Micromagnetics, Domains, and Resonance

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Abstract
Current domain theory is based largely on the wall concept and on the 1935 paper of Landau and Lifshitz. That same paper contained the germ of another theory; in it the basic concept is a spontaneous magnetization whose direction varies continuously with position. This approach, micromagnetics, can in principle yield a complete, self‐consistent theory, from which the domain and wall concepts when valid will emerge naturally, without having to be postulated. The present paper summarizes the history, accomplishments, and possibilities of such a theory. The basic partial differential equations of the theory are nonlinear; they have been attacked by four methods. (1) Study of one‐dimensional cases formed the basis of traditional domain theory and of other early work. (2) Linearization of the equations proved possible in the study of the approach to saturation. (3) The Ritz method has been used in the study of fine particles and of films. (4) Numerical calculations with electronic computers have been made in some nonlinear cases. The single‐domain problem, in certain of its aspects, has been rigorously solved by use of linear equations. The equilibrium equations of micromagnetostatics are closely related to dynamic equations used in the theory of ferromagnetic resonance and of spin waves.

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