* Institut für Physikalische Chemie, Universität München, Butenandtstr. 5-13, D-81377 München
^** Institute of Metal Physics, 36 Vernadskii str., 252142 Kiev, Ukraine

The calculation of the optical properties of ordered solids can nowadays be done in a more or less routine way. Even the magneto-optical effects caused by the interplay of magnetism and spin-orbit coupling can be investigated in a quantitative way by using modern methods of band structure calculation. However the interpretation of the corresponding magneto-optical spectra is by no means straightforward. In addition there are still several important classes of materials that are not accessible to ab initio type investigations.

To allow for a detailed analysis of the magneto-optical properties of periodic magnetic multi layer systems the concept of the layer resolved optical conductivity s^IJ(w) applied by means of a conventional band structure method is introduced in the first part of the talk. It will be shown that the layer projected optical conductivity s^I(w) of an atomic layer is influenced by only very few neighboring layers. This property can be exploited within the Baukasten principle that aims to predict the magneto-optical properties of a complex layer system from the properties calculated for a closely related but simpler one.

In the second part of the talk a more general scheme will be introduced that allows to define the frequency-dependent optical conductivity tensor for arbitrary layered systems in a layer-resolved way. This opens in particular the way to deal with the magneto-optical properties of magnetic surface layer systems and to calculate the corresponding magneto-optical Kerr spectra. The formalism, based on a fully relativistic description of response theory in arbitrary order, will be described in some detail. For an implementation the very flexible spin polarized relativistic Korringa-Kohn-Rostoker (SPR-KKR) method of band structure calculation has been used. This allows in particular to deal with disordered systems. First results for various systems will be presented.