Nucleation modes in ferromagnetic prolate spheroids

Magnetization reversal in a perfect ferromagnetic prolate spheroid, with no surface anisotropy, is known to start from nucleation either by coherent rotation (for small radii), or by the magnetization curling mode (above a certain size), but the possibility of a third mode has never been ruled out. It is rigorously proved here that there can be no third switching mode if the aspect ratio is not larger than 500:1, and even for larger ratios it may at most exist for a very limited size range.