An efficient parameterized self-consistent tight-binding model for transition metals using s, p and d valence atomic orbitals as a basis set is presented. The parameters of our tight binding model for pure elements are determined from a fit to bulk ab-initio calculations. A very simple procedure that does not necessitate any further fitting is proposed to deal with systems made of several chemical elements. This model is extended to spin (and orbital) polarized materials by adding Stoner-like and spin-orbit interactions. Collinear and non-collinear magnetism as well as spin-spirals are considered. Finally the electron-electron intra-atomic interactions are taken into account in the Hartree-Fock approximation. This leads to an orbital dependence of these interactions, which is of a great importance for low-dimensional systems and for a quantitative description of orbital polarization and magneto-crystalline anisotropy. Several examples are discussed. (C) 2015 The Authors. Published by Elsevier Masson SAS on behalf of Academie des sciences.

We report tight-binding (TB) calculations of magnetocrystalline anisotropy energy (MAE) of Iron slabs and nanoclusters with a particuler focus on local analysis. After clarifying various concepts and formulations for the determination of MAE, we apply our realistic TB model to the analysis of the magnetic anisotropy of Fe$(001)$, Fe$(110)$ slabs and of two large Fe clusters with $(001)$ and $(110)$ facets only: a truncated pyramid and a truncated bipyramid containg 620 and 1096 atoms, respectively. It is shown that the MAE of slabs originates mainly from outer layers, a small contribution from the bulk gives rise, however, to an oscillatory behavior for large thicknesses. Interestingly, the MAE of the nanoclusters considered is almost solely due to $(001)$ facets and the base perimeter of the pyramid. We believe that this fact could be used to efficiently control the anisotropy of Iron nanoparticles and could also have consequences on their spin dynamics.

Received 17 December 2013DOI:https://doi.org/10.1103/PhysRevB.88.219908©2013 American Physical Society

An efficient tight-binding model including magnetism and spin-orbit interactions is extended to metallic alloys. The tight-binding parameters are determined from a fit to bulk ab initio calculations of each metal and rules are given to obtain the heteroatomic parameters. The spin and orbital magnetic moments as well as the magneto-crystalline anisotropy are derived. We apply this method to bulk FePt L1(0) and the results are compared with success to ab initio results where available. Finally this model is applied to a set of FePt L1(0) clusters and physical trends are derived.

An efficient tight-binding model including magnetism and spin-orbit interactions is extended to metallic alloys. The tight-binding parameters are determined from a fit to bulk ab initio calculations of each metal and rules are given to obtain the heteroatomic parameters. The spin and orbital magnetic moments as well as the magneto-crystalline anisotropy are derived. We apply this method to bulk FePt L1(0) and the results are compared with success to ab initio results where available. Finally this model is applied to a set of FePt L1(0) clusters and physical trends are derived.

Kinetic Monte Carlo simulations based on a semi-empirical description of the metal–metal interactions are developed to interpret the formation of a one-dimensional Ni/Pt alloy observed at the step feet of the vicinal Pt(997) surface. Deposition of 0.15 monolayer of Ni atoms at T<300K leads to the formation of a (2×1) well-ordered nanowire in agreement with scanning tunneling microscopy observations. Exchange process between Ni and Pt atoms at the upper step edge and neighboring influence appear to be the key point to explain such a well-ordered 1D alloy. In addition, a subtle decoration of the step adsorption sites is also necessary.

We have investigated the growth of Ni on Pt stepped surfaces with (1 1 1) terraces by means of potentials derived from the second moment approximation in a tight-binding model. The activation energies associated to these processes are determined. The Schwoebel barriers of Ni atoms descending steps of Pt stepped surfaces are calculated for different kinds of straight steps (A and B steps) differing by the orientation of the ledge. In addition, we study the diffusion of Ni adatoms at fcc or hcp sites in the presence of small adislands on the terraces, in the vicinity of the A and B steps. We show that a good estimate of the potential wells and diffusion barriers could be given by introducing a lateral effective pair interaction model, the interactions extending up to the next nearest neighbors. Finally, we have carried out Kinetic Monte-Carlo simulations to investigate the Ni wire formation at Pt step edges and the influence of the exchange processes in the alloy formation.

We study here, both experimentally and theoretically, the anisotropy of magneto resistance in atomic contacts. Our measurements on iron break junctions reveal an abrupt and hysteretic switch between two conductance levels when a large applied field is continuously rotated. We propose that this behaviour stems from the coexistence of two metastable electronic states which result from the anisotropy of electronic interactions responsible for the enhancement of orbital magnetization. In both states giant orbital moments appear on the low coordinated central atom in a realistic contact geometry. However, they differ by their orientation, parallel or perpendicular, with respect to the axis of the contact. Our explanation is totally at variance with the usual model based on the band structure of a monatomic linear chain, which we argue cannot be applied to 3d ferromagnetic metals.

We present a theoretical study of spin polarized transport in Fe atomic contacts by using a self-consistent tight-binding Hamiltonian in a nonorthogonal s, p, and d basis set, the spin polarization being obtained from a noncollinear Stoner-like model and the transmission probability from the Fisher-Lee formula. The behavior of an infinite perfect Fe wire is compared to that of an infinite chain presenting geometric defects or magnetic walls and to that of a finite chain connected to infinite one-dimensional or three-dimensional leads. In the presence of defects or contacts, the transmission probability of d electrons is much more affected than that of s electrons, in particular, contact effects may suppress some transmission channels. It is shown that the behavior of an infinite wire is never obtained even in the limit of long chains connected to electrodes. The introduction of the spin-orbit coupling term in the Hamiltonian enables us to calculate the anisotropy of the magnetoresistance. Finally, whereas the variation in the magnetoresistance as a function of the magnetization direction is steplike for an infinite wire, it becomes smooth in the presence of defects or contacts.

Growing perfect monatomic chains on surfaces is generally a hard task since it depends strongly on the experimental conditions and on the species used as templates or adsorbates. In the present study, the growth of Co and Ag monatomic wires on a Pt(997) vicinal surface is investigated over a large range of temperature. A semi-empirical potential is used to extract the main diffusion barriers responsible for the growth of Co and Ag wires on the Pt(997) vicinal surface. Kinetic Monte Carlo simulations are performed to investigate the wire formation at step-edges. We show that step decoration occurs at 150K for Ag and at temperatures higher than 250K for Co in agreement with growth experiments. If no interdiffusion is taken into account, Co and Ag behave similarly and perfect wires form between 150 and 500K for Ag and between 300 and 500K for Co. In the case of Co, an exchange mechanism leading to interlayer diffusion at step-edges is shown to strongly influence the temperature range for which the perfect wires are observed. An activation barrier of 0.65eV for this mechanism is found to be adequate to reproduce the experimental features observed by Gambardella et al. [P. Gambardella, M. Blanc, L. Burgi, K. Kuhnke, K. Kern, Surf. Sci., 449 (2000) 93]. At higher temperatures, above 500K, detachment from steps strongly hinders the wire formation at step feet. As a main conclusion, the exchange diffusion barrier can be extracted directly from the comparison between observation of step decoration and numerical simulations.

We show that considerable orbital magnetic moments and magneto-crystalline anisotropy energies are obtained for a Fe monatomic wire described in a tight-binding method with intra-atomic electronic interactions treated in a full Hartree Fock (HF) decoupling scheme. Even though the use of the orbital polarization ansatz with simplified Hamiltonians leads to fairly good results when the spin magnetization is saturated this is not the case of unsaturated systems. We conclude that the full HF scheme is necessary to investigate low dimensional systems.

The orbital contribution to the magnetic properties of Fe in systems of decreasing dimensionality bulk, surfaces, wire, and free clusters is investigated using a tight-binding Hamiltonian in an s, p, and d atomic orbital basis set including spin-orbit coupling and intra-atomic electronic interactions in the full Hartree-Fock HF scheme, i.e., involving all the matrix elements of the Coulomb interaction with their exact orbital dependence. Spin and orbital magnetic moments and the magnetocrystalline anisotropy energy MAE are calculated for several orientations of the magnetization. The results are systematically compared with those of simplified Hamiltonians which give results close to those obtained from the local spin density approximation. The full HF decoupling leads to much larger orbital moments and MAE which can reach values as large as 1B and several tens of meV, respectively, in the monatomic wire at the equilibrium distance. The reliability of the results obtained by adding the so-called orbital polarization ansatz OPA to the simplified Hamiltonians is also discussed. It is found that when the spin magnetization is saturated, the OPA results for the orbital moment are in qualitative agreement with those of the full HF model. However, there are large discrepancies for the MAE, especially in clusters. Thus, the full HF scheme must be used to investigate the orbital magnetism and MAE of low dimensional systems.

The validity of the Orbital Polarization Ansatz (OPA) is discussed on the model of a Fe monatomic wire described in the tight-binding method. The intra-atomic electronic interactions are treated in the Hartree-Fock (HF) scheme either by keeping all terms in the decoupling or by making usual approximations. The comparison between the orbital magnetic moments and magneto-crystalline anisotropy energies obtained with simplified Hamiltonians including the OPA and the full HF scheme reveals that, if the OPA leads to fairly good results when the spin magnetization is saturated even though some discrepancies exist in the band structure, it is not justified in the unsaturated case.

The chemical order and magnetic behavior of Fe-dilute fcc Fe-Pd nanoparticles are theoretically investigated using many-body potentials derived in the framework of the generalized second moment approximation (SMA) and self-consistent spin-polarized tight-binding electronic structure calculations, respectively. The SMA total energy calculations reveal that surface sites and the core region are not favorable positions for the Fe impurities and that they prefer to accumulate in the subsurface region of the particles, showing a very strong tendency to separate. However, additional contrasting atomic configurations close in energy are also found which could imply the coexistence in real samples of several Fe-Pd nanoparticles with a well-defined composition, but having different chemical orderings. Magnetic properties are first investigated for a single Fe impurity in bulk Pd, allowing an extension of the polarization cloud around the Fe atom much larger than in an ab initio calculation. The results are in good agreement with experiments and serve as a reference to identify surface and size effects in FePd nanoparticles. Nanoparticles containing from 135 to 561 atoms with up to three Fe substitutional impurities are then investigated, as well as more concentrated (similar or equal to 10% Fe content) shell structures. The extension and magnetic structure of the Fe-induced polarization cloud is studied in detail as a function of the size, surface termination, and the precise location and number of the iron impurities in the particles. The local electronic structure at the Pd sites located at the outermost atomic shell is considerably perturbed by the subsurface position of the Fe atoms and could modify the catalytic properties of palladium nanoparticles. Finally, we show that the value of the orbital-to-spin ratio in our Fe-Pd clusters is very sensitive to the changes in the internal position of the Fe impurities, a result that suggests that x-ray magnetic circular dichroism experiments can be very useful in order to reveal precise features of the chemical order in these magnetic nanoparticles.

The magnetic properties of iron (spin and orbital magnetic moments, magnetocrystalline anisotropy energy) in various geometries and dimensionalities are investigated by using a parametrized tight-binding model in an s, p and d atomic orbital basis set including spin polarization and the effect of spin–orbit coupling. The validity of this model is well established by comparing the results with those obtained by using an ab initio code. This model is applied to the study of iron in bulk bcc and fcc phases, (110) and (001) surfaces and the monatomic wire, at several interatomic distances. New results are derived. In the case of surfaces the variation of the component of the orbital magnetic moment on the spin quantization axis has been studied as a function of depth, revealing a significant enhancement in the first two layers, especially for the (001) surface. It is found that the magnetic anisotropy energy is drastically increased in the wire and can reach several meV. This is also true for the orbital moment, which in addition is highly anisotropic. Furthermore, it is shown that when the spin quantization axis is neither parallel nor perpendicular to the wire the average orbital moment is not aligned with the spin quantization axis. At equilibrium distance the easy magnetization axis is along the wire but switches to the perpendicular direction under compression. The success of this model opens up the possibility of obtaining accurate results on other elements and systems with much more complex geometries.

The spin and orbital moments of fcc Fe-Ni cluster alloys are determined within the framework of a d-band Hamiltonian including the spin-orbit coupling non perturbatively. Different sizes (up to 321 atoms), compositions, and chemical configurations (random alloys as well as core-shell arrays of iron and nickel atoms) are considered in order to reveal the crucial role played by local order and stoichiometry on the magnetic moments of the clusters. Interestingly, we have found considerably reduced average magnetizations for Fe-Ni clusters with Fe cores compared to that of the bulk alloy with the same composition. Indeed, in these configurations not only antiparallel arrangements between the local moments of some Fe atoms within the iron core are found, but also the total magnetization of the surface Ni atoms is significantly quenched. On the opposite, the disordered and Ni-core cluster alloys are characterized by high magnetizations resulting from saturated-like contributions from both Ni and Fe atoms, in agreement with recent ab-initio calculations. In general, the local orbital magnetic moments are strongly enhanced with respect to their bulk values. Finally, the variation of the orbital-to-spin moment ratio with the chemical order is discussed.

The surface diffusion of Cu adatoms in the presence of an adisland at FCC or HCP sites on Cu(111) is studied using the EAM potential derived by Mishin {\it et al.} [Phys. Rev. B {\bf 63} 224106 (2001)]. The diffusion rates along straight (with close-packed edges) steps with (100) and (111)-type microfacets (resp. step A and step B) are first investigated using the transition state theory in the harmonic approximation. It is found that the classical limit beyond which the diffusion rates follow an Arrhenius law is reached above the Debye temperature. The Vineyard attempt frequencies and the (static) energy barriers are reported. Then a comparison is made with the results of more realistic classical molecular dynamic simulations which also exhibit an Arrhenius-like behavior. It is concluded that the corresponding energy barriers are completely consistent with the static ones within the statistical errors and that the diffusion barrier along step B is significantly larger than along step A. In contrast the prefactors are very different from the Vineyard frequencies. They increase with the static energy barrier in agreement with the Meyer-Neldel compensation rule and this increase is well approximated by the law proposed by Boisvert {\it et al.} [Phys. Rev. Lett. {\bf 75} 469 (1995)]. As a consequence, the remaining part of this work is devoted to the determination of static energy barriers for a large number of diffusion events that can occur in the presence of an adisland. In particular, it is found that the corner crossing diffusion process for triangular adislands is markedly different for the two types of borders (A or B). From this set of results the diffusion rates of the most important atomic displacements can be predicted and used as input in Kinetic Monte-Carlo simulations.

We have applied the full-potential linearized augmented plane-wave (FLAPW) ab initio method and the $spd$ tight-binding (TB) model to the calculations of the surface energies ${E}_{S}(hkl)$ and relaxations of the three low-index [(111), (100), (110)] surfaces of platinum. The two methods give similar results, and in particular the anisotropy ratios ${E}_{S}(110)∕{E}_{S}(111)$ and ${E}_{S}(100)∕{E}_{S}(111)$ are very close. The calculation of surface energy of reconstructed $(1\ifmmode\times\else\texttimes\fi{}2)$ Pt(110) confirms that this face undergoes a missing-row reconstruction and the corresponding structural parameters agree well with experiment. The local densities of states (LDOS) calculated by each of the methods on the flat surfaces are almost the same. We have also investigated the $6(111)\ifmmode\times\else\texttimes\fi{}(\overline{1}11)$ vicinal surface and found a similar agreement for the LDOS.

The EAM potential set up by Mishin [Phys. Rev. B 63 224106 (2001)] is used to study some elementary processes in the homoepitaxy of Cu on Cu(111). After having checked its ability to reproduce surface physical quantities, this potential is applied to an investigation of the energetics, the vibrations and the surface diffusion of Cu-N close-packed adislands (1less than or equal toNless than or equal to7). In each case we determine the most stable configurations, the corresponding activation barriers, the local vibrational spectra, and the Vineyard prefactors. In particular it is found that, at room temperature, dimers and trimers are still very mobile and move by concerted jumps much faster than tetramers while heptamers can be considered as immobile. The very good agreement of our results with scanning tunneling microscopy observations justifies the use of Mishin potential for treating surface diffusion. This allowed us to study in details the influence of the lateral atomic environment of the adatoms along its diffusion path. An effective lateral pair interaction model is set up which is able to predict the existence of a saddle point along the path and to give a very good estimation of the activation barrier height. This model will be very useful in kinetic Monte Carlo simulations of homoepitaxial growth of Cu(111).