Rigorous Approach to the Theory of Ferromagnetic Microstructure

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Abstract
Current ``domain'' theory relies heavily on Bloch walls and the Landau‐Lifshitz method of assembling them. A rigorous attack on the same problem leads to a nonlinear boundary‐value problem; with electronic computers available, this problem is now less formidable than when it was first formulated. Numerical calculations have been carried out for an infinite cylinder that reverses its magnetization by ``magnetization curling.'' The conditions under which this process occurs can be determined by means of a linear theory, similar to the theory of elastic stability, developed independently by the author and by Frei, Shtrikman, and Treves. To follow the process beyond its initial stages, a nonlinear differential equation must be integrated by numerical methods. The calculations show that the only stable states are ones of uniform positive or negative longitudinal magnetization; the transition between them occurs in a single jump, and only during the jump is the magnetization nonuniform. Thus a particle with no stable states other than ``single‐domain'' ones may be ``multidomain'' during transitions. The results suggest that stable nonuniform states will be found in a finite body, and even in an infinite cylinder if imperfections are present.