Low-dimensional hybrid structures of heterogeneous constituents usually exhibit abnormal properties, a fact that makes such hybrids attractive for various cryogenic and room-temperature applications. Here, we studied Co/(1 - x)Pb(Mg 1/3 Nb 2/3 )O 3 -xPbTiO 3 /Co (Co/PMN-xPT/Co) with x=0.29 and 0.30, specifically focusing on the evolution of the remanent ferromagnetic state, m rem of the Co outer layers in the whole temperature range from 300K down to 10K, upon application of an external electric field, E ex . We observed that m rem was vulnerable to degradation through the occurrence of electric field-induced magnetic instabilities (EMIs) that appeared only when E ex ≠0kV/cm and were facilitated as E ex increases. However, EMIs completely ceased below a characteristic temperature T ces =170K even for the maximum |E ex |=5kV/cm applied in this work. A direct comparison of the magnetization data of the Co/PMN-xPT/Co hybrids reported here with the electromechanical properties of the parent PMN-xPT crystals plausibly indicates that EMIs are motivated by the coupling of the ferromagnetic domains of the Co outer layers with the ferroelectric domains of the PMN-xPT crystal. These results highlight the drawback of EMIs in relevant hybrids and delimit the temperature regime for the reliable operation of the Co/PMN-xPT/Co ones studied here.