Symmetry, incommensurate magnetism and ferroelectricity: the case of the rare-earth manganites RMnO3

The complete irreducible co-representations of the paramagnetic space group provide a simple and direct path to explore the symmetry restrictions of magnetically driven ferroelectricity. The method consists of a straightforward generalization of the method commonly used in the case of displacive modulated systems and allows us to determine, in a simple manner, the full magnetic symmetry of a given phase originated from a given magnetic order parameter. The potential ferroic and magneto-electric properties of that phase can then be established and the exact Landau free energy expansions can be derived from general symmetry considerations. In this work, this method is applied to the case of the orthorhombic rare-earth manganites RMnO3. This example will allow us to stress some specific points, such as the differences between commensurate or incommensurate magnetic phases regarding the ferroic and magnetoelectric properties, the possible stabilization of ferroelectricity by a single irreducible order parameter or the possible onset of a polarization oriented parallel to the magnetic modulation. The specific example of TbMnO3 will be considered in more detail, in order to characterize the role played by the magneto-electric effect in the mechanism for the polarization rotation induced by an external magnetic field.Comment: Conference: Aperiodic`0

Nonlinear acoustic waves in channels with variable cross sections

The point symmetry group is studied for the generalized Webster-type equation describing non-linear acoustic waves in lossy channels with variable cross sections. It is shown that, for certain types of cross section profiles, the admitted symmetry group is extended and the invariant solutions corresponding to these profiles are obtained. Approximate analytic solutions to the generalized Webster equation are derived for channels with smoothly varying cross sections and arbitrary initial conditions.Comment: Revtex4, 10 pages, 2 figure. This is an enlarged contribution to Acoustical Physics, 2012, v.58, No.3, p.269-276 with modest stylistic corrections introduced mainly in the Introduction and References. Several typos were also correcte

X-ray Diffraction Study of Superstructure in GdBaCo2O5.5

A single crystal of GdBaCo2O5.47(2) has been studied by means of X-ray diffraction. Appearance of superstructure reflections at T = 341.5(7) K gives an evidence of continuous transition to the phase with unit cell doubled along the shortest edge a1. Critical exponent for the order parameter is found to be beta=0.33(1). The superstructure reflections are about 2-4 orders of magnitude weaker than the basic ones. Their systematic extinction indicates the crystal symmetry change from Pmmm to Pmma. The integrated intensities allow to calculate displacements of atoms from the positions in the high-temperature phase. The cobalt-ligand distances in the ordered phase are discussed in terms of the spin-state/orbital ordering of Co3+ ions.Comment: 4 page

On the magnetically driven ferroelectric phase in GdMnO3

At room temperature, GdMnO3 is a paraelectric and paramagnetic with a distorted perovskite structure of orthorhombic symmetry (space group Pnma). On cooling, it undergoes a phase transition sequence to a magnetic incommensurate phase (k=delta a*; Tc1=42K) and a A-type antiferromagnetic phase (Tc2=27K). At low temperatures (T<12K), a magnetic field applied along the a-axis destabilizes the antiferromagnetic phase and induces a first order transition to a magnetic commensurate modulated phase (delta=1/4) that is also ferroelectric (P//c). This work analyses this field induced phase transition from the point of view of the symmetry and Landau theory.Comment: 13 pages, communication to the 11th European Meeting on Ferroelectricity, Bled (Slovenia)2007; submitted to Ferroelectric

Acoustomagnetoelectric effect in two-dimensional materials: Geometric resonances and Weiss oscillations

We study electron transport in two-dimensional materials with parabolic and linear (graphene) dispersions of the carriers in the presence of surface acoustic waves and an external magnetic field using semiclassical Boltzmann equations approach. We observe an oscillatory behavior of both the longitudinal and Hall electric currents as functions of the surface acoustic wave frequency at a fixed magnetic field and as functions of the inverse magnetic field at a fixed frequency of the acoustic wave. We explain the former by the phenomenon of geometric resonances, while we relate the latter to the Weiss-like oscillations in the presence of the dynamic superlattice created by the acoustic wave. Thus we demonstrate the dual nature of the acoustomagnetoelectric effect in two-dimensional electron gas.Comment: Manuscript: 9 pages, 2 figure

Quasisymmetric graphs and Zygmund functions

A quasisymmetric graph is a curve whose projection onto a line is a quasisymmetric map. We show that this class of curves is related to solutions of the reduced Beltrami equation and to a generalization of the Zygmund class $\Lambda_*$. This relation makes it possible to use the tools of harmonic analysis to construct nontrivial examples of quasisymmetric graphs and of quasiconformal maps.Comment: 21 pages, no figure