In light of directives around the world to eliminate toxic materials in various technologies, finding lead-free materials with high piezoelectric responses constitutes an important current scientific goal. As such, the recent discovery of a large electromechanical conversion near room temperature in (1−x)Ba(Zr0.2Ti0.8)O3−x(Ba0.7Ca0.3)TiO3 compounds has directed attention to understanding its origin. Here, we report the development of a large-scale atomistic scheme providing a microscopic insight into this technologically promising material. We find that its high piezoelectricity originates from the existence of large fluctuations of polarization in the orthorhombic state arising from the combination of a flat free-energy landscape, a fragmented local structure, and the narrow temperature window around room temperature at which this orthorhombic phase is the equilibrium state. In addition to deepening the current knowledge on piezoelectricity, these findings have the potential to guide the design of other lead-free materials with large electromechanical responses.

We propose the existence, via analytical derivations, novel phenomenologies, and first-principlesbased simulations, of a new class of materials that are not only spontaneously optically active, but also for which the sense of rotation can be switched by an electric field applied to themvia an induced transition between the dextrorotatory and laevorotatory forms. Such systems possess electric vortices that are coupled to a spontaneous electrical polarization. Furthermore, our atomistic simulations provide a deep microscopic insight into, and understanding of, this class of naturally optically active materials.

Heat capacity measurements on pure but twinned single crystals of reveal a sharp peak at , which according to thermal expansion, neutron diffraction, and magnetic susceptibility measurements originates from an antiferromagnetic ordering of the Pr-ion moments. A modest coupling to the Cu(2) spin system is observed. Below a first-order transition in the magnetic structure of the Pr spin system (at 13.4 K in warming; in cooling) is found. Field-dependent heat capacity data show anisotropic temperature dependences of the -peaks and recover a Schottky-like anomaly due to the crystal-field-split ground state of the .

We numerically investigate the phase diagram of the giant-piezoelectric (1 − x)Ba(Zr 0.2 Ti 0.8)O 3x(Ba 0.7 Ca 0.3)TiO 3 system, treating the ions either as classical objects (via classical Monte-Carlo or CMC simulations) or quantum mechanically (via Path-integral Quantum Monte-Carlo or PI-QMC simulations). It is found that PI-QMC not only provides a better agreement with available experimental data for the temperature-composition phase diagram but also leads to the existence of an orthorhombic ground state in a narrow range of composition, unlike CMC that "only" yields ground states of rhombohedral or tetragonal symmetry. X-ray powder diffraction experiments are further conducted at 20 K. They confirm the occurrence of a quantum-fluctuation-induced orthorhombic state for some compositions and therefore validate the PI-QMC prediction. The role of quantum effects on the local structure, such as the annihilation of a homogeneous rhombohedral system in favor of an inhomogeneous mixing of orthorhombic and rhombohedral clusters, is also documented and discussed.

This paper completes the construction of arbitrary order conformally invariant differential operators in higher spin spaces. Jan Slovák has classified all conformally invariant differential operators on locally conformally flat manifolds. We complete his results in higher spin theory in Euclidean space by giving explicit expressions for arbitrary order conformally invariant differential operators, where by conformally invariant we mean equivariant with respect to the conformal group of S m acting in Euclidean space R m . We name these the fermionic operators when the order is odd and the bosonic operators when the order is even. Our approach explicitly uses convolution type operators to construct conformally invariant differential operators. These convolution type operators are examples of Knapp-Stein operators and they can be considered as the inverses of the corresponding differential operators. Intertwining operators of these convolution type operators are provided and intertwining operators of differential operators follow immediately. This reveals that our convolution type operators and differential operators are all conformally invariant. This also gives us a class of conformally invariant convolution type operators in higher spin spaces. Their inverses, when they exist, are conformally invariant pseudo-differential operators. Further we use Stein Weiss gradient operators and representation theory for the Spin group to naturally motivate the construction of Rarita-Schwinger operators.