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A scheme is presented to calculate on a first-principles level the spin-lattice coupling (SLC) parameters needed to perform combined molecular-spin dynamics (MSD) simulations. By treating changes to the spin configuration and atomic positions on the same level, closed expressions for the atomic SLC parameters could be derived in a coherent way up to any order. The properties of the SLC parameters are discussed considering separately the symmetric and antisymmetric parts of the SLC tensor. The changes due to atomic displacements of the spin-spin exchange coupling (SSC) parameters estimated using the SLC parameters are compared with the SSC parameters calculated for an embedded cluster with the central atom displaced, demonstrating good agreement of these results. Moreover, this allows to study the impact of different SLC contributions, linear and quadratic with respect to displacements, on the properties of the modified SSC parameters. In addition, we represent an approach to calculate the site-diagonal SLC parameters characterizing local magnetic anisotropy induced by a lattice distortion, which is a counterpart of the approach based on magnetic torque used for the investigations of magneto-crystalline anisotropy (MCA) as well as for calculations of the MCA constants. In particular, the dependence of the induced magnetic torque on different types of atomic displacements is analyzed., Comment: 16 pages

We explore possibilities for control of magnons in two-dimensional heterostructures by an external electric field acting across a dielectric barrier. By performing ab initio calculations for a Fe monolayer and Fe bilayer, both suspended in vacuum and deposited on Cu(001), we demonstrate that external electric field can significantly modify magnon lifetimes and that these changes can be related to field-induced changes in layer-resolved Bloch spectral functions. For systems with more magnon dispersion branches, the gap between high- and low-energy eigenmodes varies with the external field. These effects are strongly influenced by the substrate. Considerable variability in how the magnon spectra are sensitive to the external electric field can be expected, depending on the substrate and on the thickness of the magnetic layer.

Herein, we present an extensive study of the magnetic and magnetotransport properties of iron-inserted transition-metal dichalcogenide Fe1/3TaS2. High-quality single crystals were prepared by an im...

The transfer and control of angular momentum is a key aspect for spintronic applications. Only recently, it was shown that it is possible to transfer angular momentum from the spin system to the lattice on ultrashort time scales. In an attempt to contribute to the understanding of angular momentum transfer between spin and lattice degrees of freedom we present a scheme to calculate fully-relativistic spin-lattice coupling parameters from first-principles. By treating changes in the spin configuration and atomic positions at the same level, closed expressions for the atomic spin-lattice coupling parameters can be derived in a coherent manner up to any order. Analyzing the properties of these parameters, in particular their dependence on spin-orbit coupling, we find that even in bcc Fe the leading term for the angular momentum exchange between the spin system and the lattice is a Dzyaloshiskii-Moriya-type interaction, which is due to the symmetry breaking distortion of the lattice., Comment: 4 figures

In the spirit of multi-scale modeling, we develop a theoretical framework for spin-lattice coupling that connects, on the one hand, to ab initio calculations of spin-lattice coupling parameters and, on the other hand, to the magneto-elastic continuum theory. The derived Hamiltonian describes a closed system of spin and lattice degrees of freedom and explicitly conserves the total momentum, angular momentum and energy. Using a new numerical implementation that corrects earlier Suzuki-Trotter decompositions we perform simulations on the basis of the resulting equations of motion to investigate the combined magnetic and mechanical motion of a ferromagnetic nanoparticle, thereby validating our developed method. In addition to the ferromagnetic resonance mode of the spin system we find another low-frequency mechanical response and a rotation of the particle according to the Einstein-de-Haas effect. The framework developed herein will enable the use of multi-scale modeling for investigating and understanding a broad range of magneto-mechanical phenomena from slow to ultrafast time scales.

We develop a formulation of the coherent potential approximation (CPA) on the basis of the Wannier representation to develop a computationally efficient method for the treatment of homogeneous random alloys that is independent on the applied first-principles electric structure code. To verify the performance of this CPA implementation within the Wannier representation, we examine the Bloch spectral function, the density of states (DOS), and the magnetic moment in Fe-based transition-metal alloys Fe-X (X = V, Co, Ni, and Cu), and compare the results with those of the well-established CPA implementation based on the KKR Green's function method. The Wannier-CPA and the KKR-CPA lead to results very close to each other. The presented Wannier-CPA method has a wide potential applicability to other physical quantities and large compound systems because of its low computational effort required., 10 pages, 7 figures

Imaging a chemisorption process At low temperatures, a molecule may adsorb to a surface only through weak forces (physisorption), and only upon heating and overcoming an energetic barrier does it form a strong covalent bond (chemisorption). Huber et al. imaged this transition for an atomic force microscopy tip terminating in a carbon monoxide molecule. Although the oxygen atom of the tip is normally considered to act like a rare gas atom, interacting only through van der Waals interactions, at short distances directly above a transition metal atom, it transitions to a strongly interacting chemisorption state. Science , this issue p. 235

While the ground state of magnetic materials is in general well described on the basis of spin density functional theory (SDFT), the theoretical description of finite-temperature and non-equilibrium properties require an extension beyond the standard SDFT. Time-dependent SDFT (TD-SDFT), which give for example access to dynamical properties are computationally very demanding and can currently be hardly applied to complex solids. Here we focus on the alternative approach based on the combination of a parameterized phenomenological spin Hamiltonian and SDFT-based electronic structure calculations, giving access to the dynamical and finite-temperature properties for example via spin-dynamics simulations using the Landau–Lifshitz–Gilbert (LLG) equation or Monte Carlo simulations. We present an overview on the various methods to calculate the parameters of the various phenomenological Hamiltonians with an emphasis on the KKR Green function method as one of the most flexible band structure methods giving access to practically all relevant parameters. Concerning these, it is crucial to account for the spin–orbit coupling (SOC) by performing relativistic SDFT-based calculations as it plays a key role for magnetic anisotropy and chiral exchange interactions represented by the DMI parameters in the spin Hamiltonian. This concerns also the Gilbert damping parameters characterizing magnetization dissipation in the LLG equation, chiral multispin interaction parameters of the extended Heisenberg Hamiltonian, as well as spin–lattice interaction parameters describing the interplay of spin and lattice dynamics processes, for which an efficient computational scheme has been developed recently by the present authors.

The mechanism behind the three-spin chiral interaction (TCI) included in the extended Heisenberg Hamiltonian and represented by an expression worked out recently (Phys.\ Rev.\ B, {\bf 101}, 174401 (2020)) is discussed. It is stressed that this approach provides a unique set of the multispin exchange parameters which are independent of each other either due to their different order of perturbation or due to different symmetry. This ensures in particular the specific properties of the TCI that were demonstrated previously via fully relativistic first principles calculations, and that result from the common influence of several issues not explicitly seen from the expression for the TCI parameters. Therefore, an interpretation of the TCI is suggested, showing explicitly its dependence on the relativistic spin-orbit coupling and on the topological orbital susceptibility (TOS). This is based on an expression for the TOS that is worked out on the same footing as the expression for the TCI. Using first-principles calculations we demonstrate in addition numerically the common topological properties of the TCI and TOS. To demonstrate the role of the relativistic spin-orbit coupling (SOC) for the TCI, a so-called topological' spin susceptibility (TSS) is introduced. This quantity characterizes the SOC induced spin magnetic moment on the atom in the presence of non-collinear magnetic structure, giving a connection between the TOS and TCI. Numerical results again support our conclusions., 11 pages, 6 figures

Based on first principles calculations we investigate the electronic and magnetic properties of Pt layers in Pd$(001)$/Co/Pt thin film structures exposed to an external electric field. Due to the Co underlayer, the surface Pt layers have induced moments that are modified by an external electric field. The field induced changes can be explained by the modified spin-dependent orbital hybridization that varies non-linearly with the field strength. We calculate the x-ray absorption and the x-ray magnetic circular dichroism spectra for an applied external electric field and examine its impact on the spectra in the Pt layer around the L$_{2}$ and L$_{3}$ edges. We also determine the layer dependent magneto-crystalline anisotropy and show that the anisotropy can be tuned easily in the different layers by the external electric field., 9 pages, 11 figures

Magnetic isotropic and Dzyaloshinskii-Moriya interactions in yttrium iron garnet have been obtained by ab initio fully relativistic calculations. The calculated coupling constants are in agreement with available experimental data. Using linear spin-wave theory, we are able to reproduce the experimental magnon spectrum including the spin-wave gap and stiffness. The way to calculate the exchange coupling constants using the Korringa-Kohn-Rostoker formalism for large magnetic systems such as complex oxides is discussed in detail.

Magnetic multilayers are promising tunable systems for hosting magnetic skyrmions at/above room temperature. Revealing their intriguing switching mechanisms and associated inherent electrical responses are prerequisites for developing skyrmionic devices. In this Letter, we theoretically demonstrate the annihilation of single skyrmions occurring through a multilayer structure, which is mediated by the hopping dynamics of topological hedgehog singularities known as Bloch points. The emerging intralayer dynamics of Bloch points are dominated by the Dzyaloshinskii-Moriya interaction, and their propagation can give rise to solenoidal emergent electric fields in the vicinity. Moreover, as the topology of spin textures can dominate their emergent magnetic properties, we show that the Bloch-point hopping through the multilayer will modulate the associated topological Hall response, with the magnitude proportional to the effective topological charge. We also investigate the thermodynamic stability of these states regarding the layer-dependent magnetic properties. This study casts light on the emergent electromagnetic signatures of skyrmion-based spintronics, rooted in magnetic-multilayer systems.

We demonstrate the low temperature suppression of the platinum (Pt) spin Nernst angle in bilayers consisting of the antiferromagnetic insulator hematite ($\alpha$-Fe$_2$O$_3$) and Pt upon measuring the transverse spin Nernst magnetothermopower (TSNM). We show that the observed signal stems from the interplay between the interfacial spin accumulation in Pt originating from the spin Nernst effect and the orientation of the N\'eel vector of $\alpha$-Fe$_2$O$_3$, rather than its net magnetization. Since the latter is negligible in an antiferromagnet, our device is superior to ferromagnetic structures, allowing to unambiguously distinguish the TSNM from thermally excited magnon transport (TMT), which usually dominates in ferri/ferromagnets due to their non-zero magnetization. Evaluating the temperature dependence of the effect, we observe a vanishing TSNM below ~100 K. We compare these results with theoretical calculations of the temperature dependent spin Nernst conductivity and find excellent agreement. This provides evidence for a vanishing spin Nernst angle of Pt at low temperatures and the dominance of extrinsic contributions to the spin Nernst effect., Comment: 4 pages, 4 figures

The notion of non-trivial topological winding in condensed matter systems represents a major area of present-day theoretical and experimental research. Magnetic materials offer a versatile platform that is particularly amenable for the exploration of topological spin solitons in real space such as skyrmions. First identified in non-centrosymmetric bulk materials, the rapidly growing zoology of materials systems hosting skyrmions and related topological spin solitons includes bulk compounds, surfaces, thin films, heterostructures, nano-wires and nano-dots. This underscores an exceptional potential for major breakthroughs ranging from fundamental questions to applications as driven by an interdisciplinary exchange of ideas between areas in magnetism which traditionally have been pursued rather independently. The skyrmionics roadmap provides a review of the present state of the art and the wide range of research directions and strategies currently under way. These are, for instance, motivated by the identification of the fundamental structural properties of skyrmions and related textures, processes of nucleation and annihilation in the presence of non-trivial topological winding, an exceptionally efficient coupling to spin currents generating spin transfer torques at tiny current densities, as well as the capability to purpose-design broad-band spin dynamic and logic devices., J. Phys. D, accepted for publication

An approach to account for the effect of thermal lattice vibrations when calculating exchange coupling parameters is presented on the basis of the Korringa-Kohn-Rostoker Green function method making use of the alloy analogy model. Using several representative systems, it is shown that depending on the material the effect of thermal lattice vibrations can have a significant impact on the isotropic exchange as well as the Dzyaloshinskii-Moriya interactions (DMI). This should lead in turn to an additional contribution to the temperature dependence of the magnetic properties of solids, which cannot be neglected in the general case. As an example, we discuss such an influence on the critical temperature of various magnetic phase transitions. In particular, in the case of skyrmion hosting materials, a strong impact of lattice vibrations on the DMI is an additional source for the temperature dependent skyrmion size and stability, which should be taken into consideration. The present approach gives also access to features of magnetic properties that are associated with static atomic displacements as, for example, in random high-entropy alloys.

Ab initio calculations of the spin wave stiffness constant $D$ for elemental Fe and Ni performed by different groups in the past have led to values with a considerable spread of 50-100 %. We present results for the stiffness constant $D$ of Fe, Ni, and permalloy Fe$_{0.19}$Ni$_{0.81}$ obtained by three different approaches: (i) by finding the quadratic term coefficient of the power expansion of the spin wave energy dispersion, (ii) by a damped real-space summation of weighted exchange coupling constants, and (iii) by integrating the appropriate expression in reciprocal space. All approaches are implemented by means of the same Korringa-Kohn-Rostoker (KKR) Green function formalism. We demonstrate that if properly converged, all procedures yield comparable values, with uncertainties of 5-10 % remaining. By a careful analysis of the influence of various technical parameters we estimate the margin of errors for the stiffness constants evaluated by different approaches and suggest procedures to minimize the risk of getting incorrect results., Comment: 11 pages, 7 figures, 12 tables

The electronic structure and magnetic properties of the compound 2H-NbS2 intercalated by 3d elements from Cr to Ni, have been investigated using the Korringa–Kohn–Rostoker electronic structure method. Here, we consider the phases with 33% of intercalation within the ordered phase having a 3 × 3 $\sqrt 3 \times \sqrt 3 $ arrangement of the magnetic atoms. We analyze the relationship of the magnetic and electronic properties on the structural parameters dependent on the intercalant. The exchange coupling parameters calculated from first principles have been used for subsequent Monte Carlo simulations. Within these investigations, the FM order was found for the Cr and Mn intercalated phases as ground state configuration with a Curie temperature being in good agreement with the experiment. According to the Monte Carlo simulation, Fe1/3NbS2 has a complicated noncollinear magnetic structure with a noncompensated total magnetic moment, whereas Co1/3NbS2 and Ni1/3NbS2 are found to be antiferromagnetic, all in line with experimental observations.

Taking the noncollinear antiferromagnetic hexagonal Heusler compound ${\mathrm{Mn}}_{3}\mathrm{Ge}$ as a reference system, the contributions to linear response phenomena arising solely from the chiral coplanar and noncoplanar spin configurations are investigated. Orbital moments, x-ray absorption, and anomalous and spin Hall effects, as well as corresponding spin-orbit torques and Edelstein polarizations, are studied depending on a continuous variation of the polar angle relative to the kagome planes of corner-sharing triangles between the noncollinear antiferromagnetic and the ferromagnetic limits. By scaling the speed of light from the relativistic Dirac case to the nonrelativistic limit the chirality-induced or topological contributions can be identified by suppressing the spin-orbit coupling.

Previous studies on the anomalous Hall effect in coplanar noncollinear antiferromagnets are revisited and extended to magneto-optic properties, namely magneto-optic Kerr effect (MOKE) and x-ray magnetic dichroism (XMCD). Starting from group-theoretical considerations the shape of the frequency-dependent conductivity tensor for various actual and hypothetical spin configurations in cubic and hexagonal ${\mathrm{Mn}}_{3}X$ compounds is determined. Calculated MOKE and x-ray dichroism spectra are used to confirm these findings and to give estimates of the size of the effects. For ${\mathrm{Mn}}_{3}\mathrm{IrPt}$ and ${\mathrm{Mn}}_{3}\mathrm{PtRh}$ alloys the concentration dependence of the anomalous and spin Hall conductivity is studied in addition.

An extension of the Heisenberg Hamiltonian is discussed that allows us to go beyond the standard bilinear spin Hamiltonian taking into account various contributions due to multispin interactions having both chiral and nonchiral character. The parameters of the extended Hamiltonian are calculated from first principles within the framework of the multiple-scattering Green's function formalism giving access to an explicit representation of these parameters in real space. The discussions are focused on the chiral interactions, i.e., biquadratic and three-spin Dzyaloshinskii-Moriya-like vector interactions ${\stackrel{P\vec}{\mathcal{D}}}_{ijij}$ (BDMI) and ${\stackrel{P\vec}{\mathcal{D}}}_{ijkj}$ (TDMI), respectively, as well as the three-spin chiral interaction ${J}_{ijk}$. Although all parameters are driven by spin-orbit coupling (SOC), some differences in their properties are demonstrated by calculations for real materials. In particular it is shown that the three-spin chiral interactions ${J}_{ijk}$ may be topology as well as SOC induced, while the TDMI is associated only with the SOC. As the magnitude of the chiral interactions can be quite sizable, they can lead to a stabilization of a noncollinear magnetic texture in some materials that is absent when these interactions are neglected.

Small metal clusters have been investigated for decades due to their beneficial catalytic activity. It was found that edges are most reactive and the number of catalytic events increases with the cluster's size. However, a direct measurement of chemical reactivity of individual atoms within the clusters has not been reported yet. We combine the high-resolution capability of CO-terminated tips in scanning probe microscopy with their ability to probe chemical binding forces on single Fe atoms to study the chemical reactivity of atom-by-atom assembled Fe clusters from 1 to 15 atoms on the atomic scale. We find that the chemical reactivity of individual atoms within flat Fe clusters does not depend on the cluster size but on the coordination number of the investigated atom. Furthermore, we explain the atomic contrast of the investigated Fe clusters by relating the force spectra of individual atoms with atomic force microscopy images of the clusters.

Transport properties of permalloy doped with V, Co, Pt, and Au are explored via ab-initio calculations. The Kubo-Bastin formula is evaluated within the fully relativistic Korringa-Kohn-Rostoker Green function formalism. Finite temperature effects are treated by means of the alloy analogy model. It is shown that the fact that the host is disordered and not crystalline has a profound effect on how the conductivities characterizing the anomalous Hall effect and the spin Hall effect depend on the dopant concentration. Several relationships between quantities characterizing charge and spin transport are highlighted. The decrease of the longitudinal charge conductivity with increasing doping depends on the dopant type, following the sequence Co-Au-Pt-V. The dependence of the anomalous Hall and spin Hall conductivities on the dopant concentration is found to be non-monotonic. Introducing a finite temperature changes the overall trends significantly. The theoretical results are compared with available experimental data., Comment: 29 pages, 15 figures, 2 tables

A scheme is presented that allows to account for finite temperature effects when calculating response functions or spectroscopic properties of solids. The approach is based on the alloy analogy model and treats thermally induced disorder as chemical disorder in substitutional alloys by means of the Coherent Potential Approximation (CPA). The reliability of the approach is demonstrated by calculations of the temperature dependent resistivity of ferromagnetic Fe. Calculations of angle-resolved photoemission show for increasing temperature the expected smearing of band-like features in the spectra, i.e. a transition from the so-called UPS to the XPS regime.

As a fundamental parameter in magnetism, the phenomenological Gilbert damping constant a determines the performance of many spintronic devices. For most magnetic materials, a is treated as an isotropic parameter entering the Landau-Lifshitz-Gilbert equation. However, could the Gilbert damping be anisotropic? Although several theoretical approaches have suggested that anisotropic a could appear in single-crystalline bulk systems, experimental evidence of its existence is scarce. Here, we report the emergence of anisotropic magnetic damping by exploring a quasi-two-dimensional single-crystalline ferromagnetic metal/semiconductor interface-that is, a Fe/GaAs(001) heterojunction. The observed anisotropic damping shows twofold C-2v symmetry, which is expected from the interplay of interfacial Rashba and Dresselhaus spin-orbit interaction, and is manifested by the anisotropic density of states at the Fe/GaAs (001) interface. This discovery of anisotropic damping will enrich the understanding of magnetization relaxation mechanisms and can provide a route towards the search for anisotropic damping at other ferromagnetic metal/semiconductor interfaces.

The new metastable compound Cr{sub 1+x}Sb with x up to 0.6 has been prepared via a thin film approach using modulated elemental reactants and investigated by in-situ X-ray reflectivity, X-ray diffraction, differential scanning calorimetry, energy dispersive X-ray analysis as well as transmission electron microscopy and atomic force microscopy. The new Cr-rich antimonide crystallizes in a structure related to the Ni{sub 2}In-type structure, where the crystallographic position (1/3, 2/3, 3/4) is partially occupied by excess Cr. The elemental layers of the pristine material interdiffused significantly before Cr{sub 1+x}Sb crystallized. A change in the activation energy was observed for the diffusion process when crystal growth starts. First-principles electronic structure calculations provide insight into the structural stability, magnetic properties and resistivity of Cr{sub 1+x}Sb. - Graphical abstract: 1 amorphous multilayered film 2 interdiffused amorphous film 3 metastable crystalline phase 4 thermodynamic stable phase (and by-product). - Highlights: • Interdiffusion of amorphous Cr and Sb occurs before crystallization. • Crystallization of a new metastable phase Cr{sub 1.6}Sb in Ni{sub 2}In-type structure. • The new Cr-rich phase shows half-metallic behavior.

Band structure calculations are reported to describe the effects of Ta for Hf substitution on the electronic structure of the Laves phase of HfFe 2 . According to experimental results emphasis is put on the investigation of the Hf 0.825 Ta 0.175 Fe 2 composition in comparison with the reference HfFe 2 and TaFe 2 compounds. By investigation of the theoretical interatomic exchange interactions constants, we showed the influence of the magnetovolume effect on the magnetic phase stability for one intermediate composition Hf 0.825 Ta 0.175 Fe 2 , chosen in the most interesting part of the magnetic phase diagram with coexistence of ferromagnetic (FM) and antiferromagnetic (AF) behaviour. Evolution of the a lattice parameter is found to drive the change from FM to AF magnetic order. A detailed study of the interatomic Fe–Fe exchange coupling constants and their lattice dependence reveals that the ferromagnetic interaction with the first shell is strongly reduced upon contraction of the a lattice parameter.

An accurate scheme to calculate the interatomic Dzyaloshinskii-Moriya interaction (DMI) parameters is presented, which is based on the fully relativistic Korringa-Kohn-Rostoker Green function (KKR-GF) technique. Corresponding numerical results are compared with those obtained using other schemes reported in the literature. The differences found can be attributed primarily to the different reference states used in the various approaches. The advantage of the present approach is that the DMI vectors can in a natural way be connected with the DMI-related torques on local magnetic moments. In addition an expression for the DMI parameters formulated for a micromagnetic model Hamiltonian is presented that provides a connection to the DMI parameters calculated for atomistic Hamiltonians. This formulation also allows the discussion of the DMI in terms of specific features of the electronic band structure.

A new metastable compound Cr3Sb was synthesized as thin film starting from modulated elemental reactant layers. The new compound is cubic and crystallizes in the A15 structure (Cr3Si-type). A variation of the occupancy of the Sb position (0, 0, 0) was observed leading to a Cr-rich sample with formula Cr∼6Sb. In-situ X-ray diffraction and reflectivity investigations indicate an interdiffusion of the multilayers and crystallization of the new compound below 350°C. Calculations of the crystal structure and lattice parameter agree well with the experimental results. In addition the existence of a further metastable phase, a Heusler-like alloy, is discussed and supported by DFT calculations.

The structural as well as electronic and magnetic properties of chromium chalcogenides and pnictides with NiAs structure were studied using the Korringa-Kohn-Rostoker (KKR) band structure method. The magnetic properties at finite temperature were investigated by means of Monte Carlo simulations on the basis of a classical Heisenberg Hamiltonian and the exchange coupling parameters calculated from first principles. Combination of ab initio electronic structure calculations with Monte Carlo simulations allowed to investigate both the ground state magnetic properties as well as the finite-temperature properties. In the case of stoichiometric systems, these calculations allowed to explain the origin of magnetic structures in this system as observed experimentally. In case of non-stoichiometric Cr-(Te, Se) alloys the origin of finite-temperature spin-glass and cluster-glass behaviors was clarified. In all cases a reasonable agreement with the experiment was obtained for the value of the critical temperature.

A Kubo-Greenwood-like equation for the Gilbert damping parameter α is presented that is based on the linear response formalism. Its implementation on the basis of the fully relativistic Korringa-Kohn-Rostoker (KKR) band structure method together with the Coherent Potential Approximation (CPA) alloy theory allows application to a wide range of situations. This is demonstrated by results obtained for the alloy system bcc FexCo1-x as well as for a series of alloys of permalloy with 5d transition metals. To account for the thermal displacements of atoms as a scattering mechanism, an alloy-analogy model is introduced. In line with experiment, calculations for Ni correctly describe the rapid change of α when small amounts of Cu are introduced substitutionally.

Máme zprávy o zhášení jednotlivých Ni adatom momentů na Te-zakončeného BI2 Te2Se a Bi2Te3 topologických izolátor povrchy. Tento efekt je známý jako chybějící x-ray magnetické cirkulární dichroismus pro rezonanční přechody L3,2 Částečně naplní do Ni 3d stavů teorie odvozené od obsazení nd = 9,2. Na základě srovnávací studie Ni a Fe pomocí řádkovací tunelový mikroskop a ab initio výpočtů jsme schopni se týkají konkrétního prvku Tvorba moment na místní kritérium Stoner. Naše teorie pořady dělal, zatímco Fe adatoms vytvářejí velké spin momenty z MS = 2.54μB s out-ofrovině anizotropie v důsledku dostatečně velkou hustotu stavů na Fermiho energie, Ni zůstává hluboko pod prahem na efektivní Stoner pro tvorbu místní moment. S úrovní Fermi setrvání v mezera bulk band po adatom depozice, nonmagnetic Ni a přednostně out-of-rovině orientované magnetické Fe s podobnými strukturálními reality na BI2 TE2 Se plochy představují ideální platformu pro studium účinků off-on time-obrácení porušení symetrie na topologické povrchových stavů. We report on the quenching of single Ni adatom moments on Te-terminated Bi2 Te2Se and Bi2Te3 topological insulator surfaces. The effect is noted as a missing x-ray magnetic circular dichroism for resonant L3,2 transitions into partially filled Ni 3d states of theory-derived occupancy nd = 9.2. On the basis of a comparative study of Ni and Fe using scanning tunneling microscopy and ab initio calculations, we are able to relate the element specific moment formation to a local Stoner criterion. Our theory shows that while Fe adatoms form large spin moments of ms = 2.54μB with out-of-plane anisotropy due to a sufficiently large density of states at the Fermi energy, Ni remains well below an effective Stoner threshold for local moment formation. With the Fermi level remaining in the bulk band gap after adatom deposition, nonmagnetic Ni and preferentially out-of-plane oriented magnetic Fe with similar structural properties on Bi2 Te2 Se surfaces constitute a perfect platform to study the off-on effects of time-reversal symmetry breaking on topological surface states.

Various technical developments enlarged the potential of angle-resolved photo emission spectroscopy (ARPES) tremendously during the last one or two decades. In particular improved momentum and energy resolution as well as the use of photon energies from few eV up to several keV makes ARPES a rather unique tool to investigate the electronic properties of solids and surfaces. Obviously, this rises the need for a corresponding theoretical formalism that allows to accompany experimental ARPES studies in an adequate way. As will be demonstrated by several examples this goal could be achieved by various recent developments on the basis of the one-step model of photo emission: the spin–orbit induced Rashba-splitting of Shockley-type surface states is discussed using a fully relativistic description. The impact of chemical disorder within surface layers can be handled by means of the coherent potential approximation (CPA) alloy theory. Calculating phonon properties together with the corresponding electron–phonon self-energy allows a direct comparison with features in the ARPES spectra caused by electron–phonon interaction. The same holds for the influence of electronic correlation effects. These are accounted for by means of the dynamical mean field theory (DMFT) that removes the most serious short comings of standard calculations based on the standard local density approximation (LDA). The combination of this approach with the CPA allows the investigation of correlated transition metal alloys. Finally, accounting for the photon momentum and going beyond the single scatter approximation for the final state allows to deal quantitatively with ARPES in the high-energy regime (HAXPES) that reduces the influence of the surface on the spectra and probing primarily the bulk electronic structure this way. Corresponding calculations of ARPES spectra, however, have to deal with thermal vibrations in an adequate way. For this, a new scheme is suggested that makes use of the CPA.

We investigated experimentally and theoretically the effect of the substitution of Te by Se onto the structural, magnetic and electronic properties of ferromagnetic Cr 5±x Te 8 as parent material. Whereas Cr 5 Te 8 is dimorphic crystallizing in a monoclinic and trigonal modification, Se substituted samples crystallize in two different trigonal modifications depending on the synthesis conditions. One of the modifications can be viewed as self-intercalated dichalcogenides Cr 1+x Q 2 (Q = Te, Se) and the other is a superstructure which is isostructural to one of the Cr 5±x Te 8 modifications. For the Se richest samples (Te:Se = 1:7) a new modification is identified which was formerly reported for Cr 3+x Se 4 . For a distinct Cr content the replacement of Se by Te induces a reduction of the unit cell volumes, of the Cr-Cr and Cr-Te/Se distances. Increasing the Cr content for a constant Te:Se ratio has the opposite effect. The results also suggest that the homogeneity range extends to more Cr rich compounds with decreasing Te content. For a given Cr content the substitution of Te by Se weakens the ferromagnetic exchange interactions and strengthens the antiferromagnetic exchange. With increasing Cr content and a fixed Te:Se ratio ferromagnetic properties become more pronounced. The low temperature magnetic behavior is characterized by spin-glass, spin-glass like or cluster-glass properties depending on the Cr content and the Te:Se ratio. Electronic structure calculations done within the framework of LSDA (local spin density approximation) gave a detailed insight into the electronic and magnetic properties of the investigated systems supporting the interpretation of the achieved experimental results. This applies in particular for the calculated exchange coupling constants that provided the necessary input for Monte Carlo simulations used for theoretical investigations on the magnetic properties at finite temperatures.

The title compounds were synthesized via the high-temperature (HT) route. The materials are characterized by Rietveld analysis, magnetic measurements, and electronic band-structure calculations. Two different structural modifications depending on the synthesis conditions are observed: a HT modification with trigonal basic cells (space group: P-3m1) for Cr{sub (1+x)}Q{sub 2} ((1+x)=1.25, 1.28, 1.34, 1.37, 1.41, 1.43) and a low-temperature (LT) modification with trigonal super-cell (space group: P-3m1) for Cr{sub (5+x)}Q{sub 8} ((5+x)=5.00, 5.12, 5.36, 5.48, 5.64, 5.72). The crystal structures are closely related to the NiAs-type structure with metal vacancies in every second metal layer. The substitution of Te by Se and the change of the Cr concentration induce significant alterations of the magnetic properties. With increasing Cr content the Weiss constant {theta} changes drastically from negative to strong positive values, i.e., with increasing Cr concentration a shift from predominant antiferromagnetic exchange to ferromagnetic exchange occurs. At LTs a complex magnetic behavior is observed. For some members a spin-glass (SG) behavior is found with the freezing temperature T{sub f} following the Vogel-Fulcher law. At the highest Cr concentrations ferromagnetic characteristics dominate with spontaneous magnetizations below the Curie temperatures. The differences of the magnetic properties of the LT and HT phases can bemore » explained on the basis of interatomic distances and angles. For a deeper understanding of the experimental results, they have been compared with the results of spin polarized relativistic Korringa-Kohn-Rostoker electronic band-structure calculations and both results are consistent. To explain the features of temperature-dependent magnetization of the compounds, Monte Carlo (MC) simulations based on the Heisenberg model have been performed with the exchange coupling parameters obtained within the ab-initio calculations of the electronic structure. The possible reasons for a modification of the exchange coupling parameters responsible for the temperature-dependent features are also analyzed. - Graphical abstract: The magnetic properties of Cr{sub 1+x}Q{sub 2} and Cr{sub 5+x}Te{sub 5}Se{sub 3} (Q=Te, Se; ratio=5:3) are strongly influenced by the Cr content and the crystal structure with the Weiss constant and Curie temperature covering a large range.« less

The temperature dependent stability of the magnetic phases of FeRh were investigated by means of total energy calculations with magnetic disorder treated within the uncompensated disordered local moment (uDLM) approach. In addition, Monte Carlo simulations based on the extended Heisenberg model have been performed, using exchange coupling parameters obtained rom first principles. The crucial role and interplay of two factors in the metamagnetic transition in FeRh has been revealed, namely the dependence of the Fe-Fe exchange coupling parameters on the temperature-governed degree of magnetic disorder in the system and the stabilizing nature of the induced magnetic moment on Rh-sites. An important observation is the temperature dependence of these two competing factors.

The formal basis for fully relativistic Korringa-Kohn-Rostoker (KKR) or multiple scattering calculations for the electronic Green function in case of a general potential is discussed. Simple criteria are given to identify situations that require to distinguish between right and left hand side solutions to the Dirac equation when setting up the electronic Green function. In addition various technical aspects of an implementation of the relativistic KKR for general local and non-local potentials will be discussed.

Metal clusters really close-up Atomic force microscopy (AFM) can be used to reveal subatomic structures. By this means, Emmrich et al. found that individual copper and iron atoms formed toroidal structures on a copper surface. These shapes arise from the electrostatic attractions in the center of the atoms and Pauli repulsions at their edges. Individual atoms within clusters have underlying surface symmetry and can bind to different surface sites as clusters form. Science , this issue p. 308

A scheme is presented that is based on the alloy analogy model and allows one to account for thermal lattice vibrations as well as spin fluctuations when calculating response quantities in solids. Various models to deal with spin fluctuations are discussed concerning their impact on the resulting temperature-dependent magnetic moment, longitudinal conductivity, and Gilbert damping parameter. It is demonstrated that, by using the Monte Carlo (MC) spin configuration as input, the alloy analogy model is capable of reproducing the results of MC simulations on the average magnetic moment within all spin fluctuation models under discussion. On the other hand, the response quantities are much more sensitive to the spin fluctuation model. Separate calculations accounting for the thermal effect due to either lattice vibrations or spin fluctuations show that they give comparable contributions to the electrical conductivity and Gilbert damping. However, comparison to results accounting for both thermal effects demonstrates violation of Matthiessen's rule, showing the nonadditive effect of lattice vibrations and spin fluctuations. The results obtained for bcc Fe and fcc Ni are compared with the experimental data, showing rather good agreement for the temperature-dependent electrical conductivity and the Gilbert damping parameter.

The effect of substitution of up to two Te atoms by Se atoms on the crystal structure, the magnetic and electronic properties has been studied in the system Cr(5+x)Te8−ySey. Trigonal basic cells with space group P - 3 m 1 for Cr(1+x)Q2 and trigonal supercells (doubling of the unit cell in all directions) with space group P - 3 m 1 for Cr(5+x)Q8 ((1+x)=1.27, 1.32, 1.36; (5+x)=5.08, 5.28, 5.44; Q=Te, Se; Te:Se=6:2) have been identified in X-ray powder diffraction patterns and Rietveld refinements as high-temperature and low-temperature phases, respectively. The crystal structures are related to the hexagonal NiAs-type structure with metal vacancies in every second metal layer. The magnetic properties are closely related to the Cr content and the structure type. Cluster-glass and spin-glass behavior at low temperatures are observed for high and low Cr contents, respectively. For the same Cr content, the phases with trigonal basic cells have higher values for the Curie temperature Tc and the freezing temperature Tf, and larger magnetization than those for the phases with trigonal supercells. For the same structure type, the values for Tc/Tf do not show a linear relationship with the change of Cr content but exhibit a V-shape fashion. Our experimental investigations were accompanied by spin-polarized relativistic Korringa–Kohn–Rostoker (SPR-KKR) electronic structure calculations. Cr deficiencies as well as atomic disorder on the chalcogen sites was accounted for using the coherent potential approximation (CPA) alloy theory. Calculation of the exchange coupling parameters Jij provided the basis for subsequent Monte Carlo simulations of the magnetic properties at finite temperatures.

An incorporation of the LDA+U formalism into the spin-polarized relativistic Korringa–Kohn–Rostoker (SPR-KKR) method of band-structure calculations is presented. This new approach accounts for one-particle relativistic effects in a proper way when applying the LDA+U method to get an improved description of correlation effects compared to plain LDA-based calculations. In addition, it allows to deal with disordered systems in a straight forward manner by a combination with the coherent potential approximation (CPA) alloy theory. These features are demonstrated by results obtained for fictitious ferromagnetic fcc-Uranium and the disordered alloy system FexCo1−x.

Clusters built from individual iron atoms adsorbed on surfaces (adatoms) were investigated by atomic force microscopy (AFM) with subatomic resolution. Single copper and iron adatoms appeared as toroidal structures and multiatom clusters as connected structures, showing each individual atom as a torus. For single adatoms, the toroidal shape of the AFM image depends on the bonding symmetry of the adatom to the underlying structure [twofold for copper on copper(110) and threefold for iron on copper(111)]. Density functional theory calculations support the experimental data. The findings correct our previous work, in which multiple minima in the AFM signal were interpreted as a reflection of the orientation of a single front atom, and suggest that dual and triple minima in the force signal are caused by dimer and trimer tips, respectively.

We present a comprehensive study on the low-temperature orthorhombic phase of $\mathrm{Ba}{({\mathrm{Fe}}_{1\ensuremath{-}x}{\mathrm{Co}}_{x})}_{2}{\mathrm{As}}_{2}$ based on the Korringa-Kohn-Rostoker-Green function approach. Using this band-structure method in combination with the coherent potential approximation alloy theory we are able to investigate the evolution of the magnetic and electronic properties of this prototype iron pnictide for arbitrary concentrations $x$, while dealing with the chemical disorder without uncontrolled simplifications by using solely a rigid-band shift or the virtual crystal approximation. We discuss the development of the site-resolved magnetic moments for the experimentally observed stripe antiferromagnetic order together with the strong electronic anisotropy of the Fermi surface and compare it with angle-resolved photoemission spectroscopy measurements of detwinned crystals. We furthermore calculate magnetic exchange coupling parameters ${J}_{ij}$ and use them for Monte Carlo simulations on the basis of the classical Heisenberg model to get an insight on the temperature dependence of the magnetic ordering on the cobalt concentration.

The effect of the Dzyaloshinsky-Moriya interaction on the magnetic structure of an ordered FePt monolayer deposited on the $\mathrm{Pt}(\mathrm{111})$ surface has been investigated. In the ground state, the pronounced anisotropic geometry of the FePt layer with alternating Fe and Pt chains gives rise to a helimagnetic structure with a strong difference in the helicity period along the chains and perpendicular to them. In the presence of an external magnetic field, the region of stable Skyrmion magnetic structures in the B-T phase diagram has been demonstrated via Monte Carlo simulations using the parameters obtained within first-principles electronic structure calculations. The present study demonstrates clearly that the ratio of the exchange coupling parameters $J/D$ for a deposited magnetic film\char22{}being of central importance for the formation of Skyrmions\char22{}can be manipulated by growing an overlayer of 2-dimensional compounds with the atoms carrying spontaneous magnetic moments separated by the atoms of nonmagnetic elements.

We investigate to what extent the magnetic properties of deposited nanostructures can be influenced by selecting as a support different surfaces of the same substrate material. Fully relativistic ab initio calculations were performed for Co monolayers and adatoms on Pd(100), Pd(111), and Pd(110) surfaces. Changing the crystallographic orientation of the surface has a moderate effect on the spin magnetic moment, a larger effect on the orbital magnetic moment, but sometimes a dramatic effect on the magnetocrystalline anisotropy energy and on the magnetic dipole term ${T}_{\ensuremath{\alpha}}$. The dependence of ${T}_{\ensuremath{\alpha}}$ on the magnetization direction $\ensuremath{\alpha}$ can lead to a strong apparent anisotropy of the spin magnetic moment as deduced from the x-ray magnetic circular dichroism sum rules. For systems in which the spin-orbit coupling is not very strong, the ${T}_{\ensuremath{\alpha}}$ term can be understood as arising from the differences between components of the spin magnetic moment associated with different magnetic quantum numbers $m$.

We present a theory of temperature-dependent photoemission which accurately describes phonon effects in soft and hard x-ray angle-resolved photoemission. Our approach is based on a fully relativistic one-step theory of photoemission that quantitatively reproduces the effects of phonon-assisted transitions beyond the usual $\mathbf{k}$-conserving dipole selection rules which lead to the so-called XPS limit in the hard x-ray and/or high temperature regime. Vibrational atomic displacements have been included using the coherent potential approximation in analogy to the treatment of disordered alloys. The applicability of this alloy analogy model is demonstrated by direct comparison to experimental soft x-ray data from W(110) showing very satisfying agreement.

We present a detailed theoretical investigation on the magnetic properties of small single-layered Fe, Co, and Ni clusters deposited on Ir(111), Pt(111), and Au(111). For this, a fully relativistic ab initio scheme based on density functional theory has been used. We analyze the element, size, and geometry specific variations of the atomic magnetic moments and their mutual exchange interactions as well as the magnetic anisotropy energy in these systems. Our results show that the atomic spin magnetic moments in the Fe and Co clusters decrease almost linearly with increasing coordination number on all three substrates, while the corresponding orbital magnetic moments appear to be much more sensitive to the local atomic environment. The isotropic exchange interaction among the cluster atoms is always very strong for Fe and Co exceeding the values for bulk bcc Fe and hcp Co, whereas the anisotropic Dzyaloshinski-Moriya interaction is, in general, one or two orders of magnitude smaller when compared to the isotropic one. For the magnetic properties of Ni clusters, the magnetic properties can show quite a different behavior, and we find in this case a strong tendency towards noncollinear magnetism.

A spin reorientation accompanying the temperature-induced antiferromagnetic (AFM) to ferromagnetic (FM) phase transition is reported in strained epitaxial FeRh thin films. $^{57}\mathrm{Fe}$ conversion electron M\"ossbauer spectrometry showed that the Fe moments have different orientations in FeRh grown on thick single-crystalline MgO and in FeRh grown on ion-beam-assist-deposited (IBAD) MgO. It was also observed, in both samples, that the Fe moments switch orientations at the AFM to FM phase transition. Perpendicular anisotropy was evidenced in the AFM phase of the film grown on IBAD MgO and in the FM phase of that grown on regular MgO. Density-functional theory calculations enabled this spin-reorientation transition to be accurately reproduced for both FeRh films across the AFM-FM phase transition and show that these results are due to differences in strain.

Magnetic Compton profiles (MCPs) of Ni and Fe along [111] direction have been calculated using a combined Density Functional and many-body theory approach. At the level of the local spin density approximation the theoretical MCPs does not describe correctly the experimental results around the zero momentum transfer. In this work we demonstrate that inclusion of electronic correlations as captured by Dynamical Mean Field Theory (DMFT) improves significantly the agreement between the theoretical and the experimental MCPs. In particular, an energy decomposition of Ni MCPs gives indication of spin polarization and intrinsic nature of Ni 6 eV satellite, a genuine many-body feature., 4 pages, 4 figures