Point singularities in micromagnetic systems with radial symmetry

Abstract

The existence of point singularities in micromagnetic materials has been pointed out by Feldkeller (1965) and Doring (1968), essentially due to the multivalued nature of the magnetic vector in angular variables. In the present paper, the existence of point (isolated essential) singularities at the origin in the radial part of the spins is demonstrated by explicitly finding the equilibrium configurations for a Heisenberg ferromagnetic system with circular, spherical, planar and axial symmetries. While the energy density diverges at these points, it is shown that by excluding a small region around these singularities a finite total energy may be obtained. By comparing the above solutions with that of the linear one-dimensional case, it is explained how the singularity develops as the dimensionality increases.