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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.

We study here, both experimentally and theoretically, the anisotropy of magnetoresistance 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 show 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 using a self-consistent tight-binding Hamiltonian in a non-orthogonal $s$, $p$ and $d$ basis set, the spin-polarization being obtained from a non-collinear Stoner-like model and the transmission probability from the Fisher-Lee formula. The behaviour of an infinite perfect Fe wire is compared with that of an infinite chain presenting geometric defects or magnetic walls and with 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 behaviour 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 magneto-resistance. Finally whereas the variation of the magneto-resistance as a function of the magnetization direction is step-like for an infinite wire, it becomes smooth in the presence of defects or contacts.

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 1$\mu_B$ 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.

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 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 to the monatomic wire, at several interatomic distances. New results are derived. 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 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.

The energetics of transition and noble metal (Rh, Pd, Cu) vicinal surfaces, i.e., surface energy, step energy, kink energy and electronic interactions between steps, is studied at 0K from electronic structure calculations in the tight-binding approximation using a {\it s, p} and {\it d} valence orbital basis set. Then, the surface phonon spectra of copper are investigated in the harmonic approximation with the help of a semi-empirical inter-atomic potential. This allows to derive the contribution of phonons at finite temperatures to the step free energy and to the interactions between steps. The last part is devoted to the stability of vicinal surfaces relative to faceting with special attention to the domain of orientations (100)-(111). Semi-empirical potentials are shown to be not realistic enough to give a reliable answer to this problem. The results derived from electronic structure calculations predict a variety of behaviors and, in particular, a possible faceting into two other vicinal orientations. Finally, temperature effects are discussed. Comparisons are made with other theoretical works and available experiments.

We reanalyze the condition for metallic ferromagnetism in the framework of the tight-binding approximation and investigate the consequences of the inter-site Coulomb interactions using the Hartree-Fock approximation. We first consider a non-degenerate $s$ band and we show that the inter-site interactions modify the occurrence of ferromagnetism, and we derive a generalized Stoner criterion. We analyze the main effects due to the renormalization of the hopping integrals by the inter-site Coulomb interactions. These effects are strongly dependent on the relative values of the inter-site electron-electron interactions and on the shape of the density of states as illustrated by a study of cubic crystals from which we establish general trends. We then investigate a realistic $spd$ tight-binding model, including intra (Coulomb and exchange) and inter-site charge-charge Coulomb integrals. This model is used to study the electronic structure (band structure, densities of states, magnetic moment) of bulk ferromagnetic 3d transition metals Fe(bcc), Co(hcp and fcc) and Ni(fcc). An excellent agreement with local spin density functional calculations is obtained for the three metals, in particular concerning the relative widths of the majority and minority spin bands. Thus our tight-binding Hartree-Fock model provides a consistent interpretation of this effect.