Energetics and switching of quasi-uniform states in small ferromagnetic particles

We present a numerical algorithm to solve the micromagnetic equations based on tangential-plane minimization for the magnetization update and a homothethic-layer decomposition of outer space for the computation of the demagnetization field. As a first application, detailed results on the flower-vortex transition in the cube of Micromagnetic Standard Problem number 3 are obtained, which confirm, with a different method, those already present in the literature, and validate our method and code. We then turn to switching of small cubic or almost-cubic particles, in the single-domain limit. Our data show systematic deviations from the Stoner-Wohlfarth model due to the non-ellipsoidal shape of the particle, and in particular a non-monotone dependence on the particle size

Computational design of rare-earth reduced permanent magnets

Multiscale simulation is a key research tool in the quest for new permanent magnets. Starting with first principles methods, a sequence of simulation methods can be applied to calculate the maximum possible coercive field and expected energy density product of a magnet made from a novel magnetic material composition. Iron (Fe)-rich magnetic phases suitable for permanent magnets can be found by means of adaptive genetic algorithms. The intrinsic properties computed by ab intro simulations are used as input for micromagnetic simulations of the hysteresis properties of permanent magnets with a realistic structure. Using machine learning techniques, the magnet's structure can be optimized so that the upper limits for coercivity and energy density product for a given phase can be estimated. Structure property relations of synthetic permanent magnets were computed for several candidate hard magnetic phases. The following pairs (coercive field (T), energy density product (kJ.m(-3))) were obtained for iron-tin-antimony (Fe3Sn0.75Sb0.25): (0.49, 290), L1(0) -ordered iron-nickel (L1(0) FeNi): (1, 400), cobalt-iron-tantalum (CoFe6Ta): (0.87, 425), and manganese-aluminum (MnAl): (0.53, 80).Web of Science6215314

A literature survey of low-rank tensor approximation techniques

During the last years, low-rank tensor approximation has been established as a new tool in scientific computing to address large-scale linear and multilinear algebra problems, which would be intractable by classical techniques. This survey attempts to give a literature overview of current developments in this area, with an emphasis on function-related tensors

Micromagnetics and spintronics: Models and numerical methods

Computational micromagnetics has become an indispensable tool for the theoretical investigation of magnetic structures. Classical micromagnetics has been successfully applied to a wide range of applications including magnetic storage media, magnetic sensors, permanent magnets and more. The recent advent of spintronics devices has lead to various extensions to the micromagnetic model in order to account for spin-transport effects. This article aims to give an overview over the analytical micromagnetic model as well as its numerical implementation. The main focus is put on the integration of spin-transport effects with classical micromagnetics

Zero modes in magnetic systems: general theory and an efficient computational scheme

The presence of topological defects in magnetic media often leads to normal modes with zero frequency (zero modes). Such modes are crucial for long-time behavior, describing, for example, the motion of a domain wall as a whole. Conventional numerical methods to calculate the spin-wave spectrum in magnetic media are either inefficient or they fail for systems with zero modes. We present a new efficient computational scheme that reduces the magnetic normal-mode problem to a generalized Hermitian eigenvalue problem also in the presence of zero modes. We apply our scheme to several examples, including two-dimensional domain walls and Skyrmions, and show how the effective masses that determine the dynamics can be calculated directly. These systems highlight the fundamental distinction between the two types of zero modes that can occur in spin systems, which we call special and inertial zero modes. Our method is suitable for both conservative and dissipative systems. For the latter case, we present a perturbative scheme to take into account damping, which can also be used to calculate dynamical susceptibilities.Comment: 64 pages, 15 figure

Numerical Methods for a Reduced Model in Thin-Film Micromagnetics

We address the conformal finite element approximation to a reduced 2-d model arising in thin-film micromagnetics. The model was derived by DeSimone, Kohn, Müller, and Otto for a thin-film ferromagnetic element under an external magnetic field. The micromagnetic energy of the in-plane magnetization consists of two contributions: the energy of the stray field, and the Zeeman energy. The magnetization itself has to satisfy a convex constraint. We consider the approximation of the magnetization by Raviart-Thomas elements, which fits naturally in the theory of discrete de Rham complexes, a common concept of computational electromagnetism. The numerical challenge in micromagnetic simulations is the determination of the stray field, which in our case amounts to the evaluation of the single layer potential operator. We apply the method of hierarchical matrices developed by Hackbusch et al. to carry out calculations in sub-quadratic time. For weak external fields the problem for the magnetostatic charge distribution is a variational formulation of the Dirichlet screen problem. The charge distribution is known to have characteristic singularities near the edges and corners of the thin film cross-section. We establish the minimal regularity theory required later. We establish an a-priori error estimate in the energy norm and derive the necessary refinement rule for triangulations to retain the optimal rate of convergence. When the convex constraint on the magnetization becomes active, we apply an interior point method to compute an energy minimizing magnetization. A logarithmic barrier leads to a well-characterized, unique minimizer, the analytic center, though the energy is highly degenerate. Then we consider how to construct minimizers close to unit length: these correspond to saturated magnetizations observed in physical experiments. We apply modifications of well-established numerical schemes for the computation of viscosity solutions to Hamilton-Jacobi equations. We confront our numerical simulations with pictures from physical experiments, kindly provided by R. Schäfer. </p