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The general approach for the consideration of the magnetoelectric effects inferroic nanorods is proposed in the framework of the phenomenological theory.The intrinsic surface stress, magneto- and electrostriction as well aspiezoelectric and piezomagnetic effects are included into the free energy. Theintrinsic surface stress under the curved nanoparticle surface is shown to playan important role in the shift of ferroelectric and ferromagnetic transitiontemperatures and built-in magnetic and electric fields appearance, which areinversely proportional to the nanorod radius. We consider the case of quadraticand linear magnetoelectric coupling coefficients. The linear couplingcoefficient is radius independent, whereas the quadratic ones include termsinversely proportional to the nanorod radius and thus strongly increase withdecrease of the radius. The predicted giant relative dielectric tunability inthe vicinity of ferromagnetic and ferroelectric phase transition points inducedby quadratic magnetoelectric coupling increases by 2-50 times. The quadraticmagnetoelectric coupling dramatically changes the phase diagrams of ferroicnanorods when the radius decreases. In particular the second order phasetransition may become a first one, the triple point state characterized bycontinuous set of order parameters appears at zero external electric andmagnetic fields and the tricritical points appear under external fields.

Giant magnetoelectric effect induced by intrinsic surface stress in ferroic nanorods