Ferromagnetic/metallic manganese perovskites, such as La2/3Sr1/3MnO3 (LSMO)are promising materials for the design and implementation of novel spintronic devices working at room temperature. However, their implementation in practical applications has been severely hampered due to the breakdown of their magnetotransport properties at temperatures well below their magnetic transition temperature. This breakdown has been usually associated to surface and interface related problems but its physical origin has not been clearly established yet. In this work we investigate the interface between La2/3Sr1/3MnO3 (LSMO) thin films and different capping layers by means of x-ray linear dichroism and transport measurements. Our data reveal that, irrespective to the capping material, LSMO/capping layer bilayers exhibit an antiferromegnetic/insulating phase at the interface, likely to originate from a preferential occupancy of Mn 3d 3z2-r2 eg orbitals. This phase, which extends ca. 2 unit cells, is also observed in an uncapped LSMO reference sample thus, pointing to an intrinsic interfacial phase separation phenomenon, likely to be promoted by the structural disruption and symmetry breaking at the LSMO free surface/interface. These experimental observations strongly suggest that the structural disruption at the LSMO interfaces play a major role on the observed depressed magnetotransport properties in manganite-based magnetic tunneling junctions and it is at the origin of the so-called dead layer.