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The remarkable polarization properties of synchrotron light have lead to the advent of modern synchrotron-related spectroscopic studies with angular and/or magnetic selectivity. Here an overview is given of the prominent aspects of the polarization of the light delivered by a bending magnet, and some dichroic properties in X-ray absorption spectroscopy (XAS). Two studies developed at the Brazilian Synchrotron Light Laboratory are then reported, exemplifying the profit gained using linear and circular polarization of X-rays for the study of magnetic thin films and multilayers. Angle-resolved XAS was used in strained manganite thin films to certify a model of local distortion limited within the MnO_{6} polyhedron. A pioneering experience of X-ray magnetic scattering at grazing incidence associated with dispersive XAS in a Co/Gd multilayer draws new perspectives for magnetic studies in thin films and multilayers under atmospheric conditions in the hard X-ray range.

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