We show that misfit strain originated from the film-substrate lattice mismatch strongly increases the value of the quadratic magnetoelectric coupling. The giant magnetoelectric coupling, size effects and misfit strain cause strong changes of ferroic films phase diagrams at zero external magnetic and electric fields, in particular, the transformation of antiferromagnetic phase into ferromagnetic or ferrimagnetic ones for compressive or tensile misfit strains correspondingly as well as thickness induced paramagnetic or/and paraelectric phases appearance. Ferromagnetism appearance and magnetoelectric coupling increase in thin ferroelectric-antiferromagnetic films is in agreement with available experimental data and opens the way for tailoring of ferroic films magnetic and electric properties.
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