Finite Element Formalism for Micromagnetism

The aim of this work is to present the details of the finite element approach we developed for solving the Landau-Lifschitz-Gilbert equations in order to be able to treat problems involving complex geometries. There are several possibilities to solve the complex Landau-Lifschitz-Gilbert equations numerically. Our method is based on a Galerkin-type finite element approach. We start with the dynamic Landau-Lifschitz-Gilbert equations, the associated boundary condition and the constraint on the magnetization norm. We derive the weak form required by the finite element method. This weak form is afterwards integrated on the domain of calculus. We compared the results obtained with our finite element approach with the ones obtained by a finite difference method. The results being in very good agreement, we can state that our approach is well adapted for 2D micromagnetic systems.Comment: Proceedings of conference EMF200

Fast computation of magnetostatic fields by Non-uniform Fast Fourier Transforms

The bottleneck of micromagnetic simulations is the computation of the long-ranged magnetostatic fields. This can be tackled on regular N-node grids with Fast Fourier Transforms in time N logN, whereas the geometrically more versatile finite element methods (FEM) are bounded to N^4/3 in the best case. We report the implementation of a Non-uniform Fast Fourier Transform algorithm which brings a N logN convergence to FEM, with no loss of accuracy in the results

Contacting individual Fe(110) dots in a single electron-beam lithography step

We report on a new approach, entirely based on electron-beam lithography technique, to contact electrically, in a four-probe scheme, single nanostructures obtained by self-assembly. In our procedure, nanostructures of interest are localised and contacted in the same fabrication step. This technique has been developed to study the field-induced reversal of an internal component of an asymmetric Bloch domain wall observed in elongated structures such as Fe(110) dots. We have focused on the control, using an external magnetic field, of the magnetisation orientation within N\'eel caps that terminate the domain wall at both interfaces. Preliminary magneto-transport measurements are discussed demonstrating that single Fe(110) dots have been contacted.Comment: 5 page

Head-to-head domain walls in one-dimensional nanostructures: an extended phase diagram ranging from strips to cylindrical wires

International audienceSo far magnetic domain walls in one-dimensional structures have been described theoretically only in the cases of flat strips, or cylindrical structures with a compact cross-section, either square or disk. Here we describe an extended phase diagram unifying the two pictures, extensively covering the (width,thickness) space. It is derived on the basis of symmetry and phase-transition arguments, and micromagnetic simulations. A simple classification of all domain walls in two varieties is proposed on the basis of their topology: either with a combined transverse/vortex character, or of the Bloch-point type. The exact arrangement of magnetization within each variety results mostly from the need to decrease dipolar energy, giving rise to asymmetric and curling structures. Numerical evaluators are introduced to quantify curling, and scaling laws are derived analytically for some of the iso-energy lines of the phase diagram

Electron Microscopy Investigation of Magnetization Process in Thin Foils and Nanostructures

International audienceThis paper presents an investigation of magnetization configuration evolution during insitu magnetic processes, in materials exhibiting planar and perpendicular magnetic anisotropy. Transmission electron microscopy (TEM) has been used to perform magnetic imaging. Fresnel contrast in Lorentz Transmission Electron Microscopy (LTEM), phase retrieval methods such as Transport of Intensity Equation (TIE) solving and electron holography have all been implemented. These techniques are sensitive to magnetic induction perpendicular to the electron beam, allowing the mapping of magnetic induction distribution with a spatial resolution better than 10nm and can be extended to allow dynamical studies during in-situ observation. Thin foils of FePd alloys with a strong perpendicular magnetic anisotropy (PMA) and self-assembled Fe dots have been examined. Both are studied during magnetization processes, exhibiting the capacities of in-situ magnetic imaging in a TEM

Dimensionality cross-over in magnetism: from domain walls (2D) to vortices (1D)

Dimensionality cross-over is a classical topic in physics. Surprisingly it has not been searched in micromagnetism, which deals with objects such as domain walls (2D) and vortices (1D). We predict by simulation a second-order transition between these two objects, with the wall length as the Landau parameter. This was conrmed experimentally based on micron-sized ux-closure dots