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We propose the concept of superconducting straintronic devices based on the proximity effect at superconductor-ferromagnet interfaces and the ability of ferromagnets with a strong magnetoelastic coupling to change magnetization orientations under strain. Since strains can be generated electrically with the aid of a piezoelectric transducer attached to a superconductor-ferromagnet nanostructure, the power consumption of the resulting hybrid straintronic device could be greatly reduced in comparison with a superconducting spin valve operated by external magnetic field. To demonstrate the feasibility of our proposal, we theoretically describe the strain-mediated magnetoelectric control of the critical temperature Tc in asymmetric ferromagnet-superconductor-ferromagnet trilayers integrated onto a ferroelectric substrate. To that end, Tc is first calculated as a function of the misorientation angle Δφ between the in-plane magnetizations of the two ferromagnetic layers. Numerical calculations performed for CoFe/Nb/NiCu trilayers show that, at optimal nanoscale thicknesses of superconducting and ferromagnetic films, the variation of Δφ may change Tc significantly (ΔTc ∼ 1 K). Then electric-field-induced magnetization rotations are determined for CoFe/Nb/NiCu trilayers coupled to the Pb(Zn1/3Nb2/3)O3-6%PbTiO3 single crystal. It is found that, owing to the opposite sign of the magnetoelastic coupling in CoFe and NiCu alloys, the misorientation angle Δφ can be changed by up to 90° without the introduction of an antiferromagnetic pinning layer. As a result, the electrical switching of the Nb interlayer between the superconducting state and a finite-resistance state appears to be possible in a narrow temperature range. Hence the described multiferroic hybrid can be employed as an electrically controlled resistive switch useful for memory and logic applications in cryogenic electronics.

Ferroelectric crystallites embedded into a dielectric matrix experience temperature-dependent elastic strains caused by differences in the thermal expansion of the crystallites and the matrix. Owing to the electrostriction, these lattice strains may affect polarization states of ferroelectric inclusions significantly, making them different from those of a stress-free bulk crystal. Here, using a nonlinear thermodynamic theory, we study the mechanical effect of elastic matrix on the phase states of embedded single-domain ferroelectric nanocrystals. Their equilibrium polarization states are determined by minimizing a special thermodynamic potential that describes the energetics of an ellipsoidal ferroelectric inclusion surrounded by a linear elastic medium. To demonstrate the stability ranges of such states for a given material combination, we construct a phase diagram, where the inclusion's shape anisotropy and temperature are used as two parameters. The 'shape-temperature' phase diagrams are calculated numerically for PbTiO 3 and BaTiO 3 nanocrystals embedded into representative dielectric matrices generating tensile (silica glass) or compressive (potassium silicate glass) thermal stresses inside ferroelectric inclusions. The developed phase maps demonstrate that the joint effect of thermal stresses and matrix-induced elastic clamping of ferroelectric inclusions gives rise to several important features in the polarization behavior of PbTiO 3 and BaTiO 3 nanocrystals. In particular, the Curie temperature displays a nonmonotonic variation with the ellipsoid's aspect ratio, being minimal for spherical inclusions. Furthermore, the diagrams show that the polarization orientation with respect to the ellipsoid's symmetry axis is controlled by the shape anisotropy and the sign of thermal stresses. Under certain conditions, the mechanical inclusion-matrix interaction qualitatively alters the evolution of ferroelectric states on cooling, inducing a structural transition in PbTiO 3 nanocrystals and suppressing in BaTiO 3 inclusions some transformations occurring in their bulk counterpart. The constructed phase maps open the possibility to calculate dielectric properties of strained PbTiO 3 and BaTiO 3 nanocrystals and ferroelectric nanocomposites comprising such crystallites.

A voltage-controlled resistive switching is predicted for ferromagnetic multilayers and spin valves mechanically coupled to a ferroelectric substrate. The switching between low- and high-resistance states results from the strain-driven magnetization reorientations by about 90°, which are shown to occur in ferromagnetic layers with a high magnetostriction and weak cubic magnetocrystalline anisotropy. Such reorientations, not requiring external magnetic fields, can be realized experimentally by applying moderate electric field to a thick substrate (bulk or membrane type) made of a relaxor ferroelectric having ultrahigh piezoelectric coefficients. The proposed multiferroic hybrids exhibiting giant magnetoresistance may be employed as electric-write nonvolatile magnetic memory cells with nondestructive readout.

A nonlinear thermodynamic theory is developed for the strain-mediated direct magnetoelectric (ME) effect displayed by ferroelectric-ferromagnetic nanostructures. This effect results from transmission of magnetic-field-induced deformations of a thick ferromagnetic substrate to a thin ferroelectric overlayer, where the polarization changes due to lattice strains. The strain-dependent polarization and permittivity of an epitaxial nanolayer (few tens of nm thick) are calculated using the thermodynamic theory of single-domain ferroelectric films. The substrate magnetostrictive deformations are described phenomenologically, taking into account their nonlinear variation with magnetic field. The calculations show that ME polarization and voltage coefficients strongly depend on the initial strain state of the film. For BaTiO(3) and PbTiO(3) films deposited on Co(0.8)Zn(0.2)Fe(2)O(4), the out-of-plane polarization and related ME coefficients are calculated numerically as a function of magnetic field parallel to the interface. For films stabilized in the monoclinic phase, this transverse ME response depends on the orientation of magnetic field relative to their in-plane crystallographic axes. The longitudinal ME coefficient is also evaluated and, for a substrate geometry minimizing the demagnetizing field, predicted to be comparable to the transverse one. For BaTiO(3) and PbTiO(3) films deposited on Terfenol-D, the calculations yield high ME polarization coefficients approximately 10(-7) s m(-1) and giant ME voltage coefficients approximately 50 V cm(-1) Oe(-1).

Ferroelectric nanodomains were created in BaTiO(3) thin films by applying a voltage to a sharp conducting tip of a scanning force microscope (SFM). The films were epitaxially grown on SrRuO(3)-covered (001)-oriented SrTiO(3) substrates by a high-pressure sputtering. They appeared to be single-crystalline with the (001) crystallographic orientation relative to the substrate. Using the piezoresponse mode of the SFM to detect the out-of-plane film polarization, the domain sizes were measured as a function of the applied writing voltage and the pulse time. It was found that the time dependence of the domain diameter in a 60 nm thick BaTiO(3) film deviates significantly from the logarithmic law observed earlier in Pb(Zr(0.2)Ti(0.8))O(3) (PZT) films. At a given writing time, the domain size increases nonlinearly with increasing applied voltage, in contrast to the linear behavior reported earlier for PZT films and LiNbO(3) single crystals. The dynamics of domain growth is analyzed theoretically taking into account the strong inhomogeneity of the external electric field in the film and the influence of the bottom electrode. It is shown that the observed writing time and voltage dependences of the domain size can be explained by the domain-wall creep in the presence of random-bond disorder.

Taking into account the electrostrictive coupling between inhomogeneous polarization fluctuations and lattice strains in ferroelectric films, we show that, in heterostructures involving strained epitaxial films and metal electrodes, the single-domain state may remain stable against the transformation into a polydomain state down to the nanometer scale. This result indicates that the ferroelectric states with opposite remanent polarizations can be stabilized even in nanoscale capacitors and tunnel junctions, which opens the possibility of their application for memory storage.