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We present a phenomenological scheme to study the size-dependent electricvoltage-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 thatthe interface-charge mediated coupling is the main mechanism for themagnetoelectic coupling when the FM film thickness is below a certaintransition thickness dtr while the strain-mediated coupling dominates abovedtr.

physical review. b, condensed matter and materials physics

Size dependent electric voltage-controlled magnetic anisotropy in  multiferroic heterostructures: Interface-charge and strain co-mediated  magnetoelectric coupling