Phase transitions and ferroelectrics: revival and the future in the field

It appeared worthwhile to us to present a state-of-the-art look at the field of ferroelectrics. We are certainly not attempting to provide a complete review of all aspects of the field of ferroelectrics over the last years but we wish to transport a flavour of the current excitement in the field through the (subjective) choice of four specific examples of current interest: (i) Piezoelectrics and the morphotropic phase boundary, (ii) Multiferroics, (iii) The effect of high pressure on ferroelectrics and (iv) Strain-engineering in ferroelectric oxide thin films. For each topic we will try to work out both current interesting approaches and an outlook into future challenges. Throughout our discussion, the reader is referred to a list of significant review articles, books and papers in the field.Comment: Editorial overview, 31 pages, 4 Figures, 315 Reference

Constitutive modeling of the anisotropic behavior of Mullins softened filled rubbers

Original constitutive modeling is proposed for filled rubber materials in order to capture the anisotropic softened behavior induced by general non-proportional pre-loading histo-ries. The hyperelastic framework is grounded on a thorough analysis of cyclic experimental data. The strain energy density is based on a directional approach. The model leans on the strain amplification factor concept applied over material directions according to the Mul-lins softening evolution. In order to provide a model versatile that applies for a wide range of materials, the proposed framework does not require to postulate the mathematical forms of the elementary directional strain energy density and of the Mullins softening evo-lution rule. A computational procedure is defined to build both functions incrementally from experimental data obtained during cyclic uniaxial tensile tests. Successful compari-sons between the model and the experiments demonstrate the model abilities. Moreover, the model is shown to accurately predict the non-proportional uniaxial stress-stretch responses for uniaxially and biaxially pre-stretched samples. Finally, the model is effi-ciently tested on several materials and proves to provide a quantitative estimate of the anisotropy induced by the Mullins softening for a wide range of filled rubbers

Interpretation of scanning tunneling quasiparticle interference and impurity states in cuprates

We apply a recently developed method combining first principles based Wannier functions with solutions to the Bogoliubov-de Gennes equations to the problem of interpreting STM data in cuprate superconductors. We show that the observed images of Zn on the surface of Bi$_2$Sr$_2$CaCu$_2$O$_8$ can only be understood by accounting for the tails of the Cu Wannier functions, which include significant weight on apical O sites in neighboring unit cells. This calculation thus puts earlier crude "filter" theories on a microscopic foundation and solves a long standing puzzle. We then study quasiparticle interference phenomena induced by out-of-plane weak potential scatterers, and show how patterns long observed in cuprates can be understood in terms of the interference of Wannier functions above the surface. Our results show excellent agreement with experiment and enable a better understanding of novel phenomena in the cuprates via STM imaging.Comment: 5 pages, 5 figures, published version (Supplemental Material: 5 pages, 11 figures) for associated video file, see http://itp.uni-frankfurt.de/~kreisel/QPI_BSCCO_BdG_p_W.mp

Comparing hierarchies of total functionals

In this paper we consider two hierarchies of hereditarily total and continuous functionals over the reals based on one extensional and one intensional representation of real numbers, and we discuss under which asumptions these hierarchies coincide. This coincidense problem is equivalent to a statement about the topology of the Kleene-Kreisel continuous functionals. As a tool of independent interest, we show that the Kleene-Kreisel functionals may be embedded into both these hierarchies.Comment: 28 page

Pairing symmetry of the one-band Hubbard model in the paramagnetic weak-coupling limit: a numerical RPA study

We study the spin-fluctuation-mediated superconducting pairing gap in a weak-coupling approach to the Hubbard model for a two dimensional square lattice in the paramagnetic state. Performing a comprehensive theoretical study of the phase diagram as a function of filling, we find that the superconducting gap exhibits transitions from p-wave at very low electron fillings to d_{x^2-y^2}-wave symmetry close to half filling in agreement with previous reports. At intermediate filling levels, different gap symmetries appear as a consequence of the changes in the Fermi surface topology and the associated structure of the spin susceptibility. In particular, the vicinity of a van Hove singularity in the electronic structure close to the Fermi level has important consequences for the gap structure in favoring the otherwise sub-dominant triplet solution over the singlet d-wave solution. By solving the full gap equation, we find that the energetically favorable triplet solutions are chiral and break time reversal symmetry. Finally, we also calculate the detailed angular gap structure of the quasi-particle spectrum, and show how spin-fluctuation-mediated pairing leads to significant deviations from the first harmonics both in the singlet d_{x^2-y^2} gap as well as the chiral triplet gap solution.Comment: 11 pages 11 figure

Magentically-Induced Lattice Distortions and Ferroelectricity in Magnetoelectric GdMnO3

In this work we investigate the magnetic field dependence of Ag octahedra rotation (tilt) and B2g symmetric stretching modes frequency at different temperatures. Our field-dependent Raman investigation at 10K is interpreted by an ionic displacive nature of the magnetically induced ferroelectric phase transition. The frequency change of the Ag tilt is in agreement with the stabilization of the Mn-Gd spin arrangement, yielding the necessary conditions for the onset of ferroelectricity on the basis of the inverse Dzyaloshinskii-Moriya interaction. The role of the Jahn-Teller cooperative interaction is also evidenced by the change of the B2g mode frequency at the ferroelectric phase transition. This frequency change allows estimating the shift of the oxygen position at the ferroelectric phase transition and the corresponding spontaneous polarization of 480 {\mu}C/m2, which agrees with earlier reported values in single crystals. Our study also confirms the existence of a large magnetic hysteresis at the lowest temperatures, which is a manifestation of magnetrostiction.Comment: 5 pages, 3 figure

Structural and insulator-to-metal phase transition at 50 GPa in GdMnO3

We present a study of the effect of very high pressure on the orthorhombic perovskite GdMnO3 by Raman spectroscopy and synchrotron x-ray diffraction up to 53.2 GPa. The experimental results yield a structural and insulator-to-metal phase transition close to 50 GPa, from an orthorhombic to a metrically cubic structure. The phase transition is of first order with a pressure hysteresis of about 6 GPa. The observed behavior under very high pressure might well be a general feature in rare-earth manganites.Comment: 4 pages, 3 figures and 2 table