On Corner Singularities in Micromagnetics

The magnetization distribution in the vicinity of a sharp square edge is investigated analytically, in two and three dimensions. The aim of this calculation is to investigate the consequences of the logarithmic divergence of some components of the demagnetizing field at this point, in order to understand better some recent numerical calculations by Rave, Ramstöck and Hubert. A definite solution is found, that depends solely on the magnetization direction at the corner point, and displays a mild r2 ln (r) singularity. Possible applications of this solution range from a “plug-in” box in numerical simulations to analytical micromagnetics of square single domain particles.