Soft x-ray linear and circular dichroism (XLD, XMCD) experiments at the Ce M$_{4,5}$ edges are being used to determine the energy scales characterizing the Ce $4f$ degrees of freedom in the ultrathin ordered surface intermetallic CeAg$_x$/Ag(111). We find that all relevant interactions, i. e. Kondo scattering, crystal field splitting and magnetic exchange coupling occur on small scales. Our study demonstrates the usefulness of combining x-ray absorption experiments probing linear and circular dichroism owing to their strong sensitivity for anisotropies in both charge distribution and paramagnetic response, respectively.
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