Analysis of Exchange-Coupled Magnetic Thin Films

Abstract

Presented in this paper are some new analytical results for two exchange‐coupled magnetic thin films. The formulation of the problem which is used is similar to that of Goto et al., who reduced the determination of the magnetic configuration of the films in the presence of an external magnetic field to the evaluation of elliptic integrals. Derived herein is an expression for the second variation of the magnetic energy, thereby allowing an investigation of the stability of previously determined magnetic configurations. Evaluation of this expression, as well as determination of the magnetic configuration, must be done numerically, and tables giving magnetic configurations and critical fields are included for a variety of thickness combinations and magnetic parameters. In addition, new analytical results are presented for several limiting cases. Transcendental equations have been derived which give the threshold fields for arbitrary film parameters when the easy axes are mutually parallel in the two films and when the external field is either parallel or perpendicular to the common easy axis. Expressions are also developed for the critical fields in composites involving both very thin and very thick films, and the magnetic properties of a pair of very thin films are shown to be simple combinations of the constituents' magnetic properties. Finally, several discrepancies are discussed between the approximate results of Goto et al. and the exact results obtained herein.