Self-consistent localized KKR scheme for surfaces and interfaces

Tuning Ferromagnetism in a Single Layer of Fe above Room Temperature

The crystallographic and magnetic properties of an Fe monolayer (ML) grown on 2 ML Au/W(110) substrate are studied with spin-polarized low-energy electron microscopy, density functional theory, and relativistic screened Korringa–Kohn–Rostoker calculations. The single layer of iron atoms possesses hexagonal symmetry and reveals a ferromagnetic order at room temperature. We experimentally demonstrate the possibility of tuning the Curie temperature and the magnitude of magnetization of the Fe monolayer by capping with Au. Taking into account several structural models, the calculation results mostly show ferromagnetic states with enhanced magnetic moments of Fe atoms compared to their bulk value and a further increase in their value after covering with Au. The theoretically calculated Curie temperatures are in fair agreement with those obtained in the experiments. The calculations, furthermore, found evidence for the presence of frustrated isotropic Fe–Fe exchange interactions, and a discussion of the structural effects on the magnetic properties is provided herein.

Friedel Oscillations Induced by Magnetic Skyrmions: From Scattering Properties to All-Electrical Detection

Magnetic skyrmions are spin swirling solitonic defects that can play a major role in information technology. Their future in applications and devices hinges on their efficient manipulation and detection. Here, we explore from ab-initio their nature as magnetic inhomongeities in an otherwise unperturbed magnetic material, Fe layer covered by a thin Pd film and deposited on top of Ir(111) surface. The presence of skyrmions triggers scattering processes, from which Friedel oscillations emerge. The latter mediate interactions among skyrmions or between skyrmions and other potential surrounding defects. In contrast to their wavelengths, the amplitude of the oscillations depends strongly on the size of the skyrmion. The analogy with the scattering-off atomic defects enables the assignment of an effective scattering potential and a phase shift to the skyrmionic particles, which can be useful to predict their behavior on the basis of simple scattering frameworks. The induced charge ripples can be utilized for a noninvasive all-electrical detection of skyrmions located on a surface or even if buried a few nanometers away from the detecting electrode.

Spin waves in skyrmionic structures with various topological charges

Equilibrium properties and localized magnon excitations are investigated in topologically distinct skyrmionic textures. The observed shape of the structures and their orientation on the lattice is explained based on their vorticities and the symmetry of the crystal. The transformation between different textures and their annihilation as a function of magnetic field is understood based on the energy differences between them. The angular momentum spin-wave eigenmodes characteristic of cylindrically symmetric structures are combined in the distorted spin configurations, leading to avoided crossings in the magnon spectrum. The susceptibility of the skyrmionic textures to homogeneous external fields is calculated, revealing that a high number of modes become detectable due to the hybridization between the angular momentum eigenmodes. These findings should contribute to the observation of spin waves in distorted skyrmionic structures via experiments and numerical simulations, widening the range of their possible applications in magnonic devices.

Multiple scattering theory for dense plasmas

Dense plasmas occur in stars, giant planets, and in inertial fusion experiments. Accurate modeling of the electronic structure of these plasmas allows for prediction of material properties that can in turn be used to simulate these astrophysical objects and terrestrial experiments. But modeling them remains a challenge. Here we explore the Korringa-Kohn-Rostoker Green's function (KKR-GF) method for this purpose. We find that it is able to predict equation of state in good agreement with other state-of-the-art methods, where they are accurate and viable. In addition, it is shown that the computational cost does not significantly change with temperature, in contrast with other approaches. Moreover, the method does not use pseudopotentials-core states are calculated self consistently. We conclude that KKR-GF is a very promising method for dense plasma simulation.

Long-range focusing of magnetic bound states in superconducting lanthanum

Quantum mechanical systems with long-range interactions between quasiparticles provide a promising platform for coherent quantum information technology. Superconductors are a natural choice for solid-state based quantum devices, while magnetic impurities inside superconductors give rise to quasiparticle excitations of broken Cooper pairs that provide characteristic information about the host superconductor. Here, we reveal that magnetic impurities embedded below a superconducting La(0001) surface interact via quasiparticles extending to very large distances, up to several tens of nanometers. Using low-temperature scanning probe techniques, we observe the corresponding anisotropic and giant oscillations in the LDOS. Theoretical calculations indicate that the quasi-two-dimensional surface states with their strongly anisotropic Fermi surface play a crucial role for the focusing and long-range extension of the magnetic bound states. The quasiparticle focusing mechanism should facilitate the design of versatile magnetic structures with tunable and directed magnetic interactions over large distances, thereby paving the way toward the design of low-dimensional magnet-superconductor hybrid systems exhibiting topologically non-trivial quantum states as possible elements of quantum computation schemes based on Majorana quasiparticles.

A novel density functional theory for atoms, molecules, and solids

A theorem is proved stating that in atoms, molecules, and solids, only the set of the spherical parts of the density around each nucleus determines uniquely the external potential. Therefore, the induced Kohn and Sham (KS) potential has spherical symmetry around each nucleus, and furthermore, it has the symmetry of the external potential. In this way, the inconsistencies of standard density functional theory (DFT) concerning the asymmetry of the KS potential are remedied. As a result of the above, the ground state is uniquely determined by this set of spherical densities. In the case of a symmetry group G of a Hamiltonian H, the minimizing subspace of the Hamiltonian for each irreducible representation of G is uniquely determined by this set of spherical densities. Thus, the present theory opens the way for new density functionals and more accurate molecular calculations as it exploits local symmetries. Moreover, the theory of "Atoms in Molecules" formulated by Bader, by using the open quantum mechanics theory, can be explained in terms of DFT [R. F. W. Bader, Atoms in Molecules. A Quantum Theory (Oxford University Press, Oxford, 1990)].

Inducing skyrmions in ultrathin Fe films by hydrogen exposure

Magnetic skyrmions are localized nanometer-sized spin configurations with particle-like properties, which are envisioned to be used as bits in next-generation information technology. An essential step toward future skyrmion-based applications is to engineer key magnetic parameters for developing and stabilizing individual magnetic skyrmions. Here we demonstrate the tuning of the non-collinear magnetic state of an Fe double layer on an Ir(111) substrate by loading the sample with atomic hydrogen. By using spin-polarized scanning tunneling microscopy, we discover that the hydrogenated system supports the formation of skyrmions in external magnetic fields, while the pristine Fe double layer does not. Based on ab initio calculations, we attribute this effect to the tuning of the Heisenberg exchange and the Dzyaloshinsky–Moriya interactions due to hydrogenation. In addition to interface engineering, hydrogenation of thin magnetic films offers a unique pathway to design and optimize the skyrmionic states in low-dimensional magnetic materials.

Stabilization of skyrmions is one of the key issues in skyrmion-based spintronics. Here the authors demonstrate that hydrogenation can induce the formation of skyrmions in iron thin films, which provides an alternative way to tailor skyrmion states in low-dimensional magnetic materials.

Skyrmions with Attractive Interactions in an Ultrathin Magnetic Film

We determined the parameters of a classical spin Hamiltonian describing an Fe monolayer on Pd(111) surface with a Pt_{1-x}Ir_{x} alloy overlayer from ab initio calculations. While the ground state of the system is ferromagnetic for x=0.00, it becomes a spin spiral state as Ir is intermixed into the overlayer. Although the Dzyaloshinsky-Moriya interaction is present in the system, we will demonstrate that the frustrated isotropic exchange interactions play a prominent role in creating the spin spiral state, and these frustrated couplings lead to an attractive interaction between Skyrmions at short distances. Using spin dynamics simulations, we show that under these conditions the individual Skyrmions form clusters, and that these clusters remain stable at finite temperature.

Quantum well states and amplified spin-dependent Friedel oscillations in thin films

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 behaviour 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 (≈50 nm).

Magnetic anisotropy and chirality of frustrated Cr nanostructures on Au(1 1 1)

By using a fully relativistic embedded cluster Green's function technique we investigated the magnetic anisotropy properties of four different compact Cr trimers (equilateral triangles) and Cr mono-layers deposited on the Au(1 1 1) surface in both fcc and hcp stackings. For all trimers the magnetic ground state was found to be a frustrated 120° Néel configuration. Applying global spin rotations to the magnetic ground state, predictions of an appropriate second order spin Hamiltonian were reproduced with high accuracy by first principles calculations. For the Cr trimers with adjacent Au atoms in similar geometry, we obtained similar values for the in-plane and out-of-plane anisotropy parameters, however, the Dzyaloshinskii-Moriya (DM) interactions appeared to differ remarkably. For two kinds of trimers we found an unconventional magnetic ground state showing 90° in-the-plane rotation with respect to the high symmetry directions. Due to higher symmetry, the in-plane anisotropy term was missing for the mono-layers and distinctly different DM interactions were obtained for the different stackings. The chiral degeneracy of the Néel configurations was lifted by an energy less than 2 meV for the trimers, while this value increased up to about 15 meV per 3 Cr atoms for the hcp packed mono-layer.

Exchange interaction between magnetic impurities on surfaces of Cu(x)Pd(1-x) and Cu(x)Au(1-x) random substitutional alloys

We present fully relativistic first principles calculations of the exchange interactions between magnetic impurities deposited on the (1 1 1) surfaces of CuxPd1-x and CuxAu1-x random substitutional alloys, described using the coherent potential approximation. We show that as with pure surfaces of Cu and Au, where Shockley-type surface states mediate an RKKY-type interaction, a surface state and its dispersion can be obtained from studying the Bloch spectral function. In the second part of the paper we show how the details of the interaction are determined by the properties and dispersion of the surface states of the host material. We find an extra exponential decay in the range of the interactions compared to the 1/R(2) decay on surfaces of pure metals. The similar topology of the Fermi surface of Cu and Au allows us to scale the spin-orbit coupling and to study the Bychkov-Rashba splitting. Alternatively, the entirely different topology of the Cu and Pd Fermi surfaces allows us to study changes in the surface-state dispersion of the RKKY interaction between surface impurities.

Spin-correlations and magnetic structure in an Fe monolayer on 5d transition metal surfaces

We present a detailed first principles study on the magnetic structure of an Fe monolayer on different surfaces of 5d transition metals. We use the spin-cluster expansion technique to obtain parameters of a spin model, and predict the possible magnetic ground state of the studied systems by employing the mean field approach and, in certain cases, by spin dynamics calculations. We point out that the number of shells considered for the isotropic exchange interactions plays a crucial role in the determination of the magnetic ground state. In the case of Ta substrate we demonstrate that the out-of-plane relaxation of the Fe monolayer causes a transition from ferromagnetic to antiferromagnetic ground state. We examine the relative magnitude of nearest neighbour Dzyaloshinskii-Moriya (D) and isotropic (J) exchange interactions in order to get insight into the nature of magnetic pattern formations. For the Fe/Os(0 0 0 1) system we calculate a very large D/J ratio, correspondingly, a spin spiral ground state. We find that, mainly through the leading isotropic exchange and Dzyaloshinskii-Moriya interactions, the inward layer relaxation substantially influences the magnetic ordering of the Fe monolayer. For the Fe/Re(0 0 0 1) system characterized by large antiferromagnetic interactions we also determine the chirality of the 120° Néel-type ground state.

Exchange bias driven by Dzyaloshinskii-Moriya interactions

The exchange bias effect in a compensated IrMn3/Co(111) system is studied using multiscale modeling from ab initio to atomistic spin model calculations. We evaluate numerically the out-of-plane hysteresis loops of the bilayer for different thicknesses of the ferromagnetic layer. The results show the existence of a perpendicular exchange bias and an enhancement of the coercivity of the system. To identify the origin of the exchange bias, we analyze the hysteresis loops of a selected bilayer by tuning the different contributions to the exchange interaction across the interface. Our results indicate that the exchange bias is primarily induced by Dzyaloshinskii-Moriya interactions, while the coercivity is increased mainly due to a spin-flop mechanism.

Effect of stacking faults on the magnetocrystalline anisotropy of hcp Co: a first-principles study

In terms of the fully relativistic screened Korringa-Kohn-Rostoker method we investigate the effect of stacking faults on the magnetic properties of hexagonal close-packed (hcp) cobalt. In particular, we consider the formation energy and the effect on the magnetocrystalline anisotropy energy (MAE) of four different stacking faults in hcp cobalt-an intrinsic growth fault, an intrinsic deformation fault, an extrinsic fault and a twin-like fault. We find that the intrinsic growth fault has the lowest formation energy, in good agreement with previous first-principles calculations. With the exception of the intrinsic deformation fault which has a positive impact on the MAE, we find that the presence of a stacking fault generally reduces the MAE of bulk Co. Finally, we consider a pair of intrinsic growth faults and find that their effect on the MAE is not additive, but synergic.

Nonequilibrium thermodynamics of interacting tunneling transport: variational grand potential, density functional formulation and nature of steady-state forces

The standard formulation of tunneling transport rests on an open-boundary modeling. There, conserving approximations to nonequilibrium Green function or quantum statistical mechanics provide consistent but computational costly approaches; alternatively, the use of density-dependent ballistic-transport calculations (e.g., Lang 1995 Phys. Rev. B 52 5335), here denoted 'DBT', provides computationally efficient (approximate) atomistic characterizations of the electron behavior but has until now lacked a formal justification. This paper presents an exact, variational nonequilibrium thermodynamic theory for fully interacting tunneling and provides a rigorous foundation for frozen-nuclei DBT calculations as a lowest-order approximation to an exact nonequilibrium thermodynamic density functional evaluation. The theory starts from the complete electron nonequilibrium quantum statistical mechanics and I identify the operator for the nonequilibrium Gibbs free energy which, generally, must be treated as an implicit solution of the fully interacting many-body dynamics. I demonstrate a minimal property of a functional for the nonequilibrium thermodynamic grand potential which thus uniquely identifies the solution as the exact nonequilibrium density matrix. I also show that the uniqueness-of-density proof from a closely related Lippmann-Schwinger collision density functional theory (Hyldgaard 2008 Phys. Rev. B 78 165109) makes it possible to express the variational nonequilibrium thermodynamic description as a single-particle formulation based on universal electron-density functionals; the full nonequilibrium single-particle formulation improves the DBT method, for example, by a more refined account of Gibbs free energy effects. I illustrate a formal evaluation of the zero-temperature thermodynamic grand potential value which I find is closely related to the variation in the scattering phase shifts and hence to Friedel density oscillations. This paper also discusses the difference between the here-presented exact thermodynamic forces and the often-used electrostatic forces. Finally the paper documents an inherent adiabatic nature of the thermodynamic forces and observes that these are suited for a nonequilibrium implementation of the Born-Oppenheimer approximation.

First-principle calculations of the Berry curvature of Bloch states for charge and spin transport of electrons

Recent progress in wave packet dynamics based on the insight of Berry pertaining to adiabatic evolution of quantum systems has led to the need for a new property of a Bloch state, the Berry curvature, to be calculated from first principles. We report here on the response to this challenge by the ab initio community during the past decade. First we give a tutorial introduction of the conceptual developments we mentioned above. Then we describe four methodologies which have been developed for first-principle calculations of the Berry curvature. Finally, to illustrate the significance of the new developments, we report some results of calculations of interesting physical properties such as the anomalous and spin Hall conductivity as well as the anomalous Nernst conductivity and discuss the influence of the Berry curvature on the de Haas-van Alphen oscillation.

Magnetoelectric coupling at metal surfaces

Magnetoelectric coupling allows the magnetic state of a material to be changed by an applied electric field. To date, this phenomenon has mainly been observed in insulating materials such as complex multiferroic oxides. Bulk metallic systems do not exhibit magnetoelectric coupling, because applied electric fields are screened by conduction electrons. We demonstrate strong magnetoelectric coupling at the surface of thin iron films using the electric field from a scanning tunnelling microscope, and are able to write, store and read information to areas with sides of a few nanometres. Our work demonstrates that high-density, non-volatile information storage is possible in metals.

Density-functional theory of the magnetic anisotropy of nanostructures: an assessment of different approximations

We discuss the multiple technical choices that have to be made in ab initio density-functional calculations of the magnetic anisotropy of supported nanostructures: (i) choice of the exchange-correlation functional, (ii) degree of optimization of the geometry of the adsorbate/substrate complex, (iii) magnetic anisotropy energy calculated self-consistently or via the 'force theorem', (iv) calculations based on slab models of the substrate or using a Green's function describing a semi-infinite substrate, (v) full potential approach or atomic-sphere approximation. Using isolated Fe and Co atoms on Pt(111) as an example we demonstrate that by using a judicious combination of relatively crude approximations (complete neglect of structural relaxation, local exchange-correlation functional,...) seemingly good agreement with experimental anisotropy energies can be achieved, while the calculated orbital moments remain small. At a higher level of theory (relaxed adsorbate/substrate complex, gradient-corrected functionals,...) providing a realistic geometry of the adsorbate/substrate complex and hence a correct description of the interaction between the magnetic adatom and its ligands, anisotropy energies are also in semi-quantitative agreement with experiment, while the orbital moments of the adatoms are much too small. We suggest that the anisotropy energies provided by both approaches should be considered as lower limits of the real anisotropies. Without relaxation the ligand effect coupling the orbital moments of the adatom to the heavy atoms of the substrate is underestimated, while in a relaxed adsorbate/substrate complex the lack of orbital dependence of the exchange potential combined with a strong hybridization of adatom and substrate states leads to a strong underestimation of the orbital moment. We have briefly explored the influence of post-density-functional corrections. Adding a modest on-site Coulomb repulsion to the d states of the adatom (in a DFT+U approach) leads to a modest increase of spin and orbital moments of the adatom accompanied by a slow decrease of the induced moments, leaving the anisotropy energy almost unchanged.

Role of long range interaction in oxygen superstructure formation on Cu(001) and Ni(001)

On the basis of electronic structure calculations, we show that the long range Coulomb interaction provides the driving mechanism for oxygen overlayer formation on Cu(001). We illustrate that this interaction in the precursor c(2 x 2) phase induces a missing row reconstruction of Cu(001), and leads to the (2sqrt[2] x sqrt[2])R45 degrees O structure, which has strong covalent pO-dCu coupling. For the c(2 x 2)O overlayer on Ni(001) and Cu(001), we show that pO-dNi bonding is larger than pO-dCu and serves to neutralize the perturbation of the Coulomb interaction induced by the O overlayer. Consequently, c(2 x 2)O/Ni(001)) is stable while c(2 x 2)O/Cu(001) exists only in limited environments.

Onset of magnetic order in fcc-Fe films on Cu(100)

On the basis of an ab initio theory of metallic magnetism in layered materials, we investigate the onset of magnetic order in thin (2-8 layers) fcc-Fe films on and embedded in Cu(100) substrates. In particular, we find an oscillatory dependence of the Curie temperatures on embedding depth, in excellent agreement with experimental data. The thermally induced spin fluctuations are treated within a mean-field disordered local moment picture and give rise to layer-dependent "local exchange splittings" in the electronic structure even in the paramagnetic phase. These features determine the magnetic intralayer and interlayer interactions which are strongly influenced by the presence and extent of the Cu cap.

Theory of the fano resonance in the STM tunneling density of states due to a single kondo impurity

The conduction electron density of states nearby single magnetic impurities, as measured recently by scanning tunneling microscopy (STM), is calculated, taking into account tunneling into conduction electron states only. The Kondo effect induces a narrow Fano resonance in the conduction electron density of states. The line shape varies with the distance between STM tip and impurity, in qualitative agreement with experiments, but is very sensitive to details of the band structure. For a Co impurity the experimentally observed width and shift of the Kondo resonance are in accordance with those obtained from a combination of band structure and strongly correlated calculations.