Exponential behavior of the interlayer exchange coupling across nonmagnetic metallic superlattices

Abstract

It is shown that the coupling between magnetic layers separated by nonmagnetic metallic superlattices can decay exponentially as a function of the spacer thickness N, as opposed to the usual N Ϫ2 decay. This effect is due to the lack of constructive contributions to the coupling from extended states across the spacer. The exponential behavior is obtained by properly choosing the distinct metals and the superlattice unit cell composition. ͓S0163-1829͑98͒01337-X͔The alignment of the magnetizations of metallic layers separated by nonmagnetic metallic spacers oscillates between parallel and antiparallel as the distance N between the magnetic layers is varied. This oscillatory interlayer exchange coupling J(N) has been intensively investigated both experimentally and theoretically. 1,2 At zero temperature and for sufficiently thick metallic spacers, the amplitude of J decays usually as 1/N 2 , and its oscillation periods depend on the geometry of the spacer Fermi surface ͑FS͒. 3-7 Such a behavior has been regarded as characteristic of crystalline metallic spacers. In fact, simple theoretical arguments show that the coupling across insulating materials decays exponentially with N, 8,10 the reason being the absence of extended electronic states within the insulating spacer with energy equal to the chemical potential.There are general rules which provide a systematic way for determining the oscillation periods of J across metallic spacers. [4][5][6] In their simplest form they correspond to the RKKY criterion, which states that the periods are given by critical spanning wave vectors along the growth direction linking two points of the bulk spacer FS with antiparallel velocities. 4 Recently, it has been suggested that the periods of J across nonmagnetic metallic superlattices can be altered in a controllable way by changing the superlattice composition, and, hence, its FS. 11 In this paper we show that it is possible to find an exponentially decaying J(N) across nonmagnetic metallic superlattices. Such a behavior can be obtained by properly choosing the superlattice constituent materials and unit cell composition in such a way that the superlattice FS shows no critical wave vectors in the direction perpendicular to the layers. In this case, despite the metallic character of the spacer, the contributions to the coupling coming from extended states interfere destructively.The systems we examine are composed of two semiinfinite ferromagnetic metals separated by a nonmagnetic metallic superlattice. The superlattice unit cell consists of two layers, made of metals A and B, containing N A and N B atomic planes, respectively. We have calculated J as a function of the number of atomic planes in the spacer. However, as far as the periods are concerned, it is only when probed at regular intervals of the supercell size (N s ϭN A ϩN B atomic planes͒ that the coupling reflects the structure of the spacer superlattice FS. 11 Therefore, to highlight the oscillation periods which are associated with the superlattice FS, when we show our...

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