  We present a phenomenological scheme to study the size-dependent electric
voltage-controlled magnetic anisotropy in ferromagnetic (FM)/ferroelectric (FE)
heterostructures. The FM layers are either metallic Fe(001), Ni(001), Co(0001),
or half-metallic (La, Sr)MnO3 films. Two magnetoelectric mechanisms, i.e.,
interface-charge and strain-mediated couplings, are considered. We show that
the interface-charge mediated coupling is the main mechanism for the
magnetoelectic coupling when the FM film thickness is below a certain
transition thickness dtr while the strain-mediated coupling dominates above
dtr.
