultaneously for in-plane and out-of-plane spin orientation. Constant energy maps for Rashba-like states show a pronounced s_z spin component along the Γ̅K̅ direction, with a sign change as the contour crosses the Γ̅M̅ direction. The observed spin polarization can influence the development of spin devices based on magnetic topological insulators.

The possibility of changing the bandgap value of topological surface states in materials based on the MnBi2Te4 intrinsic antiferromagnetic topological insulator is investigated using ab initio calculations. These materials are produced by the substitution of nonmagnetic chemical elements (A = Si, Ge, Sn, Pb) for magnetic metal atoms (Mn) in the surface (Mn1 – xAxBi2Te4/MnBi2Te4) septuple layer. The results exhibit a s-ignificant modulation of the bandgap in a wide range from 60 meV to 0 meV with an increase in the doping level x. Moreover, it is found that the bandgap behavior depends on a dopant. Namely, a monotonic dependence of the bandgap on x is found for Si and Ge, whereas the bandgap minimum at x = 0.75 exists for Sn and Pb. The results obtained in this work suggest that the main mechanism of the bandgap modulation in the materials under study is a change in the localization of topological surface states.

MnBi2Te4, Mn(Bi,Sb)2Te4, and MnBi2Te4(Bi2Te3)m (m ≥ 1) are assigned to magnetic topological insulators. Successful application of these materials in nanoelectronic devices calls for comprehensive investigation of their electronic structure and magnetic properties in dependence of the Bi/Sb atomic ratio and the number m of Bi2Te3 blocks. The magnetic properties of the surface of MnBi2Te4, MnBi4Te7, and Mn(Bi _1-x Sbx)2Te4 compounds (x = 0.43 and 0.32) have been studied using the magneto-optical Kerr effect. It is shown that the temperatures of magnetic transitions on the surface and in the bulk of MnBi4Te7 and Mn(Bi, Sb)2Te4 differ significantly.

Meeting of non-trivial topology with magnetism results in novel phases of matter, such as quantum anomalous Hall (QAH) or axion insulator phases. Even more exotic states with high and tunable Chern numbers are expected at the contact of intrinsic magnetic topological insulators (IMTIs) and 2D topological insulators (TIs). Here we synthesize a heterostructures composed of 2D TI and 3D IMTIs, specifically of bismuth bilayer on top of MnBi2Te4-family of compounds and study their electronic properties by means of angle-resolved photoelectron spectroscopy (ARPES) and density functional theory (DFT). The epitaxial interface is characterized by hybridized Bi and IMTI electronic states. The Bi bilayer-derived states on different members of MnBi2Te4-family of materials are similar, except in the region of mixing with the topological surface states of the substrate. In that region, the new, substrate dependent interface Dirac state is observed. Our ab initio calculations show rich interface phases with emergence of exchange split 1D edge states, making the Bi/IMTI heterostructures promising playground for observation of novel members in the family of quantum Hall effects.

Meeting of non-trivial topology with magnetism results in novel phases of matter, such as Quantum Anomalous Hall (QAH) or axion insulator phases. Even more exotic states with high and tunable Chern numbers are expected at the contact of intrinsic magnetic topological insulators (IMTIs) and 2D topological insulators (TIs).Here we synthesize a heterostructures composed of 2D TI and 3D IMTIs, specifically of bismuth bilayer on top of MnBi$_2$Te$_4$-family of compounds and study their electronic properties by means of angle-resolved photoelectron spectroscopy (ARPES) and density functional theory (DFT). The epitaxial interface is characterized by hybridized Bi and IMTI electronic states. The Bi bilayer-derived states on different members of MnBi$_2$Te$_4$-family of materials are similar, except in the region of mixing with the topological surface states of the substrate. In that region, the new, substrate dependent interface Dirac state is observed. Our \emph{ab initio} calculations show rich interface phases with emergence of exchange split 1D edge states, making the Bi/IMTI heterostructures promising playground for observation of novel members in the family of quantum Hall effects.

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.

An Erratum to this paper has been published: https://doi.org/10.1134/S0021364023340015

We investigated the magnetic properties of antiferromagnetic (AFM) topological insulator MnBi$_2$Te$_4$ with partial substitution of Mn atoms by non-magnetic elements (A$_x^{IV}$ = Ge, Pb, Sn). Samples with various element concentrations (10-80%) were studied using SQUID magnetometry. The results demonstrate that, for all substitutes the type of magnetic ordering remains AFM, while the Nèel temperature (T$_N$) and spin-flop transition field (H$_{SF}$) decrease with increasing A$_x^{IV}$ = Ge, Pb, Sn concentration. The rate of decrease varies among the elements, being highest for Pb, followed by Sn and Ge. This behavior is attributed to combined effects of magnetic dilution and lattice parameter increase on magnetic properties, most prominent in (Mn$_{1−x}$Pb$_x$)Bi$_2$Te$_4$. Besides this, the linear approximation of experimental data of T$_N$ and H$_{SF}$ suggests higher magnetic parameters for pure MnBi$_2$Te$_4$ than observed experimentally, indicating the possibility of their non-monotonic variation at low concentrations and the potential for enhancing magnetic properties through doping MnBi$_2$Te$_4$ with small amounts of nonmagnetic impurities. Notably, the (Mn$_{1−x}$Pb$_x$)Bi$_2$Te$_4$ sample with 10% Pb substitution indeed exhibits increased magnetic parameters, which is also validated by local analyses using ARPES. Our findings shed light on tailoring the magnetic behavior of MnBi$_2$Te$_4$-based materials, offering insights for potential applications in device technologies.

The joint intercalation of Co and Fe atoms under a graphene buffer layer synthesized on a SiC(0001) single crystal has been studied. Intercalation has been performed by means of the alternating deposition of ultrathin Fe and Co metal films on the substrate heated to 450°C with the subsequent heating to 600°C in 15 min. It has been shown that Co and Fe atoms under these conditions are intercalated under graphene, forming compounds with silicon and with each other. The existence of a magnetic order in the system up to room temperature has been demonstrated using a superconducting quantum interferometer. A possible stoichiometry of the formed alloys has been analyzed using data on the shape and magnitude of hysteresis loops. In addition, it has been found that Fe and Co in the system exposed to the atmosphere are not oxidized. Thus, graphene protects the formed system. This study makes contribution to the investigation of graphene in contact with magnetic metals and promotes its application in spintronic and nanoelectronic devices.

The antiferromagnetic ordering that MnBi2Te4 shows makes it invariant with respect to the combination of the time-reversal and primitive-lattice translation symmetries, giving rise to its topologically nontrivial nature and a number of fundamental phenomena. At the same time, the possibility to control the electronic and magnetic properties of this system can provide new effective ways for its application in devices. One of the approaches to manipulate MnBi2Te4 properties is the partial substitution of magnetic atoms in the compound with atoms of non-magnetic elements, which inevitably affect the interplay of magnetism and band topology in the system. In this work, we have carried out theoretical modelling of changes in the electronic structure that occur as a result of increasing the concentration of Sn atoms at Mn positions in the (Mn1−xSnx)Bi2Te4 compound both using Korringa–Kohn–Rostoker (KKR) Green’s function method as well as the widespread approach of using supercells with impurity in DFT methods. The calculated band structures were also compared with those experimentally measured by angle-resolved photoelectron spectroscopy (ARPES) for samples with x values of 0, 0.19, 0.36, 0.52 and 0.86. We assume that the complex hybridization of Te-pz and Bi-pz orbitals with Sn and Mn ones leads to a non-linear dependence of band gap on Sn content in Mn positions, which is characterized by a plateau with a zero energy gap at some concentration values, suggesting possible topological phase transitions in the system.

We investigated the magnetic properties of the antiferromagnetic (AFM) topological insulator MnBi2Te4 with a partial substitution of Mn atoms by non-magnetic elements (AIV = Ge, Pb, Sn). Samples with various element concentrations (10–80%) were studied using SQUID magnetometry. The results demonstrate that, for all substitutes the type of magnetic ordering remains AFM, while the Néel temperature (TN) and spin-flop transition field (HSF) decrease with an increasing AIV = Ge, Pb, Sn concentration. The rate of decrease varies among the elements, being highest for Pb, followed by Sn and Ge. This behavior is attributed to the combined effects of the magnetic dilution and lattice parameter increase on magnetic properties, most prominent in (Mn1−xPbx)Bi2Te4. Besides this, the linear approximation of the experimental data of TN and HSF suggests higher magnetic parameters for pure MnBi2Te4 than observed experimentally, indicating the possibility of their non-monotonic variation at low concentrations and the potential for enhancing magnetic properties through doping MnBi2Te4 with small amounts of nonmagnetic impurities. Notably, the (Mn1−xPbx)Bi2Te4 sample with 10% Pb substitution indeed exhibits increased magnetic parameters, which is also validated by local-probe analyses using ARPES. Our findings shed light on tailoring the magnetic behavior of MnBi2Te4-based materials, offering insights into the potential applications in device technologies.