Converse magnetoelectric effect via strain-driven magnetization reorientations in ultrathin ferromagnetic films on ferroelectric substrates

Abstract

A phenomenological theory is developed for the strain-driven magnetization reorientations occurring in ultrathin ferromagnetic films coupled to ferroelectric substrates experiencing electric-field-induced piezoelectric deformations. The theory takes into account the surface/interface magnetic anisotropy playing an important role in the energetics of such films and first describes the thickness-driven spin reorientation transitions emerging in the presence of substrate-induced lattice strains. Then the threshold and critical intensities of the electric field created in a ferroelectric substrate are calculated, at which different magnetic states acquire the same energy or become unstable in a strained ferromagnetic overlayer. To demonstrate stability ranges of various possible magnetization orientations, we introduce magnetoelectric orientational diagrams, where the electric-field intensity and film thickness are employed as two variables. Such diagrams are constructed for ultrathin Ni, Fe, and $\mathrm{F}{\mathrm{e}}_{60}\mathrm{C}{\mathrm{o}}_{40}$ films coupled to single crystals of classical and relaxor ferroelectrics. The inspection of these diagrams shows that the use of multiferroic hybrids comprising ultrathin ferromagnetic films significantly enlarges the range of ferroic materials suitable for experimental observations of the strain-mediated converse magnetoelectric effect.