Upper and Lower Bounds for the Nucleation Field in an Infinite Rectangular Ferromagnetic Cylinder

Abstract

The results of Brown for the nucleation fields of an infinitely long ferromagnetic prism with a square cross section, are generalized for a rectangular cross section, using practically the same techniques used by Brown: lower bounds are found by replacing the (positive) self‐magnetostatic energy by a smaller quantity. Upper bounds are obtained by considering only certain types of functions in the variational problem. The upper and lower bounds thus found are reasonably close to each other to give a sufficient estimation for the nucleation field, for rotation in quasiunison. For the curling modes the bounds are very close to each other when the deviation from a square is not too large, but the distance between them increases when the rectangle is more elongated, giving just an order of magnitude estimation for breadth to length ratio of 1:10.