PHYSICAL REVIEW B VOLUME 44, NUMBER 13 1 OCTOBER 1991-I Calculation of electronic and magnetic properties of metallic superlattices Gabriel Fabricius, Ana Maria Llois, and Mariana Weissmann Departarnento de Fisica, Cornision Nacional de Energia Atornica, Avda de. l Iibertador 8250, 1/29 Buenos Ai res, A'rgentina (Received 11 January 1991; revised manuscript received 16 April 1991) We calculate charge-transfer profiles and layer magnetizations for Cu/Ni-like superlattices in the tight-binding approximation. The efFects of local and nonlocal electron-electron interactions and magnetic band splitting are included only in the diagonal elements of the Hamiltonian. We discuss the importance of considering the electrostatic interactions among layers through a Madelung-type term. I. INTRODUCTION Artificially made metallic multilayers have offered in the last years an interesting field of research. Much work has been done experimentally in order to study physical phenomena which seem to be characteristic of these materials and, as a consequence, a large number of metallic multilayer systems are being synthetized nowa- days. Among the phenomena studied, the supermodulus efFect, 2 that is, anomalous values of the elastic constants of these systems, either larger or smaller than the values corresponding to the constituents of the superlattice, and the magnetic properties of the metallic interfaces have attracted our attention. In order to explain the appearance of the supermod- ulus effect Grimsditch et al. suggested that it may be due to the charge transfers within these layers. On the other hand, early LMTO calculations for Cu jNi super- lattices by Jarlborg and Freeman give very small charge transfers that change sign depending on the number of layers. This has led us to calculate, within a simple tight- binding model, the charge transfer profiles. We have lim- ited ourselves, for the moment, to superlattices whose constituents have the same crystalline structure. Actu- ally, we have focused on Ni jCu-like systems with inter- faces perpendicular to the fcc [ill] direction, this direc- tion being the technologically more interesting one. As these materials can be constructed with a variable num- ber of layers, the calculations were made as a function of the number of layers and also of overall concentration. Magnetism in the Ni-like type of atoms was also consid- ered, with the aim of studying the effect of interfaces in the magnetization of the samples. In actual superlattices of two metals that are very close in the Periodic Table, the interfaces are not abrupt, as there is a tendency toward mixing, but as a first ap- proximation we consider that the interfaces are perfect and make use of periodicity in order to calculate local densities of states. Previous calculations of the electronic structure of sys- tems made of transition metals in amorphous, bilayer, or superlattice structures have been performed by differ- ent methods. In the tight-binding calculations by Fal- icov, Tersoff, and Victora they postulate local charge neutrality, and LMTO or LAPW calculations have been performed only for a few specific systems. We have chosen the tight-binding formalism because it has the advantage that it is possible to increase the complexity of the model by introducing one by one different contri- butions to the Hamiltonian. In this way it is possible to evaluate the relative contribution of each of these ef- fects on the properties we are studying. In the present work the effects of local and nonlocal e -e interactions and magnetic band splitting were studied by including them only in the diagonal elements of the Hamiltonian. To calculate charge transfers and magnetizations we used the Hartree-Fock approximation and evaluated the long- range electrostatic contributions by an explicit Madelung term. In this first approach to the problem we have also replaced d orbitals by five degenerate s bands. As our aim is to introduce the d-orbital symmetry in future work, this will enable us to separate effects coming from the superlattice symmetry from those stemming from orbital symmetry. II. DESCRIPTION OF THE MODEL We consider a tight-binding (TB) Hamiltonian with nearest-neighbor interactions for a superlattice growing in the fcc structure along the [111] direction. The superlattice consists of N~ layers of A-type atoms and N~ of B-type atoms, periodically repeated, A and B being transition metals. The TB Hamiltonian in the Hartree-Fock approximation, written in a local orbital basis set, has the general form / f I ij io jo ~ ~ I 2)g)m)7A )0 ('A&) where c, (c; ) is the creation (annihilation) operator of 6870 1991 The American Physical Society