Theory of exchange coupling in magnetic multilayers

Two layers of magnetic materials separated by a nonmagnetic "spacer" layer display an exchange coupling between the separated magnetic layers, as detailed by the papers on experimental aspects of magnetic multilayers in this issue. Here we describe from a personal perspective the current theoretical understanding of exchange coupling in magnetic multilayers. The understanding by this point is quite good, and involves contributions from a number of authors, of which we review a key subset. The organization of the paper is as follows. After an introduction to RKKY coupling, the next section discusses the effects of a realistic band structure (with emphasis on the work of Herman et al., Bruno and Chappert, and Stiles). The following section, which introduces quantum wells, covers the work of Mathon et al., Bruno et al., and this author. Finally, we include a discussion of the predictability of amplitude, period, and phase, including the effects of disorder.