The direct conversion of electrical energy to mechanical work by a material is relevant to a number of applications. This is illustrated by ferroelectric 'relaxors' such as Pb(Mg(1/3)Nb(2/3))O(3)-PbTiO(3) (PMN-PT; refs 5, 6): these materials exhibit a giant electromechanical (piezoelectric) response that is finding use in ultrasonic and medical applications, as well as in telecommunications. The origins of this effect are, however, still unclear. Here we show that the giant electromechanical response in PMN-PT (and potentially other ferroelectric relaxors) is the manifestation of critical points that define a line in the phase diagram of this system. Specifically, in the electric-field-temperature-composition phase diagram of PMN-PT (the composition being varied by changing the PT concentration), a first-order paraelectric-ferroelectric phase transition terminates in a line of critical points where the piezoelectric coefficient is maximum. Above this line, supercritical evolution is observed. On approaching the critical point, both the energy cost and the electric field necessary to induce ferroelectric polarization rotations decrease significantly, thus explaining the giant electromechanical response of these relaxors.

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Within the Landau-Ginsburg-Devonshire phenomenological approach we study the ferroic nanosystems properties changes caused by the flexo-effect (flexoelectric, flexomagnetic, flexoelastic) existing spontaneously due to the inhomogeneity of order parameters. Exact solution for the spatially inhomogeneous mechanical displacement vector allowing for flexocoupling contribution was found for nanowires and thin pills. Strong influence of flexo-effect in nanorods and thin pills leads to the displacements of the atoms resulting into the unit cell symmetry changes, which lead to the phase transition temperature shift, as well as the flat geometry in radial direction transforms into the saucer-like one. The new phenomena can be considered as true manifestation of the spontaneous flexo-effect existence. It was shown that flexo-effect leads to (a) the appearance of new linear and nonlinear contribution and renormalization of coefficients before the order parameter gradient, (b) essentially influences the transition temperature, piezoelectric response and the spatial distribution of the order parameter, (c) results in renormalization of extrapolation length in the boundary conditions. These effects cannot be neglected for ferroelectrics, the renormalization being important for nanoparticles of arbitrary shape, while the linear and nonlinear terms is essential for the thin pills only. They are absent for nanowires with the order parameter directed along the wire axis. We demonstrated that the flexoelectric coupling decreases the polarization gradient self-consistently and so makes polarization more homogeneous. The divergences of dielectric permittivity and correlation radius at some critical value of flexoelectric coefficient originate from the critical radius dependence on the coefficient. This peculiar behavior shows a new way to govern material properties. The effect of the correlation radius renormalization by the flexoelectric effect leads to the renormalization of the intrinsic width of ferroelectric domain walls.

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