Oscillatory behavior of the magnetic anisotropy energy in Cu(100)/Co-n multilayer systems

The oscillatory behavior of the magnetic-anisotropy energy in different types of Co-n multilayers on a Cu(100) substrate, including free surfaces, capped surfaces, and Co/Cu spacer systems, is shown in terms of ab initio-like calculations using the self-consistent fully relativistic spin-polarized screened Korringa-Kohn-Rostoker method. Deduced from direct representations and discrete (linear) Fourier transformations with respect to the number of Co layers, a period of two monolayers seems to be characteristic for these oscillations, whereas for a given number of Co layers and viewed with respect to the number of Cu-spacer layers they rapidly approach the value of the magnetic anisotropy energy for the corresponding Co. multilayer on Cu(100) with a semi-infinite Cu cap, the so-called biased value. By excluding the so-called preasymptotic regime a short and a long period of 2.5 and 5.5 monolayers, respectively, can be traced for the oscillations with respect to the number of Cu-spacer layers. All types of oscillations, namely, either with respect to the number of Co layers or with respect to the number of Cu-spacer layers, are analyzed in terms of layer-resolved band-energy contributions to the magnetic-anisotropy energy. Such a layerwise distribution of the magnetic-anisotropy energy allows one not only to characterize different regimes of thicknesses, but also to discuss the effect of the actual interface on the absolute values of the magnetic-anisotropy energy, shown in particular by considering a system with Co/Au interfaces.