Rigorous Calculation of the Nucleation Field in a Ferromagnetic Film or Plate

Abstract

The rigorous methods of micromagnetics have been used to calculate nucleation fields and corresponding incipient-domain widths for a ferromagnetic film or plate with the applied field along its faces and with a direction of easy magnetization perpendicular to them. The calculation requires finding the largest zero of a fourth-order determinant whose elements depend on the roots of a cubic equation, and then maximizing the result by trial-and-error variation of the parameters that determine the period and direction of the sinusoidal oscillation in the plane of the film. The calculation was therefore programmed for an electronic digital computer; and to narrow the area of search for zeros, preliminary calculations were done by use of two types of approximation, one of which set an upper and the other a lower limit to the correct zero. The results show that Muller's approximate method of solving the same problem is satisfactory in the range of parameters for which it was designed. Experimental data of Huber and Smith agree satisfactorily with the theory.