The contour integration technique applied to calculate the opticalconductivity tensor at finite temperatures in the case of inhomogeneous surfacelayered systems within the framework of the spin-polarized relativisticscreened Korringa-Kohn-Rostoker band structure method is extended to arbitrarypolarizations of the electric field. It is shown that besides the inter-bandcontribution, the contour integration technique also accounts for theintra-band contribution too. Introducing a layer-resolved complex Kerr angle,the importance of the first, non-magnetic buffer layer below the ferromagneticsurface on the magneto-optical Kerr effect in the $\mathrm{Co} \mid\mathrm{Pt}_m$ multilayer system is shown. Increasing the thickness of thebuffer Pt, the layer-resolved complex Kerr angles follow a linear dependencewith respect to m only after nine Pt mono-layers.
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