Revised theory of the magnetic surface anisotropy of impurities in metallic mesoscopic samples

In several experiments the magnitude of the contribution of magnetic impurities to the Kondo resistivity shows size dependence in mesoscopic samples. It was suggested ten years ago that magnetic surface anisotropy can be responsible for the size dependence in cases where there is strong spin-orbit interaction in the metallic host. The anisotropy energy has the form $\Delta E=K_d ({\bf n}{\bf S})^2$ where ${\bf n}$ is the vector perpendicular to the plane surface, ${\bf S}$ is the spin of the magnetic impurity and $K_d>0$ is inversely proportional to distance $d$ measured from the surface. It has been realized that in the tedious calculation an unjustified approximation was applied for the hybridizations of the host atom orbitals with the conduction electrons which depend on the position of the host atoms. Namely, the momenta of the electrons were replaced by the Fermi momentum $k_F$. That is reinvestigated considering the $k$-dependence which leads to singular energy integrals and in contrary to the previous result $K_d$ is oscillating like $\sin (2 k_F d)$ and the distance dependence goes like $1/d^3$ in the asymptotic region. As the anisotropy is oscillating, for integer spin the ground state is either a singlet or a doublet depending on distance $d$, but in the case of the doublet there is no direct electron induced transition between those two states at zero temperature. Furthermore, for half-integer ($S > 1/2$) spin it is always a doublet with direct transition only in half of the cases.Comment: 10 pages, 4 figure

Ab-initio spin dynamics applied to nanoparticles: canted magnetism of a finite Co chain along a Pt(111) surface step edge

In order to search for the magnetic ground state of surface nanostructures we extended first principles adiabatic spin dynamics to the case of fully relativistic electron scattering. Our method relies on a constrained density functional theory whereby the evolution of the orientations of the spin-moments results from a semi-classical Landau-Lifshitz equation. This approach is applied to a study of the ground state of a finite Co chain placed along a step edge of a Pt(111) surface. As far as the ground state spin orientation is concerned we obtain excellent agreement with the experiment. Furthermore we observe noncollinearity of the atom-resolved spin and orbital moments. In terms of magnetic force theorem calculations we also demonstrate how a reduction of symmetry leads to the existence of canted magnetic states.Comment: 4 pages, ReVTeX + 3 figures (Encapsulated Postscript), submitted to PR

Ab-initio calculation of Kerr spectra for semi-infinite systems including multiple reflections and optical interferences

Based on Luttinger's formulation the complex optical conductivity tensor is calculated within the framework of the spin-polarized relativistic screened Korringa-Kohn-Rostoker method for layered systems by means of a contour integration technique. For polar geometry and normal incidence ab-initio Kerr spectra of multilayer systems are then obtained by including via a 2x2 matrix technique all multiple reflections between layers and optical interferences in the layers. Applications to Co|Pt5 and Pt3|Co|Pt5 on the top of a semi-infinite fcc-Pt(111) bulk substrate show good qualitative agreement with the experimental spectra, but differ from those obtained by applying the commonly used two-media approach.Comment: 32 pages (LaTeX), 5 figures (Encapsulated PostScript), submitted to Phys. Rev.

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

On the basis of a first-principles electronic structure theory of finite temperature metallic magnetism in layered materials, we investigate the onset of magnetic order in thin (2-8 layers) fcc-Fe films on Cu(100) substrates. The nature of this ordering is altered when the systems are capped with copper. Indeed we find an oscillatory dependence of the Curie temperatures as a function of Cu-cap thickness, in excellent agreement with experimental data. The thermally induced spin-fluctuations are treated within a mean-field disordered local moment (DLM) picture and give rise to layer-dependent `local exchange splittings' in the electronic structure even in the paramagnetic phase. These features determine the magnetic intra- and interlayer interactions which are strongly influenced by the presence and extent of the Cu cap.Comment: 13 pages, 3 figure

Numerically improved computational scheme for the optical conductivity tensor in layered systems

The contour integration technique applied to calculate the optical conductivity tensor at finite temperatures in the case of layered systems within the framework of the spin-polarized relativistic screened Korringa-Kohn-Rostoker band structure method is improved from the computational point of view by applying the Gauss-Konrod quadrature for the integrals along the different parts of the contour and by designing a cumulative special points scheme for two-dimensional Brillouin zone integrals corresponding to cubic systems.Comment: 17 pages, LaTeX + 4 figures (Encapsulated PostScript), submitted to J. Phys.: Condensed Matter (19 Sept. 2000

Limitations of the two-media approach in calculating magneto-optical properties of layered systems

It is shown that in polar geometry and normal incidence the 2x2 matrix technique - as discussed in detail in a preceeding paper [Phys. Rev. B 65, 144448 (2002)] - accounts correctly for multiple reflections and optical interferences, and reduces only in the case of a periodic sequence of identical layers to the Fresnel formula of reflectivity, which in turn is the theoretical basis of the two-media approach, widely used in the literature to compute magneto-optical Kerr spectra. As a numerical example ab-initio calculations of the optical constants for an fcc Pt semi-infinite bulk using the spin-polarized relativistic screened Korringa-Kohn-Rostoker method show very good agreement with experimental data.Comment: 16 pages (LaTeX), 4 figures (Encapsulated PostScript), appears in Phys. Rev. B 66, 1744XX (2002

Fully relativistic calculation of magnetic properties of Fe, Co and Ni adclusters on Ag(100)

We present first principles calculations of the magnetic moments and magnetic anisotropy energies of small Fe, Co and Ni clusters on top of a Ag(100) surface as well as the exchange-coupling energy between two single adatoms of Fe or Co on Ag(100). The calculations are performed fully relativistically using the embedding technique within the Korringa-Kohn-Rostoker method. The magnetic anisotropy and the exchange-coupling energies are calculated by means of the force theorem. In the case of adatoms and dimers of iron and cobalt we obtain enhanced spin moments and, especially, unusually large orbital moments, while for nickel our calculations predict a complete absence of magnetism. For larger clusters, the magnitudes of the local moments of the atoms in the center of the cluster are very close to those calculated for the corresponding monolayers. Similar to the orbital moments, the contributions of the individual atoms to the magnetic anisotropy energy strongly depend on the position, hence, on the local environment of a particular atom within a given cluster. We find strong ferromagnetic coupling between two neighboring Fe or Co atoms and a rapid, oscillatory decay of the exchange-coupling energy with increasing distance between these two adatoms.Comment: 8 pages, ReVTeX + 4 figures (Encapsulated Postscript), submitted to PR

Spin-Orbit-Induced Magnetic Anisotropy for Impurities in Metallic Samples I. Surface Anisotropy

Motivated by the recent measurements of Kondo resistivity in thin films and wires, where the Kondo amplitude is suppressed for thinner samples, the surface anisotropy for magnetic impurities is studied. That anisotropy is developed in those cases where in addition to the exchange interaction with the impurity there is strong spin-orbit interaction for conduction electrons around the impurity in the ballistic region. The asymmetry in the neighborhood of the magnetic impurity exhibits the anisotropy axis $n$ which, in the case of a plane surface, is perpendicular to the surface. The anisotropy energy is $\Delta E=K_d (nS)^2$ for spin $S$, and the anisotropy constant $K_d$ is inversionally proportional to distance $d$ measured from the surface and $K_d>0$. Thus at low temperature the spin is frozen in a singlet or doublet of lowest energy. The influence of that anisotropy on the electrical resistivity is the subject of the following paper (part II).Comment: 28 pages, RevTeX (using epsfig), 8 eps figures included, submitted to PR

Use of the breeding technique to estimate the structure of the analysis 'errors of the day'

A 3D-variational data assimilation scheme for a quasi-geostrophic channel model (Morss, 1998) is used to study the structure of the background error and its relationship to the corresponding bred vectors. The "true" evolution of the model atmosphere is defined by an integration of the model and "rawinsonde observations" are simulated by randomly perturbing the true state at fixed locations. Case studies using different observational densities are considered to compare the evolution of the Bred Vectors to the spatial structure of the background error. In addition, the bred vector dimension (BV-dimension), defined by Patil et al. (2001) is applied to the bred vectors. It is found that after 3-5 days the bred vectors develop well organized structures which are very similar for the two different norms (enstrophy and streamfunction) considered in this paper. When 10 surrogate bred vectors (corresponding to different days from that of the background error) are used to describe the local patterns of the background error, the explained variance is quite high, about 85-88%, indicating that the statistical average properties of the bred vectors represent well those of the background error. However, a subspace of 10 bred vectors corresponding to the time of the background error increased the percentage of explained variance to 96-98%, with the largest percentage when the background errors are large. These results suggest that a statistical basis of bred vectors collected over time can be used to create an effective constant background error covariance for data assimilation with 3D-Var. Including the "errors of the day" through the use of bred vectors corresponding to the background forecast time can bring an additional significant improvement

Magnetoelastic mechanism of spin-reorientation transitions at step-edges

The symmetry-induced magnetic anisotropy due to monoatomic steps at strained Ni films is determined using results of first - principles relativistic full-potential linearized augmented plane wave (FLAPW) calculations and an analogy with the N\'eel model. We show that there is a magnetoelastic anisotropy contribution to the uniaxial magnetic anisotropy energy in the vicinal plane of a stepped surface. In addition to the known spin-direction reorientation transition at a flat Ni/Cu(001) surface, we propose a spin-direction reorientation transition in the vicinal plane for a stepped Ni/Cu surface due to the magnetoelastic anisotropy. We show that with an increase of Ni film thickness, the magnetization in the vicinal plane turns perpendicular to the step edge at a critical thickness calculated to be in the range of 16-24 Ni layers for the Ni/Cu(1,1,13) stepped surface.Comment: Accepted for publication in Phys. Rev.