Magnetization Curve of the Infinite Cylinder

The nucleation field for an infinite circular ferromagnetic cylinder, with the field applied along its axis, is rigorously calculated by exploring the whole eigenvalue spectrum of Brown's equations.The nucleation fields for cylinders with "large" radii are found to be those of the magnetization curling. For "small" radii the nucleation field is found to be somewhat smaller than that for the magnetization buckling. However, the difference is only about 1%, and the exact mode of reversal is very close to the buckling. The transition from exact buckling to curling is abrupt. These two modes are shown to be the only modes for nucleation for any radius, the other modes giving higher nucleation fields.It is shown that the magnetization reversal occurs in one jump, which means that the magnetization curve for the cylinder is a rectangular loop.