Flux propagation in thin-film magnetic structures

Abstract

The theoretical basis of the transmission line model (TLM), a model widely used to describe the propagation of flux in thin-film magnetic structures, is examined. The primary prediction of the model is that magnetic flux propagates along the structure exponentially with a characteristic length, simply related to the permeabilities and thicknesses of the films constituting the structure. To examine the validity of the model we analyze the solution of Maxwell’s equations for two canonical thin-film geometries and establish the following results. For the first geometry, infinite in extent, we show how the exponential flux propagation of the TLM emerges directly from the exact solution for the flux, and we derive the range in parameters over which this occurs. For the second geometry, which is of finite extent and thus includes end effects, we show that the TLM is exact in a certain limit. Practical device geometries, for which the TLM was developed (magnetic recording heads), typically approach this limit. Therefore, the solution for the magnetization in these structures will approach the limit solution, i.e., the TLM solution, and may thus, validly, be approximated by it. The physical content of this limit is discussed relative to the range of validity of the TLM. These two results confirm the general soundness of the TLM and provide a theoretical basis for it.