Topological Magnetic Materials of the (MnSb2Te4)·(Sb2Te3)n van der Waals Compounds Family.

Using density functional theory, we propose the (MnSb2Te4)·(Sb2Te3)n family of stoichiometric van der Waals compounds that harbor multiple topologically nontrivial magnetic phases. In the ground state, the first three members of the family (n = 0, 1, 2) are 3D antiferromagnetic topological insulators, while for n ≥ 3 a special phase is formed, in which a nontrivial topological order coexists with a partial magnetic disorder in the system of the decoupled 2D ferromagnets, whose magnetizations point randomly along the third direction. Furthermore, due to a weak interlayer exchange coupling, these materials can be field-driven into the FM Weyl semimetal (n = 0) or FM axion insulator states (n ≥ 1). Finally, in two dimensions, we reveal these systems to show intrinsic quantum anomalous Hall and AFM axion insulator states, as well as quantum Hall state, achieved under external magnetic field. Our results demonstrate that MnSb2Te4 is not topologically trivial as was previously believed that opens possibilities of realization of a wealth of topologically nontrivial states in the (MnSb2Te4)·(Sb2Te3)n family.

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.

Divalent EuRh2Si2 as a reference for the Luttinger theorem and antiferromagnetism in trivalent heavy-fermion YbRh2Si2.

Application of the Luttinger theorem to the Kondo lattice YbRh2Si2 suggests that its large 4f-derived Fermi surface (FS) in the paramagnetic (PM) regime should be similar in shape and volume to that of the divalent local-moment antiferromagnet (AFM) EuRh2Si2 in its PM regime. Here we show by angle-resolved photoemission spectroscopy that paramagnetic EuRh2Si2 has a large FS essentially similar to the one seen in YbRh2Si2 down to 1 K. In EuRh2Si2 the onset of AFM order below 24.5 K induces an extensive fragmentation of the FS due to Brillouin zone folding, intersection and resulting hybridization of the Fermi-surface sheets. Our results on EuRh2Si2 indicate that the formation of the AFM state in YbRh2Si2 is very likely also connected with similar changes in the FS, which have to be taken into account in the controversial analysis and discussion of anomalies observed at the quantum critical point in this system.

Robust and tunable itinerant ferromagnetism at the silicon surface of the antiferromagnet GdRh2Si2.

Spin-polarized two-dimensional electron states (2DESs) at surfaces and interfaces of magnetically active materials attract immense interest because of the idea of exploiting fermion spins rather than charge in next generation electronics. Applying angle-resolved photoelectron spectroscopy, we show that the silicon surface of GdRh2Si2 bears two distinct 2DESs, one being a Shockley surface state, and the other a Dirac surface resonance. Both are subject to strong exchange interaction with the ordered 4f-moments lying underneath the Si-Rh-Si trilayer. The spin degeneracy of the Shockley state breaks down below ~90 K, and the splitting of the resulting subbands saturates upon cooling at values as high as ~185 meV. The spin splitting of the Dirac state becomes clearly visible around ~60 K, reaching a maximum of ~70 meV. An abrupt increase of surface magnetization at around the same temperature suggests that the Dirac state contributes significantly to the magnetic properties at the Si surface. We also show the possibility to tune the properties of 2DESs by depositing alkali metal atoms. The unique temperature-dependent ferromagnetic properties of the Si-terminated surface in GdRh2Si2 could be exploited when combined with functional adlayers deposited on top for which novel phenomena related to magnetism can be anticipated.

Mirror-symmetry protected non-TRIM surface state in the weak topological insulator Bi2TeI.

Strong topological insulators (TIs) support topological surfaces states on any crystal surface. In contrast, a weak, time-reversal-symmetry-driven TI with at least one non-zero v1, v2, v3 ℤ2 index should host spin-locked topological surface states on the surfaces that are not parallel to the crystal plane with Miller indices (v1 v2 v3). On the other hand, mirror symmetry can protect an even number of topological states on the surfaces that are perpendicular to a mirror plane. Various symmetries in a bulk material with a band inversion can independently preordain distinct crystal planes for realization of topological states. Here we demonstrate the first instance of coexistence of both phenomena in the weak 3D TI Bi2TeI which (v1 v2 v3) surface hosts a gapless spin-split surface state protected by the crystal mirror-symmetry. The observed topological state has an even number of crossing points in (r-M)the directions of the 2D Brillouin zone due to a non-TRIM bulk-band inversion. Our findings shed light on hitherto uncharted features of the electronic structure of weak topological insulators and open up new vistas for applications of these materials in spintronics.

Strong ferromagnetism at the surface of an antiferromagnet caused by buried magnetic moments.

Carrying a large, pure spin magnetic moment of 7 µB per atom in the half-filled 4f shell, divalent europium is an outstanding element for assembling novel magnetic devices in which a two-dimensional electron gas may be polarized due to exchange interaction with an underlying magnetically-active Eu layer. Here we show that the Si-Rh-Si surface trilayer of the antiferromagnet EuRh2Si2 bears a surface state, which exhibits an unexpected and large spin splitting controllable by temperature. The splitting sets in below ~32.5 K, well above the ordering temperature of the Eu 4f moments (~24.5 K) in the bulk, indicating a larger ordering temperature in the topmost Eu layers. The driving force for the itinerant ferromagnetism at the surface is the aforementioned exchange interaction. Such a splitting may also be induced into states of functional surface layers deposited onto the surface of EuRh2Si2 or similarly ordered magnetic materials with metallic or semiconducting properties.

Experimental verification of PbBi2Te4 as a 3D topological insulator.

The experimental evidence is presented of the topological insulator state in PbBi2Te4. A single surface Dirac cone is observed by angle-resolved photoemission spectroscopy with synchrotron radiation. Topological invariants Z2 are calculated from the ab initio band structure to be 1;(111). The observed two-dimensional isoenergy contours in the bulk energy gap are found to be the largest among the known three-dimensional topological insulators. This opens a pathway to achieving a sufficiently large spin current density in future spintronic devices.

Ideal two-dimensional electron systems with a giant Rashba-type spin splitting in real materials: surfaces of bismuth tellurohalides.

Spintronics is aimed at actively controlling and manipulating the spin degrees of freedom in semiconductor devices. A promising way to achieve this goal is to make use of the tunable Rashba effect that relies on the spin-orbit interaction in a two-dimensional electron system immersed in an inversion-asymmetric environment. The spin-orbit-induced spin splitting of the two-dimensional electron state provides a basis for many theoretically proposed spintronic devices. However, the lack of semiconductors with large Rashba effect hinders realization of these devices in actual practice. Here we report on a giant Rashba-type spin splitting in two-dimensional electron systems that reside at tellurium-terminated surfaces of bismuth tellurohalides. Among these semiconductors, BiTeCl stands out for its isotropic metallic surface-state band with the Γ-point energy lying deep inside the bulk band gap. The giant spin splitting of this band ensures a substantial spin asymmetry of the inelastic mean free path of quasiparticles with different spin orientations.

Quantum-well-induced giant spin-orbit splitting.

We report on the observation of a giant spin-orbit splitting of quantum-well states in the unoccupied electronic structure of a Bi monolayer on Cu(111). Up to now, Rashba-type splittings of this size have been reported exclusively for surface states in a partial band gap. With these quantum-well states we have experimentally identified a second class of states that show a huge spin-orbit splitting. First-principles electronic structure calculations show that the origin of the spin-orbit splitting is due to the perpendicular potential at the surface and interface of the ultrathin Bi film. This finding allows for the direct possibility to tailor spin-orbit splitting by means of thin-film nanofabrication.

Conservation of the lateral electron momentum at a metal-semiconductor interface studied by ballistic electron emission microscopy.

We report on ballistic electron emission microscopy and spectroscopy studies on epitaxial (3-5 nm thick) Bi(111) films, grown on n-type Si substrates. The effective barrier heights of the Schottky barrier observed are 0.58 eV for the Bi/Si(100)-(2x1) and 0.68 eV for the Bi/Si(111)-(7x7). At the step edges of the epitaxial films a strong increase of the ballistic electron emission microscopy current is observed for Bi/Si(111)-(7x7), while no increase occurs for Bi/Si(100)-(2x1). These observations can be explained by the conservation of the lateral momentum of the electron at the metal-semiconductor interface.

Role of spin-orbit coupling and hybridization effects in the electronic structure of ultrathin Bi films.

The electronic structure of Bi(001) ultrathin films (thickness > or =7 bilayers) on Si(111)-7x7 was studied by angle-resolved photoemission spectroscopy and first-principles calculations. In contrast with the semimetallic nature of bulk Bi, both the experiment and theory demonstrate the metallic character of the films with the Fermi surface formed by spin-orbit-split surface states (SSs) showing little thickness dependence. Below the Fermi level, we clearly detected quantum well states (QWSs) at the M point, which were surprisingly found to be non-spin-orbit split; the films are "electronically symmetric" despite the obvious structural nonequivalence of the top and bottom interfaces. We found that the SSs hybridize with the QWSs near M and lose their spin-orbit-split character.

Role of spin in quasiparticle interference.

Quasiparticle interference patterns measured by scanning tunneling microscopy can be used to study the local electronic structure of metal surfaces and high-temperature superconductors. Here, we show that even in nonmagnetic systems the spin of the quasiparticles can have a profound effect on the interference patterns. On Bi(110), where the surface state bands are not spin degenerate, the patterns are not related to the dispersion of the electronic states in a simple way. In fact, the features which are expected for the spin-independent situation are absent and the observed interference patterns can be interpreted only by taking spin-conserving scattering events into account.

Strong spin-orbit splitting on bi surfaces.

Using first-principles calculations and angle-resolved photoemission, we show that the spin-orbit interaction leads to a strong splitting of the surface-state bands on low-index surfaces of Bi. The dispersion of the states and the corresponding Fermi surfaces are profoundly modified in the whole surface Brillouin zone. We discuss the implications of these findings with respect to a proposed surface charge density wave on Bi(111) as well as to the surface screening, surface spin-density waves, electron (hole) dynamics in surface states, and to possible applications to the spintronics.