The piezoelectric properties of tetragonal BaTiO(3) crystals with a very high density of 90 degrees twin domain boundaries are analyzed in the framework of the Ginzburg-Landau-Devonshire theory. Computer simulations predict a considerable enhancement of piezoelectric coefficients for domain thicknesses below 50 nm. This enhancement is much larger than the effect of the domain wall broadening mechanism of Rao and Wang (2007 Appl. Phys. Lett. 90 041915), but it is still a too weak effect to explain the domain density enhancement observed in the experiments of Wada and Tsurumi (2004 Br. Ceram. Trans. 103 93). The phenomenon observed here should nevertheless manifest in materials with nanoscopic domains, such as relaxor ferroelectrics and artificial ferroelectric nanostructures.

The 212 species of the structural phase transitions with a macroscopic symmetry breaking are inspected with respect to the occurrence of the ferroaxial order parameter, the electric toroidal moment. In total, 124 ferroaxial species are found, some of them being also fully ferroelectric (62) or fully ferroelastic ones (61). This ensures a possibility of electrical or mechanical switching of ferroaxial domains. Moreover, there are 12 ferroaxial species that are neither ferroelectric nor ferroelastic. For each species, we have also explicitly worked out a canonical form for a set of representative equilibrium property tensors of polar and axial nature in both high-symmetry and low-symmetry phases. This information was gathered into the set of 212 mutually different symbolic matrices, expressing graphically the presence of nonzero independent tensorial components and the symmetry-imposed links between them, for both phases simultaneously. Symmetry analysis reveals the ferroaxiality in several currently debated materials, such as VO_{2}, LuFe_{2}O_{4}, and URu_{2}Si_{2}.

Fano resonance is a phenomenon in which a discrete state interferes with a continuum of states and has been observed in many areas of science. Here, we report on the prediction of a Fano resonance in ferroelectric relaxors, whose properties are poorly understood: an ab initio molecular dynamic scheme reveals such resonance between the bare optical phonon mode of the Zr sublattice (the discrete state) and the bare optical phonon mode of the Ti sublattice (the continuum of states) in disordered lead-free Ba(Zr,Ti)O 3 . The microscopic origins of the discrete state and continuum of states are discussed in the context of relaxor properties. Furthermore, our simulations suggest that the T* characteristic temperature of relaxor is related to a hardening of the vibrational frequencies associated with fluctuation of the Ti sublattice. Finally, a terahertz relaxation mode reflecting reorientations of Ti dipoles and showing a thermally activated behaviour is predicted, in agreement with previous experiments.