Wiener algebra for the quaternions

We define and study the counterpart of the Wiener algebra in the quaternionic setting, both for the discrete and continuous case. We prove a Wiener-L\'evy type theorem and a factorization theorem. We give applications to Toeplitz and Wiener-Hopf operators

Contribution of space charges to the polarization of ferroelectric superlattices and its effect on dielectric properties

A theoretical model is developed for ferroelectric bilayers and multilayer heterostructures that employs a nonlinear Landau-Devonshire formalism coupled with a detailed analysis of the depolarizing fields arising from the polarization mismatch across interlayer interfaces and the electrical fields of localized space charges at such interfaces. We first present how space charges alter the free-energy curves of ferroelectrics and then proceed with a numerical analysis for heteroepitaxial (001) PbTiO3-SrTiO3 (PTO-STO) bilayers and (001) superlattice structures on (001) STO substrates. The switchable (ferroelectric) and nonswitchable (built-in) polarizations and the dielectric properties of PTO-STO bilayers and superlattices are calculated as a function of the planar space-charge density and the volume fraction of the PTO layer. Similar to the temperature dependence of a monolithic ferroelectric, there exists a critical volume fraction PTO below which the bilayer or the superlattice is in the paraelectric state. This critical volume fraction is strongly dependent on the density of trapped charges at the interlayer interfaces. For charge-free (001) PTO-STO heteroepitaxial bilayer and superlattices, the critical fraction is 0.40 for both constructs but increases to 0.6 and 0.72, for the bilayer and the superlattice, respectively, for a planar space-charge density of 0.05 C/m(2). Furthermore, our results show that close to the vicinity of ferroelectric-paraelectric phase transition, there is a recovery in ferroelectric polarization. The dielectric-response calculations verify that there is sharp ferroelectric phase transformation for charge-free bilayers and superlattices whereas it is progressively smeared out with an increase in the charge density. Furthermore, our analysis shows that the dielectric constant of these multilayers at a given volume fraction of PTO decreases significantly in the presence of space charges

Phase Coexistence Near a Morphotropic Phase Boundary in Sm-doped BiFeO3 Films

We have investigated heteroepitaxial films of Sm-doped BiFeO3 with a Sm-concentration near a morphotropic phase boundary. Our high-resolution synchrotron X-ray diffraction, carried out in a temperature range of 25C to 700C, reveals substantial phase coexistence as one changes temperature to crossover from a low-temperature PbZrO3-like phase to a high-temperature orthorhombic phase. We also examine changes due to strain for films greater or less than the critical thickness for misfit dislocation formation. Particularly, we note that thicker films exhibit a substantial volume collapse associated with the structural transition that is suppressed in strained thin films

Layer thickness and period as design parameters to tailor pyroelectric properties in ferroelectric superlattices

We theoretically examine the pyroelectric properties of ferroelectric-paraelectric superlattices as a function of layer thickness and configuration using non-linear thermodynamics coupled with electrostatic and electromechanical interactions between layers. We specifically study PbZr0.3Ti0.7O3/SrTiO3 superlattices. The pyroelectric properties of such constructs consisting of relatively thin repeating units are shown to exceed the pyroelectric response of monolithic PbZr0.3Ti0.7O3 films. This is related to periodic internal electric fields generated due to the polarization mismatch between layers that allows tailoring of the shift in the transition temperature. Our results indicate that higher and electric field sensitive pyroresponse can be achieved from layer-by-layer engineered ferroelectric heterostructures

A comparative ab initio study of the ferroelectric behaviour in KNO3 and CaCO3

Potassium nitrate exhibits a reentrant phase transformation, where a metastable ferroelectric phase (gamma-KNO3) is formed upon cooling from high temperature. The layered structure of this ferroelectric phase is composed of alternating layers of potassium ions and nitrate groups; wherein, a central nitrogen atom is coordinated by three equilateral triangular oxygen atoms. The group layer is located less than midway between the cation layers, giving rise to a polar structure. From a structural perspective, the calcite phase of calcium carbonate looks quite similar to this ferroelectric phase; however; it does not exhibit a ferroelectric transition. In this work we have performed an ab initio computational analysis to study the: structural stability, electronic characteristics, and bonding of various phases and ferroelectric properties of CaCO3 and KNO3. We find that both material systems have mixed covalent and ionic bonding. The covalent interactions are within the group atoms of carbonate and nitrate atoms while the ionic interactions occur between the negatively charged ( carbonate or nitrate) group and the calcium or potassium cations. For the low temperature stable phase of CaCO3 (calcite), however, there is a slight covalency between the cations and the oxygen atoms of the group. This latter interaction results in the crystallization of CaCO3 in the calcite form and prevents a ferroelectric transition. We suggest that, in analogy to KNO3, a metastable form of CaCO3 may also exist, similar to the phase of gamma-KNO3 that should have a spontaneous polarization equal to 30.6 mu C cm(-2), twice that of gamma-KNO3. Moreover, our analysis indicates that this material should have a coercive field smaller than that of gamma-KNO3

Strong dependence of dielectric properties on electrical boundary conditions and interfaces in ferroelectric superlattices

A computational study based on Landau-Ginzburg-Devonshire theory is carried out to understand the role of interfaces on the dielectric response of ferroelectric superlattices. Using heteroepitaxial (001) PbZr0.3Ti0.7O3/(001)SrTiO3 heterostructures on (001)SrTiO3 as an example, we show that electrostatic boundary conditions have a pronounced effect on the dielectric response far below the ferroelectric phase transition temperature. For a fixed total multilayer thickness, the average dielectric response can be improved significantly for superlattices with a small layer periodicity. This is due to the large total internal electric fields at the interlayer interfaces which originate from the polarization mismatch between layers

Structural phase transitions in epitaxial perovskite films

Three different film systems have been systematically investigated to understand the effects of strain and substrate constraint on the phase transitions of perovskite films. In SrTiO$_3$ films, the phase transition temperature T$_C$ was determined by monitoring the superlattice peaks associated with rotations of TiO$_6$ octahedra. It is found that T$_C$ depends on both SrTiO$_3$ film thickness and SrRuO$_3$ buffer layer thickness. However, lattice parameter measurements showed no sign of the phase transitions, indicating that the tetragonality of the SrTiO$_3$ unit cells was no longer a good order parameter. This signals a change in the nature of this phase transition, the internal degree of freedom is decoupled from the external degree of freedom. The phase transitions occur even without lattice relaxation through domain formation. In NdNiO$_3$ thin films, it is found that the in-plane lattice parameters were clamped by the substrate, while out-of-plane lattice constant varied to accommodate the volume change across the phase transition. This shows that substrate constraint is an important parameter for epitaxial film systems, and is responsible for the suppression of external structural change in SrTiO$_3$ and NdNiO$_3$ films. However, in SrRuO$_3$ films we observed domain formation at elevated temperature through x-ray reciprocal space mapping. This indicated that internal strain energy within films also played an important role, and may dominate in some film systems. The final strain states within epitaxial films were the result of competition between multiple mechanisms and may not be described by a single parameter.Comment: REVTeX4, 14 figure