and J. Bass, Phys Materials, edited lit, and D. Mauri, 191, p. 221. U. V. S. Speriosu, J. . E. Spada, F. T. 2). erein. 1990). LO18 (1975). INTERLAYER EXCHANGE COUPLING: RKKY THEORY AND BEYOND P. Bruno and C. Chappert Institut d’Electronique Fondamentale, CNRS UA 022 Bbt. 220, Universitk Paris-Sud, F-91405 Orsay CEDEX, France 1 INTRODUCTION The problem of exchange coupling between ferromagnetic transition-metal layers sep- arated by a non-magnetic metal spacer is currently attracting considerable attention. The impetus has been given by the discovery, for Fe/Cr/Fe and Co/Ru/Co systems, that the coupling oscillates periodically in sign and magnitude as a function of the non-magnetic spacer thickness 111. It has been subsequently found that oscillatory cou- pling occurs indeed for almost all transition and noble metals (as spacer material) [2]. The explaination of this remarkable phenomenon is a challenge to the theory and has motivated a number of theoretical investigations. The oscillatory behavior bears much resemblance with the one observed for Ruder- man-Kittel-Kasuya-Yosida (RKKY) interactions between magnetic impurities. Thus the RKKY interaction appears a good candidate for the mechanism of oscillatory in- terlayer coupling. However, when applied in its simplest version (i.e. making a free- electron approximation and assuming a uniform continuous spin distribution within the ferromagnetic layers) [3], the RKKY theory predicts a period A = XF/~ M 1 monolayer (ML), which is much shorter than the experimental ones. It has been shown then that long periods can i6deed be obtained within a simple RKKY theory, provided that the discreteness of the spacer thickness is taken into account [4]. Recently, we have pre- sented a general theory of RKKY interlayer exchange coupling [5]; in this approach, the coupling is related in a physically transparent manner to the topological properties of the Fermi surface of the spacer material. In particular, we showed that multiple periods may occur, depending on the in-plane atomic structure. For the first time, quantitative predictions were obtained for the oscillation periods in the case of noble-metal spacers; these predictions have been well verified by the experiment. The RKKY theory of interlayer coupling will be reviewed in Sec. 2. In spite of its success for predicting oscillation periods, the RKKY theory is not capable of describing correctly the magnitude and the phase of the coupling oscilla- tions, essentially because it relies on a poor description of the interaction between the Magnetism and Srruclure in Systems of Reduced Dimension Edited by R.F.C. Fanow el al., Plenum Press, New York, 1993 389