Exploring small energy scales with x-ray absorption and dichroism

Soft x-ray linear and circular dichroism (XLD, XMCD) experiments at the Ce M$_{4,5}$ edges are being used to determine the energy scales characterizing the Ce $4f$ degrees of freedom in the ultrathin ordered surface intermetallic CeAg$_x$/Ag(111). We find that all relevant interactions, i. e. Kondo scattering, crystal field splitting and magnetic exchange coupling occur on small scales. Our study demonstrates the usefulness of combining x-ray absorption experiments probing linear and circular dichroism owing to their strong sensitivity for anisotropies in both charge distribution and paramagnetic response, respectively.Comment: 5 pages, 4 figure

FEM–BEM coupling for the large-body limit in micromagnetics

AbstractWe present and analyze a coupled finite element–boundary element method for a model in stationary micromagnetics. The finite element part is based on mixed conforming elements. For two- and three-dimensional settings, we show well-posedness of the discrete problem and present an a priori error analysis for the case of lowest order elements

The saturation assumption yields optimal convergence of two-level adaptive BEM

We consider the convergence of adaptive BEM for weakly-singular and hypersingular integral equations associated with the Laplacian and the Helmholtz operator in 2D and 3D. The local mesh-refinement is driven by some two-level error estimator. We show that the adaptive algorithm drives the underlying error estimates to zero. Moreover, we prove that the saturation assumption already implies linear convergence of the error with optimal algebraic rates

The Mass-Lumped Midpoint Scheme for Computational Micromagnetics: Newton Linearization and Application to Magnetic Skyrmion Dynamics

We discuss a mass-lumped midpoint scheme for the numerical approximation of the Landau-Lifshitz-Gilbert equation, which models the dynamics of the magnetization in ferromagnetic materials. In addition to the classical micromagnetic field contributions, our setting covers the non-standard Dzyaloshinskii-Moriya interaction, which is the essential ingredient for the enucleation and stabilization of magnetic skyrmions. Our analysis also includes the inexact solution of the arising nonlinear systems, for which we discuss both a constraint-preserving fixed-point solver from the literature and a novel approach based on the Newton method. We numerically compare the two linearization techniques and show that the Newton solver leads to a considerably lower number of nonlinear iterations. Moreover, in a numerical study on magnetic skyrmions, we demonstrate that, for magnetization dynamics that are very sensitive to energy perturbations, the midpoint scheme, due to its conservation properties, is superior to the dissipative tangent plane schemes from the literature

Coupling of dynamical micromagnetism and a stationary spin drift-diffusion equation: A step towards a fully self-consistent spintronics framework

This is the author accepted manuscript. The final version is available from Elsevier via the DOI in this record.We consider the coupling of the Landau-Lifshitz-Gilbert equation with a quasilinear diffusion equation to describe the interplay of magnetization and spin accumulation in magnetic-nonmagnetic multilayer structures. For this problem, we propose and analyze a convergent finite element integrator, where, in contrast to prior work, we consider the stationary limit for the spin diffusion. Numerical experiments underline that the new approach is more effective, since it leads to the same experimental results as for the model with time-dependent spin diffusion, but allows for larger time-steps of the numerical integrator.The authors acknowledge support from the Vienna Science and Technology Fund (WWTF) under grant MA14-44 (GH, DP, DS), from the Austrian Science Fund (FWF) under grant W1245 (DP, MR), from TU Wien through the innovative projects initiative (DP, MR), from the Austrian Federal Ministry of Science, Research and Economy and the National Foundation for Research, Technology and Development (CA, DS), through the EPSRC grant EP/K008412/1 (GH), from the Royal Society under grant UF080837 (GH)

Electronic tuneability of a structurally rigid surface intermetallic and Kondo lattice: CePt5_5 / Pt(111)

We present an extensive study of structure, composition, electronic and magnetic properties of Ce--Pt surface intermetallic phases on Pt(111) as a function of their thickness. The sequence of structural phases appearing in low energy electron diffraction (LEED) may invariably be attributed to a single underlying intermetallic atomic lattice. Findings from both microscopic and spectroscopic methods, respectively, prove compatible with CePt$_5$ formation when their characteristic probing depth is adequately taken into account. The intermetallic film thickness serves as an effective tuning parameter which brings about characteristic variations of the Cerium valence and related properties. Soft x-ray absorption (XAS) and magnetic circular dichroism (XMCD) prove well suited to trace the changing Ce valence and to assess relevant aspects of Kondo physics in the CePt$_5$ surface intermetallic. We find characteristic Kondo scales of the order of 10$^2$ K and evidence for considerable magnetic Kondo screening of the local Ce $4f$ moments. CePt$_5$/Pt(111) and related systems therefore appear to be promising candidates for further studies of low-dimensional Kondo lattices at surfaces.Comment: 14 pages, 11 figure

Different levels of context-specificity of teacher self-efficacy and their relations with teaching quality

On the basis of Bandura’s social cognitive theory, researchers often assume that a teachers’ self-efficacy (TSE) will have a positive effect on teaching quality. However, the available empirical evidence is mixed. Building on previous research into TSE, we examined whether assessing class-/task-specific TSE gives a more accurate indication of the associations between TSE assessments and student-rated teaching quality. The analyses were based on the English sample of the Teaching and Learning International Survey (TALIS) Video Study. Mathematics teachers (N = 86) rated their self-efficacy beliefs using generalized task-specific TSE items and class-/task-specific TSE items. Their students (N = 1,930) rated the quality of teaching in their math class. Multilevel regression analyses revealed stronger associations between student-rated teaching quality and class-/task-specific TSE than generalized task-specific TSE. We discuss possible reasons for these results and outline the potential benefits of using class-specific assessments for future TSE research

Computational micromagnetics with Commics

We present our open-source Python module Commics for the study of the magnetization dynamics in ferromagnetic materials via micromagnetic simulations. It implements state-of-the-art unconditionally convergent finite element methods for the numerical integration of the Landau–Lifshitz–Gilbert equation. The implementation is based on the multiphysics finite element software Netgen/NGSolve. The simulation scripts are written in Python, which leads to very readable code and direct access to extensive post-processing. Together with documentation and example scripts, the code is freely available on GitLab. Program summary: Program title: Commics Program Files doi: http://dx.doi.org/10.17632/29wv9h78h7.1 Licensing provisions: GPLv3 Programming language: Python3 Nature of problem: Numerical integration of the Landau–Lifshitz–Gilbert equation in three space dimensions Solution method: Tangent plane scheme [1]: original first-order version, projection-free version, second-order version, efficient second-order IMEX version; Midpoint scheme [2]: original version, IMEX version; Magnetostatic Maxwell equations are treated by the hybrid FEM–BEM method [3] Additional comments including restrictions and unusual features: An installation of the finite element software Netgen/NGSolve and an installation of the boundary element library BEM++ are required. References [1] F. Alouges. A new finite element scheme for Landau–Lifchitz equations. Discrete Contin. Dyn. Syst. Ser. S, 1(2):187–196, 2008. [2] S. Bartels and A. Prohl. Convergence of an implicit finite element method for the Landau–Lifshitz–Gilbert equation. SIAM J. Numer. Anal., 44(4):1405–1419, 2006. [3] D. R. Fredkin and T. R. Koehler. Hybrid method for computing demagnetization fields. IEEE Trans. Magn., 26(2):415–417, 1990