QUANTUM-WELL THEORY OF THE EXCHANGE COUPLING IN MAGNETIC MULTILAYERS WITH APPLICATION TO CO CU/CO(001)/

Two parallel calculations of the-exchange coupling in a Co/Cu/Co(001) trilayer, both using the same realistic s, p, and d tight-binding band s with parameters determined from the ab initio band structures of bul k Cu and Co, are reported. The coupling is first calculated within the framework of the quantum-well (QW) formalism in which the periodic be havior of the spectral density is exploited to derive an analytic form ula for the coupling valid for large spacer thicknesses. On the other hand, an alternative expression for the coupling, referred to as cleav age formula, is derived that allows accurate and efficient numerical e valuation of the coupling. An analytic approximation to this expressio n, valid in the asymptotic region of large spacer thickness, is also o btained. These two approaches are discussed in relation to other exist ing theoretical formulations of the coupling. The numerical results fo r the coupling obtained from the cleavage formula are first compared w ith the analytical QW calculation. The agreement between the two calcu lations is impressive and entirely justifies the analytical QW approac h. The numerical calculation fully confirms the result of the QW forma lism that, for trilayers with thick Co layers, the short-period oscill ation due to the minority electrons from the vicinity of the Cu Fermi- surface (FS) necks is dominant, the contribution of the long-period os cillation being negligible. This is shown, in the analytical QW formal ism, to be due to the existence of bound states for the minority-spin electrons at the Cu FS necks in the ferromagnetic configuration. The d ominant short-period oscillation has been confirmed by spin-polarized scanning electron microscopy and observed directly in the most recent photoemission experiments. The full confinement of the minority electr ons at the neck of the Cu FS also leads to a strong temperature depend ence of the short-period oscillation and an initial decay of the coupl ing with spacer thickness N that is much slower than predicted by the usual 1/N-2 law. For the electrons at the belly of the Cu FS, the conf inement is weak in both spin channels and the long-period oscillation hardly changes between zero and room temperatures. In addition, the be lly contribution to the coupling decreases at T=0 K following the usua l 1/N-2 dependence. The amplitude of the calculated coupling approxima te to 1.2 mJ/m(2) at the first antiferromagnetic peak of Cu is only a factor of 3 larger than the observed coupling strength. Finally, the c oupling for 2 ML of Co embedded in Cu has also been evaluated from the cleavage formula. A large initial coupling strength (3.4 mJ/m(2)) and comparable contributions from the shea-and long-oscillation periods a re obtained. This is in complete agreement with theoretical results re ported by other groups. [S0163-1829(97)04138-6].