Some Recent Developments in Micromagnetics at the Weizmann Institute of Science

Abstract

Recent theoretical studies carried out in micromagnetics at this Institute are reviewed, and preliminary results are given for theoretical problems which are now under study. The coercive force of an infinite circular cylinder is calculated as a function of the radius and of the inclination of the cylindrical axis to the applied field. For this calculation it is assumed that only the curling and the rotation in unison modes take place; and that whenever the curling is associated with a discontinuous jump, the magnetization is brought to the values tabulated by Stoner and Wohlfarth, who assumed only rotation in unison. Using the same assumptions, the rotational hysteresis loss and integral are calculated both for an aligned and for a random assembly of cylinders. The results are found to be in fair agreement with the measurements of Jacobs and Luborsky on elongated particles. The remanence curves of a random assembly of infinite cylinders are calculated for the same model as a function of the applied field and of the radius of the cylinders. The rotation in unison and the curling are proved to be the easiest modes for magnetization reversal in a ferromagnetic sphere. The nucleation field associated with the curling mode is calculated as a function of elongation and size for a ferromagnetic prolate spheroid. For a rather wide range of elongations this suffices as an approximation for the coercive force, which should be larger than the nucleation field but smaller than the coercive force of the infinite cylinder. As an attempt to introduce interparticle interactions the following model is treated. A square lattice of infinite cylinders with a square cross section is assumed with all cylinders parallel to the applied field. Rotation in unison of the spins is assumed for each column of cylinders, and rotation in opposite directions but with equal magnitudes of the angle is assumed for neighboring columns. The coercive force of this model is found to be only slightly less than that given by Néel's formula which is valid for coherent rotation in a random distribution of infinite cylinders of any cross section. The dependence of the critical size and of the coercive force on the packing factor is discussed and compared with experiment. A first approach to the study of the dependence of coercive force on imperfections is carried out by treating each of two mathematical models for a material which is infinite in all directions. The first model is a slab of finite width in which the anisotropy constant $K$ is zero. The second one is a linear reduction of $K$ through a slab of finite width from its constant value to zero. For both models the nucleation field is given as a function of the imperfection width. For the first model the behavior after nucleation is also discussed.