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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) 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 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 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 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.

Polar Rashba-type semiconductor BiTeI doped with magnetic elements constitutes one of the most promising platforms for the future development of spintronics and quantum computing thanks to the combination of strong spin-orbit coupling and internal ferromagnetic ordering. The latter originates from magnetic impurities and is able to open an energy gap at the Kramers point (KP gap) of the Rashba bands. In the current work using angle-resolved photoemission spectroscopy (ARPES) we show that the KP gap depends non-monotonically on the doping level in case of V-doped BiTeI. We observe that the gap increases with V concentration until it reaches 3% and then starts to mitigate. Moreover, we find that the saturation magnetisation of samples under applied magnetic field studied by superconducting quantum interference device (SQUID) magnetometer has a similar behaviour with the doping level. Theoretical analysis shows that the non-monotonic behavior can be explained by the increase of antiferromagnetic coupled atoms of magnetic impurity above a certain doping level. This leads to the reduction of the total magnetic moment in the domains and thus to the mitigation of the KP gap as observed in the experiment. These findings provide further insight in the creation of internal magnetic ordering and consequent KP gap opening in magnetically-doped Rashba-type semiconductors.

Effect of magnetization generated by synchrotron or laser radiation in magnetically-doped and pristine topological insulators (TIs) is presented and analyzed using angle-resolved photoemission spectroscopy. It was found that non-equal photoexcitation of the Dirac cone (DC) states with opposite momenta and spin orientation indicated by the asymmetry in photoemission intensity of the DC states is accompanied by the k || -shift of the DC states relative to the non-spin-polarized conduction band states located at k || = 0. We relate the observed k || -shift to the induced surface in-plane magnetic field and corresponding magnetization due to the spin accumulation. The direction of the DC k || -shift and its value are changed with photon energy in correlation with variation of the sign and magnitude of the DC states intensity asymmetry. The theoretical estimations describe well the effect and predict the DC k || -shift values which corroborate the experimental observations. This finding opens new perspectives for effective local magnetization manipulation.

The energy gap was revealed in the Dirac cone of the BiSbTeSe2 topological insulator after the submonolayer deposition of a ferromagnetic metal. As a ferromagnet, cobalt and manganese were used. Such way of the energy gap opening is novel in comparison to the bulk ferromagnetic doping of topological insulators.

Modification of the gap at the Dirac point (DP) in axion antiferromagnetic topological insulator MnBi 2 Te 4 and its electronic and spin structure have been studied by angle- and spin-resolved photoemission spectroscopy (ARPES) under laser excitation at various temperatures (9–35 K), light polarizations and photon energies. We have distinguished both large (60–70 meV) and reduced ( < 20 meV ) gaps at the DP in the ARPES dispersions, which remain open above the Neél temperature ( T N = 24.5 K ). We propose that the gap above T N remains open due to a short-range magnetic field generated by chiral spin fluctuations. Spin-resolved ARPES, XMCD and circular dichroism ARPES measurements show a surface ferromagnetic ordering for the “large gap” sample and apparently significantly reduced effective magnetic moment for the “reduced gap” sample. These observations can be explained by a shift of the Dirac cone (DC) state localization towards the second Mn layer due to structural disturbance and surface relaxation effects, where DC state is influenced by compensated opposite magnetic moments. As we have shown by means of ab-initio calculations surface structural modification can result in a significant modulation of the DP gap.

A new kind of magnetically-doped antiferromagnetic (AFM) topological insulators (TIs) with stoichiometry Bi 1.09 Gd 0.06 Sb 0.85 Te 3 has been studied by angle-resolved photoemission spectroscopy (ARPES), superconducting magnetometry (SQUID) and X-ray magnetic circular dichroism (XMCD) with analysis of its electronic structure and surface-derived magnetic properties at different temperatures. This TI is characterized by the location of the Dirac gap at the Fermi level (E F ) and a bulk AFM coupling below the Neel temperature (4–8 K). At temperatures higher than the bulk AFM/PM transition, a surface magnetic layer is proposed to develop, where the coupling between the magnetic moments located at magnetic impurities (Gd) is mediated by the Topological Surface State (TSS) via surface Dirac-fermion-mediated magnetic coupling. This hypothesis is supported by a gap opening at the Dirac point (DP) indicated by the surface-sensitive ARPES, a weak hysteresis loop measured by SQUID at temperatures between 30 and 100 K, XMCD measurements demonstrating a surface magnetic moment at 70 K and a temperature dependence of the electrical resistance exhibiting a mid-gap semiconducting behavior up to temperatures of 100–130 K, which correlates with the temperature dependence of the surface magnetization and confirms the conclusion that only TSS are located at the E F . The increase of the TSS’s spectral weight during resonant ARPES at a photon energy corresponding to the Gd 4 d -4 f edge support the hypothesis of a magnetic coupling between the Gd ions via the TSS and corresponding magnetic moment transfer at elevated temperatures. Finally, the observed out-of-plane and in-plane magnetization induced by synchrotron radiation (SR) due to non-equal depopulation of the TSS with opposite momentum, as seen through change in the Dirac gap value and the k ∥ -shift of the Dirac cone (DC) states, can be an indicator of the modification of the surface magnetic coupling mediated by the TSS.

MnBi 2 Te 4 , Mn(Bi,Sb) 2 Te 4 , and MnBi 2 Te 4 (Bi 2 Te 3 ) 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 Bi 2 Te 3 blocks. The magnetic properties of the surface of MnBi 2 Te 4 , MnBi 4 Te 7 , and Mn(Bi Sb x ) 2 Te 4 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 MnBi 4 Te 7 and Mn(Bi, Sb) 2 Te 4 differ significantly.

Quantum mechanics postulates that any measurement influences the state of the investigated system. Here, by means of angle-, spin-, and time-resolved photoemission experiments and ab initio calculations we demonstrate how non-equal depopulation of the Dirac cone (DC) states with opposite momenta in V-doped and pristine topological insulators (TIs) created by a photoexcitation by linearly polarized synchrotron radiation (SR) is followed by the hole-generated uncompensated spin accumulation and the SR-induced magnetization via the spin-torque effect. We show that the photoexcitation of the DC is asymmetric, that it varies with the photon energy, and that it practically does not change during the relaxation. We find a relation between the photoexcitation asymmetry, the generated spin accumulation and the induced spin polarization of the DC and V 3d states. Experimentally the SR-generated in-plane and out-of-plane magnetization is confirmed by the \\(k_{\\parallel}\\)-shift of the DC position and by the splitting of the states at the Dirac point even above the Curie temperature. Theoretical predictions and estimations of the measurable physical quantities substantiate the experimental results.

Modification of the gap at the Dirac point (DP) in axion antiferromagnetic topological insulator$${\\hbox {MnBi}}_2 {\\hbox {Te}}_4$$MnBi 2 Te 4 and its electronic and spin structure have been studied by angle- and spin-resolved photoemission spectroscopy (ARPES) under laser excitation at various temperatures (9–35 K), light polarizations and photon energies. We have distinguished both large (60–70 meV) and reduced ($$<20~ \\hbox {meV}$$< 20 meV ) gaps at the DP in the ARPES dispersions, which remain open above the Neél temperature ($$T_{\\mathrm{N}} = 24.5~ \\hbox {K}$$T N = 24.5 K ). We propose that the gap above$$T_{\\mathrm{N}}$$T N remains open due to a short-range magnetic field generated by chiral spin fluctuations. Spin-resolved ARPES, XMCD and circular dichroism ARPES measurements show a surface ferromagnetic ordering for the “large gap” sample and apparently significantly reduced effective magnetic moment for the “reduced gap” sample. These observations can be explained by a shift of the Dirac cone (DC) state localization towards the second Mn layer due to structural disturbance and surface relaxation effects, where DC state is influenced by compensated opposite magnetic moments. As we have shown by means of ab-initio calculations surface structural modification can result in a significant modulation of the DP gap.

Modification of the gap at the Dirac point (DP) in axion antiferromagnetic topological insulator and its electronic and spin structure have been studied by angle- and spin-resolved photoemission spectroscopy (ARPES) under laser excitation at various temperatures (9-35 K), light polarizations and photon energies. We have distinguished both large (60-70 meV) and reduced ( ) gaps at the DP in the ARPES dispersions, which remain open above the Neél temperature ( ). We propose that the gap above remains open due to a short-range magnetic field generated by chiral spin fluctuations. Spin-resolved ARPES, XMCD and circular dichroism ARPES measurements show a surface ferromagnetic ordering for the \"large gap\" sample and apparently significantly reduced effective magnetic moment for the \"reduced gap\" sample. These observations can be explained by a shift of the Dirac cone (DC) state localization towards the second Mn layer due to structural disturbance and surface relaxation effects, where DC state is influenced by compensated opposite magnetic moments. As we have shown by means of ab-initio calculations surface structural modification can result in a significant modulation of the DP gap.