Numerical Methods in Micromagnetics (Finite Element Method)

Abstract

Micromagnetic simulations provide guidelines for the development of composite magnetic materials and magnetic devices. The granular structure of a material and the magnetic interactions between the different magnetic parts of a device can be easily taken into account by the finite element method and the boundary element method, respectively. The finite element equations are derived for the calculation of the magnetostatic field. Similarly, it is shown how the total energy of a magnetic system can be computed by matrix‐vector operations. Efficient methods for calculating equilibrium magnetic states and the simulation of the dynamic response of a magnetic material to a time varying external field are discussed. Numerical schemes for the simulation of magnetization dynamics in systems involving moving parts are introduced. The numerical methods are demonstrated by showing results of perpendicular magnetic recording simulation on composite media.

First order reversal curve studies of permanent magnets

“…We apply finite element micromagnetic simulations 7 for the simulation of the hysteresis loop and the first order reversal curves of a sintered permanent magnet. The method is modified in order to take into account the different characteristic length scales in a sintered magnet.…”

“…We apply a weak formulation for the computation of the exchange field, H ex , and the anisotropy field, H a , at the nodes of a tetrahedral grid. 7 The demagnetizing field at the integration points of the finite elements is computed from surface charges at the grain boundaries. We use the nodes of the grid as integration points except for nodes that are on grain boundaries.…”

Non-uniform FFT for the finite element computation of the micromagnetic scalar potential

“…stray field energy is calculated by using so-called mass lumping for the computation of the stray field as described in (e.g.) [20,Sec. 2.2.3].…”

Analysis of the structural-defect influence on the magnetization process in and above the Rayleigh region

“…A more complicated situation occurs in the presence of a pseudo-dislocation dipole, where the arrangement of individual vectors is not collinear and the centers of the deformation of these vectors are hooked at the dipole ends. [11][12][13] Ferromagnetic materials, especially the ones based on the Fe-Co-B composition are well known for their great soft-magnetic properties, in particular a low coercive field and magnetostriction while they are not expensive and have a high sensitivity to alloying additives. In the compounds of this type, iron is typically the major part (more than a 50 % amount fraction) while Co, which has similar properties, allows an increase in the magnetization.…”