Volume IS!, number 1,2 PHYSICS LETTERS A 26 November 1990 Onset of magnetism in palladium slabs S. Bouarab, C. Demangeat JPCMS, UMR46, Université Louis Pasteur, 4 rueBlaise Pascal, 67070 Strasbourg, France A. Mokrani and H. Dreyssé Laboraloire de Physique des Solides, BP 239, 54506 Vandoeuvre-les Nancy, France Received 27 July 1990; accepted for publication 28 September 1990 Communicated by J. Flouquet We report a self-consistent tight-binding calculation on Pd slabs in the unrestricted Hartree—Fock approximation of the Hub- bard Hamiltonian. By considering slabs with different thicknesses we show that, whereas the monolayer is like the bulk and thick slabs non-magnetic, a magnetic moment appears for films with 2, 3 and 4 layers. Calculations [1] for bulk palladium predict mag- netic ordering upon expanding the lattice by 10%. ~z, = N~ — N~, Preliminary results based on electron capture spec- troscopy (ECS) [2] have suggested the existence of where N 10, the number of electrons of site i and spin ferromagnetism at Pd films grown on Ag (100), con- a, is given in terms of the spin polarized local density trary to Fink et al. [3] who did not find unambig- of states (SPDOS) n.0(E) which is calculated by us- uous existence of ferromagnetism within the sensi- ing the recursion method [6] with eight levels of the bility of the magneto-optic Kerr effect. continuous fraction. In order to have the Fermi level The calculations reported in the present Letter ad- of the bulk Pd at the right ofthe higher peak of n0(E) dress the possibility of induced magnetism in Pd slabs we assume N? = 9.4 electrons per atom. &N~. is the in terms of their thickness. Three of us have recently difference between the electronic occupations N1 and developed a real space self-consistent scheme for the N?. description of metallic multilayers with variable For pure palladium we have determined the onset thicknesses [4]. The magnetism is described in the of magnetism in terms of the exchange parameter J. unrestricted Hartree—Fock approximation of the The critical value of J for the appearance of mag- Hubbard Hamiltonian ford electrons. In this model, netism is J~=0.7 15 eV. Because bulk palladium is we start with canonical hopping integrals [5] whereas paramagnetic we cannot adjust J as in the iron sys- the spin dependent diagonal term is given by tern [41 in order to recover the experimental value. Therefore we choose, in accordance with the LMTO E,g =E~ + UAN, — a(J/2 )y,, calculations of Christensen et al. [7] a value of J=0.65 eV which gives a zero moment for bulk where i is the index of the atomic plane and a is the palladium. spin. E°d is the atomic d level and can be chosen as We have investigated within our spin polarized slab zero. The exchange and effective direct intra-atomic recursion method the self-consistent magnetic po- Coulomb integrals denoted by J and U respectively larisation of Pd slabs with different thicknesses for are taken to be independent of the size of the slabs (001) crystallographic surface orientation. We first and of the position i. The local magnetic moment j~t, started, as in our previous calculation concerning Va- is given by nadium [81 where we have found that the mono- 0375-9601/90/S 03.50 © 1990 — Elsevier Science Publishers B.V. (North-Holland) 103