Investigation of Complex Impedance and Modulus Properties of Nd Doped 0.5BiFeO3-0.5PbTiO3 Multiferroic Composites

0.5BiNdxFe1-xO3-0.5PbTiO3 (x=0.05, 0.10, 0.15, 0.20) composites were successfully synthesized by a solid state reaction technique. At room temperature X-ray diffraction shows tetragonal structure for all concentrations of Nd doped 0.5BiFeO3-0.5PbTiO3 composites. The nature of Nyquist plot confirms the presence of bulk effects only for all compositions of Nd-doped 0.5BiFeO3-0.5PbTiO3 composites. The bulk resistance is found to decreases with the increasing in temperature as well as Nd concentration and exhibits a typical negative temperature coefficient of resistance (NTCR) behavior. Both the complex impedance and modulus studies have suggested the presence of non-Debye type of relaxation in the materials. Conductivity spectra reveal the presence of hopping mechanism in the electrical transport process of the materials. The activation energy of the composite increases with increasing Nd concentration and were found to be 0.28, 0.27, 0.31 and 0.32eV for x=0.05, 0.10, 0.15, 0.20 respectively at 200-275 oC for conduction process.Comment: 22 pages, 12 figures, 2 tables, 34 Referenc

Effect of electron corelation on superconducting pairing symmetry

The role of electron correlation on different pairing symmetries are discussed in details where the electron correlation has been treated within the slave boson formalism. It is shown that for a pure $s$ or pure $d$ wave pairing symmetry, the electronic correlation suppresses the $s$ wave gap magnitude (as well as the $T_c$) at a faster rate than that for the $d$ wave gap. On the otherhand, a complex order parameter of the form ($s+id$) shows anomalous temperature dependence. For example, if the temperature ($T_{c}^d$) at which the $d$ wave component of the complex order parameter vanishes happens to be larger than that for the $s$ wave component ($T_{c}^s$) then the growth of the $d$ wave component is arrested with the onset of the $s$ wave component of the order parameter. In this mixed phase however, we find that the suppression in different components of the gap as well as the corresponding $T_c$ due to coulomb correlation are very sensitive to the relative pairing strengths of $s$ and $d$ channels as well as the underlying lattice. Interestingly enough, in such a scenario (for a case of $T_{c}^s > T_{c}^d$) the gap magnitude of the $d$ wave component increases with electron correlation but not $T_{c}^d$ for certain values of electron correlation. However, this never happens in case of the $s$ wave component. We also calculate the temperature dependence of the superconducting gap along both the high symmetry directions ($\Gamma$ - M and $\Gamma$ - X) in a mixed $s+id$ symmetry pairing state and the thermal variation of the gap anisotropy ($\frac{\Delta_{\Gamma - M}}{\Delta_{\Gamma - X}}$) with electron correlation. The results are discussed with reference to experimental observations.Comment: 22 pages, latex, 12 figures (attached in ps /eps) Journal : Accepted for publication in Euro. J. Phys

Anti-isospectral Transformations, Orthogonal Polynomials and Quasi-Exactly Solvable Problems

We consider the double sinh-Gordon potential which is a quasi-exactly solvable problem and show that in this case one has two sets of Bender-Dunne orthogonal polynomials . We study in some detail the various properties of these polynomials and the corresponding quotient polynomials. In particular, we show that the weight functions for these polynomials are not always positive. We also study the orthogonal polynomials of the double sine-Gordon potential which is related to the double sinh-Gordon case by an anti-isospectral transformation. Finally we discover a new quasi-exactly solvable problem by making use of the anti-isospectral transformation.Comment: Revtex, 19 pages, No figur

Characterization and Representation of Weighted Core Inverse of Matrices

In this paper, we introduce new representation and characterization of the weighted core inverse of matrices. Several properties of these inverses and their interconnections with other generalized inverses are explored. Through one-sided core and dual-core inverse, the existence of a generalized weighted Moore-Penrose inverse of matrices is proposed. Further, by applying a new representation and using the properties of the weighted core inverse of a matrix, we discuss a few new results related to the reverse order law for these inverses.Comment: 18 page