Point Singularities in Micromagnetism

Abstract

Solutions of the micromagnetic equations for the equilibrium distribution of magnetization may have singular points, at which no spontaneous magnetization exists, because the limit of the magnetization vector for an approach to this point on different rays has different values. The boundary conditions at these points are considered. The exchange-energy density goes to infinity at such a point, but the condition that its integral should be a minimum leads to no definite boundary condition. For a special class of such singularities, namely those at which every direction of the magnetization is accepted once on a small sphere around it, the conditions for a minimum of the field energy are derived.