Magnetization buckling in a prolate spheroid

Using a rigorous lower bound to the magnetostatic self-energy, it is proved that no buckling can take place in a ferromagnetic prolate spheroid, whose aspect ratio is less than 4.6:1. The only possible reversal modes for this aspect ratio are the coherent rotation for small radii, and the curling for larger ones. Even for more elongated spheroids, a plausible argument suggests that the buckling mode is rather unlikely, except for the limit of an infinite circular cylinder.