Interlayer exchange coupling in magnetic multilayers

The discovery of the exchange coupling between ferromagnetic layers separated by nonmagnetic spacer layers has stimulated a great deal of interest recently. We present a theoretical study of the interlayer coupling in magnetic multilayers using two theoretical approaches. One such approach is to invoke the Ruderman-Kittel-Kasuya-Yosida (RKKY) theory, which is more relevant to the multilayer system in which localized magnetic moments interact weakly with conduction electrons. The other is based on spin-dependent band structures for ferromagnetic materials, which is suitable for transition metals.; The RKKY interaction in magnetic superlattices is calculated within a one-band tight-binding model. An accurate and efficient integration scheme in momentum space is introduced to calculate the RKKY exchange interaction in superlattices. This is accomplished by writing the superlattice states in terms of linear combinations of complex-band solutions in analytic form, and dividing the integration domain into many subregions according to the shape of the superlattice Fermi surface in order to take into account the singularities in one-dimensional density of states. The results are compared to those obtained from using the bulk wave functions of the spacer layer and apparent deviations due to the superlattice effect are noted.; The effects of quantum-well states on the RKKY coupling in magnetic multilayers are also studied based on an effective-mass model with a single quantum well or a superlattice potential. It is found that the oscillation period is determined by the nesting vector of the Fermi surface of the spacer regardless of the depth of the quantum well, while the coupling strength and the phase of oscillation are affected by the presence of the quantum well. The magnetic-layer thickness dependence of the RKKY coupling for the superlattice is investigated. It is found that the RKKY coupling integrated over the magnetic layer is a strong oscillatory function of the magnetic-layer thickness with a period related to the nesting vector of the Fermi surface for the magnetic material. The coupling across a quantum barrier is also studied.; The coupling strengths associated with different oscillation periods in Co/Cu/Co sandwiches for different orientations are calculated based on the spin-asymmetry of the reflection amplitude at extremal points. A realistic tight-binding model which includes {dollar}s, psp3,{dollar} and {dollar}dsp5{dollar} orbitals is adopted to calculate the reflection amplitudes. At the interface, all evanescent states are included to meet proper boundary conditions. The spin-asymmetry of the reflection amplitude which is the crucial factor for determining the coupling strength is found to depend on the details of the band structures. Unique features are found when there are more than one reflected waves, which do not exist in the single-band model. For certain periods inferred from the spacer Fermi surface, the coupling strengths are found too small to be detected.