Magnetic anisotropy of vicinal (001) fcc Co films: role of crystal splitting and structure relaxation in step-decoration effect

The uniaxial in-plane magnetic anisotropy (UIP-MA) constant is calculated for a single step on the (001) surface of fcc Co($N$) films. The calculations are done for both an undecorated step and the step decorated with one or more, up to 7, Cu wires. Our objective is to explain the mechanisms by which the decoration decreases the UIP-MA constant, which is the effect observed experimentally for ultrathin Co films deposited on vicinal (001) Cu surfaces and can lead to reorientation of magnetization within the film plane. Theoretical calculations performed with a realistic tight-binding model show that the step decoration changes the UIP-MA constant significantly only if the splitting between the on-site energies of various $d$-orbitals is included for atoms located near the step edge. The local relaxation of atomic structure around the step is also shown to have a significant effect on the shift of the UIP-MA constant. The influence of these two relevant factors is analyzed further by examining individual contributions to the UIP-MA constant from atoms around the step. The magnitude of the obtained UIP-MA shift agrees well with experimental data. It is also found that an additional shift due to possible charge transfer between Cu and Co atoms is very small.Comment: 12 pages,9 figures, RevTeX, submitted to Physical Review B version 3: additions to content version 2: minor correction

Exact exchange potential evaluated solely from occupied Kohn-Sham and Hartree-Fock solutions

The reported new algorithm determines the exact exchange potential v_x in a iterative way using energy and orbital shifts (ES, OS) obtained - with finite-difference formulas - from the solutions (occupied orbitals and their energies) of the Hartree-Fock-like equation and the Kohn-Sham-like equation, the former used for the initial approximation to v_x and the latter - for increments of ES and OS due to subsequent changes of v_x. Thus, solution of the differential equations for OS, used by Kummel and Perdew (KP) [Phys. Rev. Lett. 90, 043004 (2003)], is avoided. The iterated exchange potential, expressed in terms of ES and OS, is improved by modifying ES at odd iteration steps and OS at even steps. The modification formulas are related to the OEP equation (satisfied at convergence) written as the condition of vanishing density shift (DS) - they are obtained, respectively, by enforcing its satisfaction through corrections to approximate OS and by determining optimal ES that minimize the DS norm. The proposed method, successfully tested for several closed-(sub)shell atoms, from Be to Kr, within the DFT exchange-only approximation, proves highly efficient. The calculations using pseudospectral method for representing orbitals give iterative sequences of approximate exchange potentials (starting with the Krieger-Li-Iafrate approximation) that rapidly approach the exact v_x so that, for Ne, Ar and Zn, the corresponding DS norm becomes less than 10^{-6} after 13, 13 and 9 iteration steps for a given electron density. In self-consistent density calculations, orbital energies of 10^{-4} Hartree accuracy are obtained for these atoms after, respectively, 9, 12 and 12 density iteration steps, each involving just 2 steps of v_x iteration, while the accuracy limit of 10^{-6}--10^{-7} Hartree is reached after 20 density iterations.Comment: 21 pages, 5 figures, 3 table

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

Ferromagnetism and Temperature-Driven Reorientation Transition in Thin Itinerant-Electron Films

The temperature-driven reorientation transition which, up to now, has been studied by use of Heisenberg-type models only, is investigated within an itinerant-electron model. We consider the Hubbard model for a thin fcc(100) film together with the dipole interaction and a layer-dependent anisotropy field. The isotropic part of the model is treated by use of a generalization of the spectral-density approach to the film geometry. The magnetic properties of the film are investigated as a function of temperature and film thickness and are analyzed in detail with help of the spin- and layer-dependent quasiparticle density of states. By calculating the temperature dependence of the second-order anisotropy constants we find that both types of reorientation transitions, from out-of-plane to in-plane (``Fe-type'') and from in-plane to out-of-plane (``Ni-type'') magnetization are possible within our model. In the latter case the inclusion of a positive volume anisotropy is vital. The reorientation transition is mediated by a strong reduction of the surface magnetization with respect to the inner layers as a function of temperature and is found to depend significantly on the total band occupation.Comment: 10 pages, 8 figures included (eps), Phys Rev B in pres

Gilbert damping in magnetic layered systems

The Gilbert damping constant present in the phenomenological Landau-Lifshitz-Gilbert equation describing the dynamics of magnetization is calculated for ferromagnetic metallic films as well as Co/nonmagnet (NM) bilayers. The calculations are done within a realistic nine-orbital tight-binding model including spin-orbit coupling. The convergence of the damping constant expressed as a sum over the Brillouin zone is remarkably improved by introducing finite temperature into the electronic occupation factors and subsequent summation over the Matsubara frequencies. We investigate how the Gilbert damping constant depends on the ferromagnetic film thickness as well as on the thickness of the nonmagnetic cap in Co/NM bilayers (NM=Cu, Pd, Ag, Pt, and Au). The obtained theoretical dependence of the damping constant on the electron-scattering rate, describing the average lifetime of electronic states, varies substantially with the ferromagnetic film thickness and it differs significantly from the dependence for bulk ferromagnetic metals. The presence of nonmagnetic caps is found to largely enhance the magnetic damping in Co/NM bilayers in accordance with experimental data. Unlike Cu, Ag, and Au a particularly strong enhancement is obtained for Pd and Pt caps. This is attributed to the combined effect of the large spin-orbit couplings of Pd and Pt and the simultaneous presence of d states at the Fermi level in these two metals. The calculated Gilbert damping constant also shows an oscillatory dependence on the thicknesses of both ferromagnetic and nonmagnetic parts of the investigated systems which is attributed to quantum-well states. Finally, the expression for contributions to the damping constant from individual atomic layers is derived. The obtained distribution of layer contributions in Co/Pt and Co/Pd bilayers proves that the enhanced damping which affects the dynamics of the magnetization in the Co film originates mainly from a region within the nonmagnetic part of the bilayer. Such a nonlocal damping mechanism, related to spin pumping, is almost absent in other investigated bilayers: Co/Cu, Co/Ag, and Co/Au

Measurements of derivations of facade wells of the building from vertical plane

W artykule zaprezentowano pomiary odchyleń ścian elewacyjnych budynku od płaszczyzny pionowej z zastosowaniem dwóch metod geodezyjnych: kątowych wcięć przestrzennych w przód i biegunowej 3D z użyciem tachimetru Leica TC407 POWER. Zawarto: założenia organizacyjno-techniczne towarzyszące tym pomiarom, ostateczne wyniki wraz z graficzną interpretacją obejmującą siatkę modelu GRID oraz mapę izolinii odchyłek od płaszczyzny pionowej ścian. Autorzy przedstawiają zalety i wady poszczególnych metod rozważane w zakresie optymalizacji sposobu pomiaru. W pracy przedstawiono wnioski, spostrzeżenia oraz propozycje, co powinno się jeszcze uwzględnić i ulepszyć.The article presents the measurement deviation of elevation walls of the building from the vertical plane using two methods of surveying: “spatial resection forward (spatial intersection by angles technique)” and “3D polar survey” using the Leica TC407 Power. Contents: assumptions of organizational-technical accompanying these measurements, the final results along with graphical interpretation covering GRID model and maps isolines wall. The authors present the advantages and disadvantages of each method considered in the optimization of the measurement method. The paper presents the findings, observations and proposals, which should have taken into account and improve

Calculation of Gilbert damping in ferromagnetic films

The Gilbert damping constant in the phenomenological Landau-Lifshitz-Gilbert equation which describes the dynamics of magnetization, is calculated for Fe, Co and Ni bulk ferromagnets, Co films and Co/Pd bilayers within a nine-band tight-binding model with spin-orbit coupling included. The calculational effciency is remarkably improved by introducing finite temperature into the electronic occupation factors and subsequent summation over the Matsubara frequencies. The calculated dependence of Gilbert damping constant on scattering rate for bulk Fe, Co and Ni is in good agreement with the results of previous ab initio calculations. Calculations are reported for ferromagnetic Co metallic films and Co/Pd bilayers. The dependence of the Gilbert damping constant on Co film thickness, for various scattering rates, is studied and compared with recent experiments