Magnetoelectric (ME) materials that exhibit an induction of magnetization by an electric field or an induction of electric polarization by a magnetic field offer increased functionality and entirely new applications for electronic devices.[1] Examples of potential applications include multistate memories and logic, tunable filters, sensors, and new types of electromechanical devices. The ME response exhibited by all known singlephase materials is either too weak or occurs at temperatures too low for practical exploitation. [1,2] In contrast, laminated ceramic composites, fabricated from piezoelectric and magnetostrictive components, have been found to exhibit strain-mediated ME responses an order-of-magnitude larger than those observed in single-phase materials. [3,4] Several types of devices incorporating such composites have been demonstrated. [5][6][7] Unfortunately, existing bulk ME composites are not amenable to on-chip integration, which is a prerequisite for incorporation into microelectronic devices. The principal problem in implementing strain-mediated layered ME thin-film composites is related to the strong clamping effects of the substrate, which effectively inhibit the ME response. [8][9][10] The clamping can be significantly reduced by generating transversely modulated composite films with interphase boundaries perpendicular to the substrate. Recently, transverse nanostructures have been synthesized using epitaxial self-assembly of CoFe 2 O 4 (ferrimagnetic) and BaTiO 3 (ferroelectric) phases on singlecrystal (001) SrTiO 3 substrates. [8] These films, which consisted of CoFe 2 O 4 nanorods in a BaTiO 3 matrix, were shown to exhibit substantial ME coupling (in contrast to the layered heterostructures), which was attributed to 1) a reduced clamping effect by the substrate, and 2) efficient strain coupling resulting from the nanometer scale of the component phases and coherency of the interfaces. Subsequently, similar self-assembled nanostructures were obtained in composite CoFe 2 -O 4 -PbTiO 3 [11] and CoFe 2 O 4 -BiFeO 3 films; [12] in the latter system, a polarization reversal by the external magnetic field was demonstrated. All multiferroic nanostructures reported to date have been limited to CoFe 2 O 4 pillars embedded in a ferroelectric perovskite-type matrix.In the present report, we demonstrate that the morphologies of self-assembled multiferroic nanostructures can be varied over a wide range by modifying the epitaxial stress state in the film. In particular, morphologies ranging from rodlike (either magnetic or ferroelectric) to lamellar-like were obtained by varying the substrate orientation and phase fractions in epitaxial composite films containing ferrimagnetic CoFe 2 O 4 and ferroelectric PbTiO 3 . The approach relies on the epitaxial stress-controlled self-assembling of the component phases.

The effect of substrate orientation on the morphologies of epitaxial self-assembled nanostructures was demonstrated using multiferroic 0.67PbTiO3-0.33CoFe2O4 thin films. The two-phase composite films were grown by pulsed laser deposition on single crystal SrTiO3 substrates having (001) and (110) orientations. The nanostructures of both orientations consisted of vertical rod- or platelet-like columns of CoFe2O4 dispersed in a PbTiO3 matrix. For the (001) orientation the platelet habits were parallel to the {110} planes, whereas for the (110) orientation the platelets were parallel to the {111} planes. The differences were explained using a thermodynamic theory of heterophase structures.

The results of phase-field simulation of domain structures (DSs) in ferroelectric nanorods of different shapes and sizes are presented. It is shown that equilibrium DSs consist of an electrostatically compatible circuit of 180 degrees and 90 degrees domains. A DS in a thin rod contains 90 degrees cubic elastic domains. The trend to minimize the residual stress and the stray field results in the formation of crater-shaped sets of closed circuits of 90 degrees domains, which can be mechanically incompatible but able to maintain electrostatic compatibility during the evolution under an applied electric field.

Combined theoretical and experimental studies of self-assembled multiferroic nanostructures in epitaxial films reveal the dominant role of elastic interactions, caused by epitaxial stresses, in defining the morphology of the nanostructures. The phase field model, which considered the individual phases in the film as elastic domains, has predicted successfully the complex morphologies observed in epitaxial multiferroic CoFe 2 O 4-PbTiO 3 films grown on SrTiO 3 substrates with ͕001͖, ͕110͖, and ͕111͖ orientations. It is shown that nanostructures containing isolated magnetic nanorods in a ferroelectric matrix or vice versa can be obtained by varying the substrate orientation and phase fraction.

We consider a phase field model that includes a stress field during nonisothermal phase transformation of a single-component system. The model is applied to the solidification and melting of confined spherical volumes, where sharp interface solutions can be obtained and compared with the results of the phase field simulations. Numerical solutions to the phase field model for a spherically symmetric geometry have been obtained, with particular emphasis on the computation of surface energy, surface stress, and surface strain. The analysis of the equilibrium states for the phase field model allows us to obtain the value of the surface energy in the presence of stress, which can then be compared to the analogous calculation of the energy of a planar liquid-solid interface. It is also demonstrated that modeling the liquid as a solid with zero shear modulus is realistic by comparing the long-range stress fields in phase field calculations with those calculated using sharp interface models of either a coherent or a relaxed liquid-solid interface.