Nucleation Fields of an Infinitely Long Square Ferromagnetic Prism

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Abstract
When a homogeneous ferromagnetic specimen possesses an equilibrium state of uniform magnetization, the equilibrium becomes unstable at a certain (usually negative) value of the field component along the magnetization. This ``nucleation field'' is known for a longitudinally magnetized circular cylinder; the mode of deviation from the initial state is ``magnetization curling'' at large diameters and, to a good approximation, ``rotation in unison'' at small diameters. Values for square cross section would be useful for interpreting measurements on iron whiskers; but here the modes are more complicated, and rigorous solution would be difficult. The present calculation establishes upper and lower bounds to the nucleation fields for the modes described. The term that must be added to the crystalline‐anisotropy term is determined to within a factor π/2 for ``rotation in quasi‐unison'' and to within a factor 2 for curling; the corresponding values for a cylinder of the same cross section lie at the upper bound for the former mode and slightly above the lower bound for the latter; the critical thickness for change of mode is between 0.85 and 1.51 times the critical diameter for a cylinder.

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