We have optimized the perpendicular magnetic anisotropy of piezoelectric/ferromagnetic and dielectric/ferromagnetic heterostructures based on Co/Pt multilayers. These hybrid systems are promising for electric field control of magnetism for applications to ultra-low power spintronics devices. Epitaxial (PbMg1/3Nb2/3O3)(0.7)-(PbTiO3)(0.3) has been used for the piezoelectric layer and several dielectric layers (MgO, Al2O3, HfO2, Ta2O5 and TiO2) have been tested. We show that for both heterostructures perpendicularmagnetic anisotropy of Co/Pt multilayers can be obtained with small coercivity. (C) 2013 Elsevier B.V. All rights reserved.