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 study of canted magnetism of finite atomic chains at surfaces

By using ab initio methods on different levels we study the magnetic ground state of (finite) atomic wires deposited on metallic surfaces. A phenomenological model based on symmetry arguments suggests that the magnetization of a ferromagnetic wire is aligned either normal to the wire and, generally, tilted with respect to the surface normal or parallel to the wire. From a first principles point of view, this simple model can be best related to the so--called magnetic force theorem calculations being often used to explore magnetic anisotropy energies of bulk and surface systems. The second theoretical approach we use to search for the canted magnetic ground state is first principles adiabatic spin dynamics extended to the case of fully relativistic electron scattering. First, for the case of two adjacent Fe atoms an a Cu(111) surface we demonstrate that the reduction of the surface symmetry can indeed lead to canted magnetism. The anisotropy constants and consequently the ground state magnetization direction are very sensitive to the position of the dimer with respect to the surface. We also performed calculations for a seven--atom 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 experiment. Moreover, the magnetic ground state turns out to be slightly noncollinear.Comment: 8 pages, 5 figures; presented on the International Conference on Nanospintronics Design and Realizations, Kyoto, Japan, May 2004; to appear in J. Phys.: Cond. Matte

Magnetic properties of Quantum Corrals from first principles calculations

We present calculations for electronic and magnetic properties of surface states confined by a circular quantum corral built of magnetic adatoms (Fe) on a Cu(111) surface. We show the oscillations of charge and magnetization densities within the corral and the possibility of the appearance of spin--polarized states. In order to classify the peaks in the calculated density of states with orbital quantum numbers we analyzed the problem in terms of a simple quantum mechanical circular well model. This model is also used to estimate the behaviour of the magnetization and energy with respect to the radius of the circular corral. The calculations are performed fully relativistically using the embedding technique within the Korringa-Kohn-Rostoker method.Comment: 14 pages, 9 figures, submitted to J. Phys. Cond. Matt. special issue on 'Theory and Simulation of Nanostructures

Relativistic corrections in magnetic systems

We present a weak-relativistic limit comparison between the Kohn-Sham-Dirac equation and its approximate form containing the exchange coupling, which is used in almost all relativistic codes of density-functional theory. For these two descriptions, an exact expression of the Dirac Green's function in terms of the non-relativistic Green's function is first derived and then used to calculate the effective Hamiltonian, i.e., Pauli Hamiltonian, and effective velocity operator in the weak-relativistic limit. We point out that, besides neglecting orbital magnetism effects, the approximate Kohn-Sham-Dirac equation also gives relativistic corrections which differ from those of the exact Kohn-Sham-Dirac equation. These differences have quite serious consequences: in particular, the magnetocrystalline anisotropy of an uniaxial ferromagnet and the anisotropic magnetoresistance of a cubic ferromagnet are found from the approximate Kohn-Sham-Dirac equation to be of order $1/c^2$, whereas the correct results obtained from the exact Kohn-Sham-Dirac equation are of order $1/c^4$ . We give a qualitative estimate of the order of magnitude of these spurious terms

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

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.

Magnetocrystalline Anisotropy Energy of Transition Metal Thin Films: A Non-perturbative Theory

The magnetocrystalline anisotropy energy E(anis) of free-standing monolayers and thin films of Fe and Ni is determined using two different semi-empirical schemes. Within a tight-binding calculation for the 3d bands alone, we analyze in detail the relation between bandstructure and E(anis), treating spin-orbit coupling non-pertubatively. We find important contributions to E(anis) due to the lifting of band degeneracies near the Fermi level by SOC. The important role of degeneracies is supported by the calculation of the electron temperature dependence of the magnetocrystalline anisotropy energy, which decreases with the temperature increasing on a scale of several hundred K. In general, E(anis) scales with the square of the SOC constant. Including 4s bands and s-d hybridization, the combined interpolation scheme yields anisotropy energies that quantitatively agree well with experiments for Fe and Ni monolayers on Cu(001). Finally, the anisotropy energy is calculated for systems of up to 14 layers. Even after including s-bands and for multilayers, the importance of degeneracies persists. Considering a fixed fct-Fe structure, we find a reorientation of the magnetization from perpendicular to in-plane at about 4 layers. For Ni, we find the correct in-plane easy-axis for the monolayer. However, since the anisotropy energy remains nearly constant, we do not find the experimentally observed reorientation.Comment: 15 pages, Revtex, 15 postscript figure

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