Giant magnetoelectric effect induced by intrinsic surface stress in ferroic nanorods

The general approach for the consideration of the magnetoelectric effects in ferroic nanorods is proposed in the framework of the phenomenological theory. The intrinsic surface stress, magneto- and electrostriction, as well as piezoelectric and piezomagnetic effects are included in the free energy. The intrinsic surface stress under the curved nanoparticle surface is shown to play an important role in the shift of ferroelectric and ferromagnetic transition temperatures and appearance of built-in magnetic and electric fields, which are inversely proportional to the nanorod radius. We consider the case of quadratic and linear magnetoelectric coupling coefficients. The linear coupling coefficient is radius independent, whereas the quadratic ones include terms inversely proportional to the nanorod radius and thus strongly increase with radius decrease. We predicted that quadratic magnetoelectric coupling induces dielectric tunability increase by 2-50 times in the vicinity of ferromagnetic and ferroelectric phase transition points. The quadratic magnetoelectric coupling dramatically changes the phase diagrams of ferroic nanorods under their radius decrease. In particular, the second order phase transition may become the first one. Special attention is paid to the case when polarization, magnetization, and magnetoelectric couplings are induced by intrinsic surface stress in nanorods.