We report on the magnetic properties of Co$x$Pt${1-x}$ clusters embedded in various matrices. Using a careful analysis of magnetization curves and ZFC susceptibility measurements, we determine the clusters magnetic anisotropy energy (MAE) and separate the surface and volume contributions. By comparing different chemical compositions, we show that a small amount of Pt (15~\%) induces an important increase in the volume anisotropy with respect to pure Co clusters, even in chemically disordered fcc clusters. Comparing the measurements of clusters embedded in Nb and MgO matrices, we show that the oxide matrix induces an important increase of the surface MAE attributed to the formation of an antiferromagnetic CoO shell around the clusters.
