Topological phase transition in the antiferromagnetic topological insulator MnBi[Formula: see text]Te[Formula: see text] from the point of view of axion-like state realization.

This work aims to study the conditions of topological phase transition (TPT) between the topological and trivial states in the antiferromagnetic topological insulator (AFM TI) MnBi[Formula: see text]Te[Formula: see text] and propose some theory about the relationship of this TPT with the possibility of axion-like state realization in this material. Using the density functional approach we have analyzed the changes in the electronic and spin structure of topological surface states (TSSs) and the nearest conduction and valence bands (CB and VB) including the changes in the bulk band gap as well as the Dirac point (DP) gap in TSSs under variation of the spin-orbit coupling strength in the region of the TPT for infinite crystal and slab with a surface both. We have shown that in both cases the TPT occurs with inversion of the contributions of the Bi-[Formula: see text] and Te-[Formula: see text] states of different parity at the gap edges related to change in the gap sign. In the case of surface calculations, the Bi-[Formula: see text] and Te-[Formula: see text] states at the edges of the bulk band gap and their inversion at the TPT point are transformed into the TSSs with an energy gap at the DP. In this case the TPT takes place without closing the band gap, i.e. with a "jump" through zero and the formation of the nonzero gap during such a transition. Our calculations show that the TPT point is also characterized by an inversion of the out-of-plane spin polarization [Formula: see text] at the [Formula: see text] point for lower and upper parts of the Dirac cone and a significant spatial redistribution of the TSSs between the surface and the bulk. We suppose that the nonzero Dirac gap can have some relationship with the formation of the axion-like state, which presumably couples nonmagnetic spin-orbit and magnetic contributions at the boundary between the topological and trivial phases for a system with parameters close to the TPT conditions. A practically realized system is proposed - the AFM TI with a stoichiometry close to that of MnBi[Formula: see text]Te[Formula: see text]Se[Formula: see text] with partial (about 50%) substitution of Te atoms for Se atoms in MnBi[Formula: see text]Te[Formula: see text] which can be an experimental platform for the implementation and experimental analysis of the TPT and the corresponding possibility of the axion-like state realization in Condensed Matter. Besides, such system could serve as a good platform for studying the dynamic axion effect, where the axion field fluctuations are maximised when a small external field is applied to the system which state is close to the TPT.

Non-monotonic variation of the Kramers point band gap with increasing magnetic doping in BiTeI.

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.

Nature of the Dirac gap modulation and surface magnetic interaction in axion antiferromagnetic topological insulator [Formula: see text].

Modification of the gap at the Dirac point (DP) in axion antiferromagnetic topological insulator [Formula: see text] 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 ([Formula: see text]) gaps at the DP in the ARPES dispersions, which remain open above the Neél temperature ([Formula: see text]). We propose that the gap above [Formula: see text] 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.

Advanced graphene recording device for spin-orbit torque magnetoresistive random access memory.

The non-volatile spin-orbit torque magnetic random access memory (SOT-MRAM) is a very attractive memory technology for near future computers because it has various advantages such as non-volatility, high density and scalability. In the present work we propose a model of a graphene recording device for the SOT-MRAM unit cell, consisting of a quasi-freestanding graphene intercalated with Au and an ultra-thin Pt layer sandwiched between graphene and a magnetic tunnel junction. As a result of using the claimed graphene recording memory element, a faster operation and lower energy consumption will be achieved under the recording information by reducing the electric current required to record. The efficiency of the graphene recording element was confirmed by the experimental results and the theoretical estimations.

Prediction and observation of an antiferromagnetic topological insulator.

Magnetic topological insulators are narrow-gap semiconductor materials that combine non-trivial band topology and magnetic order1. Unlike their nonmagnetic counterparts, magnetic topological insulators may have some of the surfaces gapped, which enables a number of exotic phenomena that have potential applications in spintronics1, such as the quantum anomalous Hall effect2 and chiral Majorana fermions3. So far, magnetic topological insulators have only been created by means of doping nonmagnetic topological insulators with 3d transition-metal elements; however, such an approach leads to strongly inhomogeneous magnetic4 and electronic5 properties of these materials, restricting the observation of important effects to very low temperatures2,3. An intrinsic magnetic topological insulator-a stoichiometric well ordered magnetic compound-could be an ideal solution to these problems, but no such material has been observed so far. Here we predict by ab initio calculations and further confirm using various experimental techniques the realization of an antiferromagnetic topological insulator in the layered van der Waals compound MnBi2Te4. 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 a ℤ2 topological classification; ℤ2 = 1 for MnBi2Te4, confirming its topologically nontrivial nature. Our experiments indicate that the symmetry-breaking (0001) surface of MnBi2Te4 exhibits a large bandgap in the topological surface state. We expect this property to eventually enable the observation of a number of fundamental phenomena, among them quantized magnetoelectric coupling6-8 and axion electrodynamics9,10. Other exotic phenomena could become accessible at much higher temperatures than those reached so far, such as the quantum anomalous Hall effect2 and chiral Majorana fermions3.

Dirac gap opening and Dirac-fermion-mediated magnetic coupling in antiferromagnetic Gd-doped topological insulators and their manipulation by synchrotron radiation.

A new kind of magnetically-doped antiferromagnetic (AFM) topological insulators (TIs) with stoichiometry Bi1.09Gd0.06Sb0.85Te3 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 (EF) 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 EF. The increase of the TSS's spectral weight during resonant ARPES at a photon energy corresponding to the Gd 4d-4f 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.

Dirac cone intensity asymmetry and surface magnetic field in V-doped and pristine topological insulators generated by synchrotron and laser radiation.

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.

Giant Magnetic Band Gap in the Rashba-Split Surface State of Vanadium-Doped BiTeI: A Combined Photoemission and Ab Initio Study.

One of the most promising platforms for spintronics and topological quantum computation is the two-dimensional electron gas (2DEG) with strong spin-orbit interaction and out-of-plane ferromagnetism. In proximity to an s-wave superconductor, such 2DEG may be driven into a topologically non-trivial superconducting phase, predicted to support zero-energy Majorana fermion modes. Using angle-resolved photoemission spectroscopy and ab initio calculations, we study the 2DEG at the surface of the vanadium-doped polar semiconductor with a giant Rashba-type splitting, BiTeI. We show that the vanadium-induced magnetization in the 2DEG breaks time-reversal symmetry, lifting Kramers degeneracy of the Rashba-split surface state at the Brillouin zone center via formation of a huge gap of about 90 meV. As a result, the constant energy contour inside the gap consists of only one circle with spin-momentum locking. These findings reveal a great potential of the magnetically-doped semiconductors with a giant Rashba-type splitting for realization of novel states of matter.

Spin-resolved band structure of heterojunction Bi-bilayer/3D topological insulator in the quantum dimension regime in annealed Bi2Te2.4Se0.6.

Two- and three-dimensional topological insulators are the key materials for the future nanoelectronic and spintronic devices and quantum computers. By means of angle- and spin-resolved photoemission spectroscopy we study the electronic and spin structure of the Bi-bilayer/3D topological insulator in quantum tunneling regime formed under the short annealing of Bi2Te2.4Se0.6. Owing to the temperature-induced restructuring of the topological insulator's surface quintuple layers, the hole-like spin-split Bi-bilayer bands and the parabolic electronic-like state are observed instead of the Dirac cone. Scanning Tunneling Microscopy and X-ray Photoemission Spectroscopy measurements reveal the appearance of the Bi2 terraces at the surface under the annealing. The experimental results are supported by density functional theory calculations, predicting the spin-polarized Bi-bilayer bands interacting with the quintuple-layers-derived states. Such an easily formed heterostructure promises exciting applications in spin transport devices and low-energy electronics.

The graphene/Au/Ni interface and its application in the construction of a graphene spin filter.

A modification of the contact of graphene with ferromagnetic electrodes in a model of the graphene spin filter allowing restoration of the graphene electronic structure is proposed. It is suggested for this aim to intercalate into the interface between the graphene and the ferromagnetic (Ni or Co) electrode a Au monolayer to block the strong interaction between the graphene and Ni (Co) and, thus, prevent destruction of the graphene electronic structure which evolves in direct contact of graphene with Ni (Co). It is also suggested to insert an additional buffer graphene monolayer with the size limited by that of the electrode between the main graphene sheet providing spin current transport and the Au/Ni electrode injecting the spin current. This will prevent the spin transport properties of graphene from influencing contact phenomena and eliminate pinning of the graphene electronic structure relative to the Fermi level of the metal, thus ensuring efficient outflow of injected electrons into the graphene. The role of the spin structure of the graphene/Au/Ni interface with enhanced spin-orbit splitting of graphene π states is also discussed, and its use is proposed for additional spin selection in the process of the electron excitation.

Giant Rashba splitting in graphene due to hybridization with gold.

Graphene in spintronics is predominantly considered for spin current leads of high performance due to weak intrinsic spin-orbit coupling of the graphene π electrons. Externally induced large spin-orbit coupling opens the possibility of using graphene in active elements of spintronic devices such as the Das-Datta spin field-effect transistor. Here we show that Au intercalation at the graphene-Ni interface creates a giant spin-orbit splitting (~100 meV) of the graphene Dirac cone up to the Fermi energy. Photoelectron spectroscopy reveals the hybridization with Au 5d states as the source for this giant splitting. An ab initio model of the system shows a Rashba-split spectrum around the Dirac point of graphene. A sharp graphene-Au interface at the equilibrium distance accounts for only ~10 meV spin-orbit splitting and enhancement is due to the Au atoms in the hollow position that get closer to graphene and do not break the sublattice symmetry.

Is there a rashba effect in graphene on 3d ferromagnets?

Graphene is considered a candidate material for spintronics. Recently, graphene grown on Ni(111) has been reported to show a Rashba effect which depends on the magnetization. By spin- and angle-resolved photoelectron spectroscopy, we investigate the preconditions for such an effect for graphene on Ni as well as on Co which has a approximately 3x larger 3d magnetic moment: (i) spin polarization or (ii) exchange splitting of graphene pi states in normal emission geometry, and (iii) Rashba-type spin-orbit splitting off normal. As none of these are found to be of considerable size, the reported effect is neither Rashba-type, nor due to the spin-orbit coupling, nor involving the electron spin.

Quantum cavity for spin due to spin-orbit interaction at a metal boundary.

A quantum cavity for spin is created using a tungsten crystal as substrate of high nuclear charge and breaking the structural inversion symmetry through deposition of a gold quantum film. Spin- and angle-resolved photoelectron spectroscopy shows directly that quantum-well states and the "matrioshka" or Russian nested doll Fermi surface of the gold film are spin polarized and spin-orbit split up to a thickness of at least nine atomic layers. Ferromagnetic materials or external magnetic fields are not required, and the quantum film does not need to possess a high atomic number as analogous results with silver show.

Electronic and magnetic properties of quasifreestanding graphene on Ni.

For the purpose of recovering the intriguing electronic properties of freestanding graphene at a solid surface, graphene self-organized on a Au monolayer on Ni(111) is prepared and characterized by scanning tunneling microscopy. Angle-resolved photoemission reveals a gapless linear pi-band dispersion near K[over] as a fingerprint of strictly monolayer graphene and a Dirac crossing energy equal to the Fermi energy (EF) within 25 meV meaning charge neutrality. Spin resolution shows a Rashba effect on the pi states with a large (approximately 13 meV) spin-orbit splitting up to EF which is independent of k.

Origin of spin-orbit splitting for monolayers of au and ag on w(110) and mo(110).

Spin-orbit coupling can give rise to spin-split electronic states without a ferromagnet or an external magnetic field. We create large spin-orbit splittings in a Au and Ag monolayer on W(110) and show that the size of the splitting does not depend on the atomic number of the Au or Ag overlayer but of the W substrate. Spin- and angle-resolved photoemission and Fermi-surface scans reveal that the overlayer states acquire spin polarization through spin-dependent overlayer-substrate hybridization.

Probing the ground state electronic structure of a correlated electron system by quantum well states: Ag/Ni(111).

The ground state electronic properties of the strongly correlated transition metal Ni are usually not accessible from the excitation spectra measured in photoelectron spectroscopy. We show that the bottom of the Ni d band along [111] can be probed through the energy dependence of the phase of quantum-well states in Ag/Ni(111). Our model description of the quantum-well energies measured by angle-resolved photoemission determines the bottom of the empty set 1 d band of Ni as 2.6 eV, in full agreement with standard local density theory and at variance with the values of 1.7-1.8 eV from direct angle-resolved photoemission experiments of Ni.

Photoemission from stepped W(110): initial or final state effect?

The electronic structure of the (110)-oriented terraces of stepped W(331) and W(551) is compared to the one of flat W(110) using angle-resolved photoemission. We identify a surface-localized state which develops perpendicular to the steps into a repeated band structure with the periodicity of the step superlattices. It is shown that a final-state diffraction process rather than an initial-state superlattice effect is the origin of the observed behavior and why it does not affect the entire band structure.

An elastic "sieve" to probe momentum space: Gd chains on W(110).

Electron scattering conditions of one-dimensional nanostructures are explored in angle-resolved photoelectron spectroscopy. Tiny increments of the Gd submonolayer coverage on W(110) lead to strong modifications in the spectra. It is shown that the Gd overlayer represents an elastic superlattice of chains which performs a systematic mapping of the electronic band dispersion of the W substrate through a quasicontinuous series of umklapp wave vectors. Conversely, a single valence-band spectrum contains essential and precise structural information readily accessible by comparison to the band dispersion.

Electronic structure of carbon nanostripes.

Carbon nanostripes of graphene structure prepared on the stepped Ni(771) surface have been studied by angle-resolved photoemission. The electronic structure is anisotropic: parallel to the stripe direction, a graphite-type dispersion is measured, whereas the perpendicular direction displays two entangled band structures shifted in energy with respect to each other. These are experimentally identified as the microsurface-centered band structure and its umklapp scattered image caused by the superlattice.