Interlayer exchange coupling in (111) Co/Cu/Co trilayers: Full-band versus reflection-amplitude calculations

We calculate the interlayer exchange coupling in (111) Co/Cu/Co trilayers with tight-binding band structures in two independent ways: a full-band calculation and an approximate calculation in terms of reflection amplitudes. An analytic Green's function method is used for the full-band calculation. The calculation involves solving the Green's function analytically for each fixed in-plane wave vector (k(parallel to)) and an accurate integration over k(parallel to) with nonuniform sampling. In the approximate method, we calculate the spin-dependent reflection amplitudes, which are complex numbers due to the effects of evanescent waves, and their phase factors depend on both the energy and wave vector. In the approximate method, the integration over k(parallel to) near the extremal points is carried out analytically with the stationary phase approximation and contributions for k(parallel to) far away from the extremal points are ignored. The method describes well the overall behavior of the interlayer exchange coupling for thick spacers. However, for thin spacers we found that the stationary phase approximation gives poor results and the full-band calculation is needed for accurate estimate of the coupling strength.