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The concepts of Weyl fermions and topological semimetals emerging in three-dimensional momentum space are extensively explored owing to the vast variety of exotic properties that they give rise to. On the other hand, very little is known about semimetallic states emerging in two-dimensional magnetic materials, which present the foundation for both present and future information technology. Here, we demonstrate that including the magnetization direction into the topological analysis allows for a natural classification of topological semimetallic states that manifest in two-dimensional ferromagnets as a result of the interplay between spin-orbit and exchange interactions. We explore the emergence and stability of such mixed topological semimetals in realistic materials, and point out the perspectives of mixed topological states for current-induced orbital magnetism and current-induced domain wall motion. Our findings pave the way to understanding, engineering and utilizing topological semimetallic states in two-dimensional spin-orbit ferromagnets., Whether topological semimetal states can emerge in two-dimensional magnetic materials remains less understood. Here, Niu and Hanke et al. propose the concepts of mixed Weyl and nodal-line semimetallic phases by including the magnetization direction into the topological analysis in two-dimensional ferromagnets.

Spin caloric transport refers to the coupling of heat with spin transport. Its applications primarily concern the generation of spin currents and control of magnetisation by temperature gradients for information technology, known by the synonym spin caloritronics. Within the framework of ab initio theory, new tools are being developed to provide an additional understanding of these phenomena in realistic materials, accounting for the complexity of the electronic structure without adjustable parameters. Here, we review this progress, summarising the principles of the density-functional-based approaches in the field and presenting a number of application highlights. Our discussion includes the three most frequently employed approaches to the problem, namely the Kubo, Boltzmann, and Landauer-Büttiker methods. These are showcased in specific examples that span, on the one hand, a wide range of materials, such as bulk metallic alloys, nano-structured metallic and tunnel junctions, or magnetic overlayers on heavy metals, and, on the other hand, a wide range of effects, such as the spin-Seebeck, magneto-Seebeck, and spin-Nernst effects, spin disorder, and the thermal spin-transfer and thermal spin-orbit torques.

A hybrid MPI+OpenMP parallelization strategy has been implemented into the density functional theory code FLEUR. Based on the full-potential linearized augmented plane-wave (FLAPW) method, FLEUR is a well-established all-electron code specialized on the simulation of materials properties of crystalline bulk solids and surfaces with significant electronic and magnetic complexity. Developed in over 30 years the Fortran implementation included two layers of MPI-based distributed memory parallelization that serves as a reference for our work. The revised code version shows superior performance, improved scalability and thereby opens the path to exploit current and future high performance computing architectures efficiently. Multiple threads per MPI process can be utilized by interfacing with optimized linear algebra subroutines from the BLAS and LAPACK libraries as well as in code sections with explicit OpenMP statements. We demonstrate that the additional multithreading helps to avoid the communication induced scalability limit of the pure-MPI version and simultaneously boosts the single node-performance on current multi-core systems. This enables FLEUR calculations for unit cells with over 1000 atoms to simulate extended defects, surfaces and disordered solids.

In topological semimetals the Dirac points can form zero-dimensional and one-dimensional manifolds, as predicted for Dirac/Weyl semimetals and topological nodal line semimetals, respectively. Here, based on first-principles calculations, we predict a topological nodal line semimetal phase in the two-dimensional compounds ${X}_{2}Y$ ($X$ = Ca, Sr, and Ba; $Y$ = As, Sb, and Bi) in the absence of spin-orbit coupling (SOC) with a band inversion at the M point. A nontrivial ${\mathbb{Z}}_{2}$ invariant of ${\mathbb{Z}}_{2}=1$ remains although a tiny gap appears at the nodal line when SOC is included. The mirror symmetry as well as the electrostatic interaction, which can be engineered via strain, are responsible for the nontrivial phase. In addition, the nontrivial phase is further explicitly confirmed via the existence of exotic edge states without and with SOC.

We demonstrate that topological invariants of band insulators can be derived efficiently from the eigenvalues of the local-orbital (LO) based embedding potential, called also the contact (lead) self-energy. The LO based embedding potential is a bulk quantity. Given the tight-binding Hamiltonian describing the bulk valence and conduction bands, it is constructed straightforwardly from the bulk wave functions satisfying the generalized Bloch condition. When the one-electron energy ɛ is located within a projected bulk band gap at a given planar wave vector k, the embedding potential becomes Hermitian. Its real eigenvalues exhibit distinctly different behavior depending on the topological properties of the valence bands, thus enabling unambiguous identification of bulk topological invariants. We consider the Bernevig-Hughes-Zhang model as an example of a time-reversal invariant topological insulator and tin telluride (SnTe) crystallized in a rock-salt structure as an example of a topological crystalline insulator

The properties that distinguish topological crystalline insulator (TCI) and topological insulator (TI) rely on crystalline symmetry and time-reversal symmetry, respectively, which encodes different bulk and surface/edge properties. Here, we predict theoretically that electron-doped TlM (M = S and Se) (110) monolayers realize a family of two-dimensional (2D) TCIs characterized by mirror Chern number CM = -2. Remarkably, under uniaxial strain (≈ 1%), a topological phase transition between 2D TCI and 2D TI is revealed with the calculated spin Chern number CS = -1 for the 2D TI. Using spin-resolved edge states analysis, we show different edge-state behaviors, especially at the time reversal invariant points. Finally, a TlBiSe2/NaCl quantum well is proposed to realize an undoped 2D TCI with inverted gap as large as 0.37 eV, indicating the high possibility for room-temperature observation.

The search for new large band gap quantum spin Hall (QSH) and quantum anomalous Hall (QAH) insulators is critical for their realistic applications at room temperature. Here we predict, based on first principles calculations, that the band gap of QSH and QAH states can be as large as 1.01 eV and 0.35 eV in an H-decorated Bi(111) film. The origin of this giant band gap lies both in the large spin-orbit interaction of Bi and the H-mediated exceptional electronic and structural properties. Moreover, we find that the QAH state also possesses the properties of quantum valley Hall state, thus intrinsically realising the so-called valley-polarized QAH effect. We further investigate the realization of large gap QSH and QAH states in an H-decorated Bi(\={1}10) film and X-decorated (X=F, Cl, Br, and I) Bi(111) films., submitted to Physical Reveiw Letters on 25th of September 2014

Different from the two-dimensional (2D) topological insulator, the 2D topological crystalline insulator (TCI) phase disappears when the mirror symmetry is broken, e.g., upon placing on a substrate. Here, based on a new family of 2D TCIs - SnTe and PbTe monolayers - we theoretically predict the realization of the quantum anomalous Hall effect with Chern number C = 2 even when the mirror symmetry is broken. Remarkably, we also demonstrate that the considered materials retain their large-gap topological properties in quantum well structures obtained by sandwiching the monolayers between NaCl layers. Our results demonstrate that the TCIs can serve as a seed for observing robust topologically non-trivial phases., 5 pages, submitted on 27th Feb 2015

In this paper we present a density functional theory investigation of complex magnetic structures in ultra-thin films. The focus is on magnetically frustrated antiferromagnetic Cr and Mn monolayers deposited on a triangular lattice provided by a Ag (111) substrate. This involves non-collinear magnetic structures, which we treat by first-principles calculations on the basis of the vector spin-density formulation of the density functional theory. We find for Cr/Ag (111) a coplanar non-collinear periodic 120° Neel structure, for Mn/Ag (111) a row-wise antiferromagnetic structure, and for Fe/Ag (111) a ferromagnetic structure as magnetic ground states. The spin-polarized scanning tunneling microscope (SP–STM) operated in the constant-current mode is proposed as a powerful tool to investigate complex atomic-scale magnetic structures of otherwise chemically equivalent atoms. We discuss a recent application of this operation mode of the SP–STM on Mn/W (110), which led to the first observation of a two-dimensional antiferromagnet on a non-magnetic metal. The future potential of this approach is demonstrated by calculating SP–STM images for different magnetic structures of Cr/Ag (111). The results show that the predicted non-collinear magnetic ground state structure can clearly be discriminated from competing magnetic structures. A general discussion of the application of different operation modes of the SP–STM is presented on the basis of the model of Tersoff and Hamann.

We present a density functional theory (DFT) investigation of magnetically frustrated Mn monolayers deposited on the triangular lattice of the Cu(1 1 1) surface. Noncollinear magnetic structures are treated on the basis of the vector spin-density formulation of the DFT. The spin-polarized scanning tunneling microscope operated in the constant-current mode is proposed as a powerful tool to investigate these complex magnetic structures.

At ferroelectric longitudinal domain walls there is an uncompensated charge, which could form a two-dimensional electron gas in the insulator. However, the uncompensated charges can be accommodated by, e.g., defects or localized states that split off from the conduction band. We carried out density functional theory calculations to study these scenarios in PbTiO3 with and without consideration of strong correlation effects simulated via inclusion of a Hubbard parameter U. The optimized structure and electronic structure depend on the choice of this parameter: For vanishing U, a broad, conducting domain wall is obtained, while increasing U leads to localized Ti 3d states and an insulating, sharp domain wall. We also investigated the effects of varying the ferroelectric polarization on the electronic structure of these domain walls.

The fundamental aspects of spin-dependent transport processes and their interplay with temperature gradients, as given by the spin Seebeck coefficient, are still largely unexplored and a multitude of contributing factors must be considered. We used density functional theory together with a Monte-Carlo-based statistical method to simulate simple nanostructures, such as Co nanowires and films embedded in a Cu host or in vacuum, and investigated the influence of spin-disorder scattering on electron transport at elevated temperatures. While we show that the spin-dependent scattering of electrons due to temperature induced disorder of the local magnetic moments contributes significantly to the resistance, thermoelectric and spin-caloric transport coefficients, we also conclude that the actual magnitude of these effects cannot be predicted, quantitatively or qualitatively, without such detailed calculations., 10 pages, 6 figures

Electrons mediate many of the interactions between atoms in a solid. Their propagation in a material determines its thermal, electrical, optical, magnetic and transport properties. Therefore, the constant energy contours characterizing the electrons, in particular the Fermi surface, have a prime impact on the behavior of materials. If anisotropic, the contours induce strong directional dependence at the nanoscale in the Friedel oscillations surrounding impurities. Here we report on giant anisotropic charge density oscillations focused along specific directions with strong spin-filtering after scattering at an oxygen impurity embedded in the surface of a ferromagnetic thin film of Fe grown on W(001). Utilizing density functional theory, we demonstrate that by changing the thickness of the Fe films, we control quantum well states confined to two dimensions that manifest as multiple flat energy contours, impinging and tuning the strength of the induced charge oscillations which allow to detect the oxygen impurity at large distances ($\approx$ 50nm)., Comment: This paper has an explanatory supplement

In many scientific applications the solution of non-linear differential equations are obtained through the set-up and solution of a number of successive eigenproblems. These eigenproblems can be regarded as a sequence whenever the solution of one problem fosters the initialization of the next. In addition, in some eigenproblem sequences there is a connection between the solutions of adjacent eigenproblems. Whenever it is possible to unravel the existence of such a connection, the eigenproblem sequence is said to be correlated. When facing with a sequence of correlated eigenproblems the current strategy amounts to solving each eigenproblem in isolation. We propose a alternative approach which exploits such correlation through the use of an eigensolver based on subspace iteration and accelerated with Chebyshev polynomials (ChFSI). The resulting eigensolver is optimized by minimizing the number of matrix-vector multiplications and parallelized using the Elemental library framework. Numerical results show that ChFSI achieves excellent scalability and is competitive with current dense linear algebra parallel eigensolvers., Comment: 23 Pages, 6 figures. First revision of an invited submission to special issue of Concurrency and Computation: Practice and Experience

A half-metal has been defined as a material with propagating electron states at the Fermi energy only for one of the spin directions. But is it fully half-metallic, that is without electrons with opposite spin at that energy? We have studied the spin-conserving process of tunnelling between La0.7Sr0.3MnO3 half-metallic electrodes across an ultrathin SrTiO3 insulator. This experiment demonstrates that the class of half-metallic materials indeed exists at non-zero temperatures, even at interfaces. It also shows that a fully spin-polarized tunnelling current may persist at large bias.

We report on the epitaxial fabrication and electronic properties of a topological phase in strained \alpha-Sn on InSb. The topological surface state forms in the presence of an unusual band order not based on direct spin-orbit coupling, as shown in density functional and GW slab-layer calculations. Angle-resolved photoemission including spin detection probes experimentally how the topological spin-polarized state emerges from the second bulk valence band. Moreover, we demonstrate the precise control of the Fermi level by dopants., Comment: version 2 with supplementary information

The new journal of physics 15, 115009 (2013). doi:10.1088/1367-2630/15/11/115009, Published by IOP Publ. [u.a.], London

We examined by two-dimensional photoemission band mapping the electronic structure of Au films epitaxially grown on an Ag(111) substrate. The very similar structural and electronic properties of the two metals make this system extremely unfavorable for the occurrence and observation of electron confinement effects. At variance with previous spectroscopic studies, we show that the electron reflectivity at the interface sustains the formation of well-defined $sp$-derived quantum well states (QWS) and weak quantum well resonance states (QWRS) in the Au layers. The character and degree of confinement of these states are analyzed and quantitatively related to the Au/Ag interface reflectivity on the basis of density functional theory (DFT) band structure calculations.

Electronic tunneling through ferroelectric insulators is considered to be a key ingredient of future oxide electronics. We investigate the role of the electronic band structure of the decaying electronic states in the band gap by first discussing the expected behavior of tunneling in the effective mass model. We demonstrate that, even for the simple prototype ferroelectric oxides in the perovskite structures PbTiO${}_{3}$ and BaTiO${}_{3}$, the basic assumption of the effective mass model is not appropriate, and that the correct interpretation of tunneling in these materials requires a material-specific description of the evanescent states as provided by the complex band structure.

We monitored the $sp$-quantum-well states of Ag films on Pt(111) by angle-resolved photoemission in order to examine the electron transmission across the Ag/Pt interface. For thin layers up to 3.5 nm, the Ag states are characterized by broad quasiparticle peaks and a reversal of the parabolic curvature near the center of the surface Brillouin zone. Remarkable departures from the expected nearly-free-electronlike band dispersion persist in films of more than 14 nm thickness. First-principles calculations and symmetry analysis demonstrate that the observed anomalies in the spectroscopic data can be straightforwardly linked to variations in the Ag/Pt transmission coefficient in the energy-momentum space.

We report on the implementation of the Wannier Functions (WFs) formalism within the full-potential linearized augmented plane wave method (FLAPW), suitable for bulk, film and one-dimensional geometries. The details of the implementation, as well as results for the metallic SrVO3, ferroelectric BaTiO3 grown on SrTiO3, covalently bonded graphene and a one-dimensional Pt-chain are given. We discuss the effect of spin-orbit coupling on the Wannier Functions for the cases of SrVO3 and platinum. The dependency of the WFs on the choice of the localized trial orbitals as well as the difference between the maximally localized and "first-guess" WFs are discussed. Our results on SrVO3 and BaTiO3, e.g. the ferroelectric polarization of BaTiO3, are compared to results published elsewhere and found to be in excellent agreement., 13 pages, 9 figures, accepted for publication in Phys. Rev. B

By combining the first-principles concept based on the density functional theory with a model vacuum potential, we calculate image potential states and analogous ones in the presence of an electric field applied on a nonmagnetic Ag(100) surface and a magnetic Fe(110) surface. Our investigations are based on the Green-function embedding technique, which allows us to treat a truly semi-infinite surface and whence yields a continuum of bulk states. This turns out to be of crucial importance in order to investigate the qualitative difference between localized image or field states located in a band gap of the substrate and states in resonance with bulk states present at the same energies. This difference leads to remarkable changes in the binding energy versus field dispersion of the states. Furthermore, we show that in the case of the Fe(110) surface, the calculated magnetic exchange splitting increases with the electric field and is also modified by the transition from field states to surface resonance states.

A half-metal has been defined as a material with propagating electron states at the Fermi energy only for one of the two possible spin projections, and as such has been promoted as an interesting research direction for spin electronics. This review details recent advances on manganite thin film research within the field of spintronics, before presenting the structural, electronic and spin-polarized solid-state tunnelling transport studies that we have performed on heterostructures involving La(2/3)Sr(1/3)MnO(3) thin films separated by SrTiO(3) barriers. These experiments demonstrate that, with a polarization of spin [Formula: see text] electrons at the Fermi level that can reach 99%, the La(2/3)Sr(1/3)MnO(3)/SrTiO(3) interface for all practical purposes exhibits half-metallic behaviour. We offer insight into the electronic structure of the interface, including the electronic symmetry of any remaining spin [Formula: see text] states at the Fermi level. Finally, we present experiments that use the experimental half-metallic property of manganites as tools to reveal novel features of spintronics.

By combining first-principles calculations with transport theory we investigate the origin of the magnetoresistance of a magnetic tunnel junction consisting of a ferromagnetic and an antiferromagnetic lead. The (001) oriented Fe/vacuum/Cr planar junction serves as model junction. Even though the conduction electrons of antiferromagnetic Cr are spin-degenerate, it is possible to observe magnetoresistance due to two mechanisms: Firstly, the surface magnetism of Cr creates a spin-dependent potential barrier, and secondly, exchange-split surface states and resonances result in a tunneling conductance which depends on the relative orientation of the Fe and Cr magnetizations. Spin-dependent tunneling between a ferromagnet and an antiferromagnet happens frequently in tunneling setups such as in spin-polarized scanning tunneling microscopy or magnetic tunnel junctions for magnetic random access memory.

The influence of local Coulomb correlations on the surface electronic structure of ${\mathrm{SrVO}}_{3}$, a strongly-correlated metal in a perovskite structure, is investigated for both the $\mathrm{SrO}$-layer and ${\mathrm{VO}}_{2}$-layer-terminated (001) surfaces. The electronic structure within the local density approximation of a semi-infinite surface is determined using the embedded Green-function approach, and the resultant density of states projected on the V ${t}_{2g}$ orbitals is used as an input to a subsequent many-body calculation within the dynamical mean field theory (DMFT) and the multiorbital quantum Monte Carlo technique. Qualitatively, the present study confirms the conclusion of recent photoemission experiments and tight-binding DMFT calculations which both indicate that the electronic structure at the surface is more strongly correlated than in the bulk. On a quantitative level significant differences are obtained as a function of orbital polarization at the surface, surface layer relaxation, and $\mathrm{SrO}$ vs ${\mathrm{VO}}_{2}$ surface termination.

Results are presented of a first-principles calculation of the spin-polarized field emission from ferromagnetic Ni(111) and Ni(001) surfaces. The electronic structure of both surfaces exposed to an external field is determined by combining the surface-embedded Green function approach and the full-potential linearized augmented plane-wave (FLAPW) method within the local spin density approximation. We discuss the contributions of different states to the field-emission current. In particular, we show that delocalized states make similar contributions to that obtained at jellium surfaces while localized Ni d states contribute mostly through surface states and resonances. These contributions dominate in the minority spin and lead to a negative spin polarization of the emitted current.

A method for the first-principles calculation of the transfer matrix is presented. The method is based on a Green-function formulation and allows one to relate the wave functions and their derivatives on boundaries at opposite sides of a film or junction of finite thickness. Both the underlying theory and an actual implementation in the full-potential linearized augmented plane wave method are described. Currently the embedding method is used to evaluate the Green-function matrix elements and in turn we show that the transfer matrix can be used to construct the embedding potential. Some possible applications of the transfer-matrix method such as the calculations of the complex band structure or the calculation of the transmission and reflection coefficients for ballistic transport are discussed. As a first example, complex band structures of Cu, Fe, and Si are presented.

We present an efficient method for calculating the conductance of ballistic electrons through an interface from first principles using the embedding approach of Inglesfield. In our method the Landauer-B\"uttiker formula for ballistic transport is expressed in terms of two quantities that are available in the embedded Green-function formalism without additional calculations. One is the embedding potential of bulk crystals on both sides of the interface and the other is the Green function in the interface region. As a proof of principle we calculate on the basis of the density-functional theory the spin-resolved electron transmission through a model system of ferromagnetic Co monolayers sandwiched between bulk Cu crystals. The relationship between our formulation and the Green-function formulation of Baranger and Stone is discussed.

The spin-polarized scanning tunneling microscope (SP-STM) operated in the constant current mode is proposed as a powerful tool to investigate complex atomic-scale magnetic structures of otherwise chemically equivalent atoms. The potential of this approach is demonstrated by successfully resolving the magnetic structure of Cr/Ag(111), which is predicted on the basis of ab initio vector spin-density calculations to be a coplanar noncollinear periodic 120\ifmmode^\circ\else\textdegree\fi{} N\'eel structure. Different operating modes of the SP-STM are discussed on the basis of the model of Tersoff and Hamann.

$c(2\ifmmode\times\else\texttimes\fi{}2)\mathrm{M}\mathrm{n}\mathrm{C}\mathrm{u}/\mathrm{C}\mathrm{u}(100)$ is an ordered two-dimensional surface alloy that exhibits a checkerboard arrangement of Mn and Cu atoms on the Cu(100) surface. Mn buckles outwards by 0.3 \AA{} with respect to Cu and in all previous scanning tunneling microscopy (STM) experiments only one chemical species was imaged which was assumed to be Mn. We analyze the STM results by first-principles calculations based on the density-functional theory and show that Cu rather than Mn is imaged, while indeed Mn is imaged as single Mn impurities at Cu(100). We explain this result in terms of the formation of Mn states bridging over the Cu atoms. These Mn states are characteristic for Mn in a $c(2\ifmmode\times\else\texttimes\fi{}2)\mathrm{MnCu}$ surface alloy. Missing Mn atoms break this bridging bond and the surrounding Cu atoms are imaged as depressions.