Phase transitions induced by confinement of ferroic nanoparticles

A general approach for considering primary ferroic (ferroelectric, ferromagnetic, ferroelastic) nanoparticle phase transitions was proposed in phenomenological theory framework. The surface stress, order parameter gradient, and striction, as well as depolarization, demagnetization, and de-elastification effects, were included into the free energy. The strong intrinsic surface stress under the curved nanoparticle surface was shown to play the important role in the shift of transition temperature (if any) up to the appearance of a new ordered phase absent in the bulk ferroic. Euler-Lagrange equations obtained after the Landau-Ginzburg-Devonshire free energy minimization were solved by direct variational method. This leads to the conventional form of the free energy with renormalized coefficients depending on nanoparticle sizes, surface stress, and electrostriction tensor values, and so opens the way for polar property calculations by algebraic transformations. Surface piezoeffect causes built-in electric field that induces an electretlike polar state and smears the phase transition point. The approximate analytical expression for the size-induced ferroelectric transition temperature dependence on cylindrical or spherical nanoparticle sizes, polarization gradient coefficient, correlation radius, intrinsic surface stress, and electrostriction coefficient was derived. Under the favorable conditions (radius of 5-50 nm and compressive surface stress), spatial confinement induces a ferroelectric phase in incipient ferroelectric nanowires and nanospheres. The prediction of size-induced ferroelectricity in KTaO3 nanorods with radius less than 5-20 nm at room temperature could be useful for the next generation of devices based on three-dimensional nanostructures.