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The rare-earth (RE) elements [Holmium (Ho) and Ytterbium (Yb)] doped vanadium pentoxide (V2O5) with a series of doping concentrations (1 mol.%, 3 mol.%, and 5 mol.%) have been successfully synthesized using environment-friendly facile hydrothermal method. The effect of RE ions on the photocatalytic efficiency of doped V2O5 has also been analyzed. The stable orthorhombic crystal structure of doped V2O5 confirms by the X-ray diffraction with no secondary phase, and high-stressed conditions are generated for the 3 mol.%. The crystallite size, strain, and dislocation density are calculated to perceive the doping effect on the bare V2O5. The optical characteristics have been measured using UV-vis spectroscopy. The absorptions are found to be increased with increasing doping concentrations; however, the bandgap remains in the visible range. The photocatalytic properties are examined for the compounds with varying pH, and it is observed that higher efficiency is exhibited for the pH 7 and catalyst concentration 500 ppm. The highest degradation efficiency is found to be 93% and 95% for the 3 mol.% of Ho and Yb-doped V2O5 samples within 2 hours, respectively. It is elucidated that the RE ions significantly impact the catalytic behavior of V2O5, and the mechanism behind these extraordinary efficiencies has been explained thoroughly.

In this study, a complete study of the effect of hydrothermal reaction temperatures on the synthesis and physical properties of V2O5 using the green facile mild hydrothermal method has been performed with six different temperatures 100 {\deg}C to 200 {\deg}C, in the step of 20 {\deg}C. . The XRD pattern confirm the stable orthorhombic crystal structure of the synthesized samples at all reaction temperatures. The SEM and TEM images demonstrate the particle-like morphology, and these characterizations affirmed that the particles size became larger with the increase of reaction temperatures. The FTIR analysis is employed to study the functional groups, and the obtained results are consistent with the XRD analysis. The bandgap has been estimated at various reaction temperatures using UV-vis diffuse reflectance spectra (UV-DRS) and was found to be varied 2.09 eV to 2.15 eV that are suitable range to absorb a significant amount of visible light. The photocatalysis of methylene blue (MB) with synthesized samples has been accomplished to investigate photocatalytic efficiency. The pure V2O5 synthesized at lower reaction temperature (100 {\deg}C) possess a lower bandgap and, accordingly, higher photocatalytic efficiency., Comment: 19 pages

Ruderman-Kittel-Kasuya-Yosida (RKKY) is an essential long range magnetic interaction between magnetic impurities or magnetic layered structures, the magnitude of which oscillates with the distance ($\mathrm{R}$) between them. We have investigated the RKKY interaction between two magnetic impurities in both time-reversal and inversion symmetry broken Weyl semimetals (WSMs) where the energy dispersion is tilted in momentum space and the momentum of the conduction electron is locked with the pseudo-spin. Two important features are revealed, firstly, at the small tilt limit, we show that the RKKY coupling varies quadratically with the tilt parameter and strikingly, at large separation distance $\mathrm{R}$, the coupling decays as $1/\mathrm{R}$ compared to the conventional of $1/\mathrm{R}^{3}$ dependence exhibited by WSMs with non-tilted dispersion. The slower decay by two orders i.e. ($1/\mathrm{R}$ as opposed to $1/\mathrm{R}^{3}$) of the RKKY coupling is significant for maintaining long range RKKY coupling. Secondly, the RKKY coupling exhibits an anisotropy with respect to the angle between the tilt direction ($\mathbf{w}$) and the separation direction $\mathbf{R}$ unlike the case of non-tilted WSMs which exhibit isotropic RKKY coupling. Consequently, the RKKY coupling in tilted WSMs alternately favours ferromagnetic and anti-ferromagnetic orders and vice-versa with the change of the angle. Our results are derived analytically and verified by numerical calculations based on realistic parameter values.

A comprehensive comparison between Bi$_{25}$FeO$_{40}$-reduced graphene oxide(rGO) nanocomposite and BiFeO$_{3}$-rGO nanocomposite has been performed to investigate their photocatalytic abilities in degradation of Rhodamine B dye and generation of hydrogen by water-splitting. The hydrothermal technique adapted for synthesis of the nanocomposites provides a versatile temperature-controlled phase selection between perovskite BiFeO$_{3}$ and sillenite Bi$_{25}$FeO$_{40}$. Both perovskite and sillenite structured nanocomposites are stable and exhibit considerably higher photocatalytic ability over pure BiFeO$_{3}$ nanoparticles and commercially available Degussa P25 titania. Notably, Bi$_{25}$FeO$_{40}$- rGO nanocomposite has demonstrated superior photocatalytic ability and stability under visible light irradiation than that of BiFeO$_{3}$-rGO nanocomposite. The possible mechanism behind the superior photocatalytic performance of Bi$_{25}$FeO$_{40}$-rGO nanocomposite has been critically discussed., Comment: 13 pages, 6 figures

Weyl semimetals (WSM) exhibit chiral anomaly in their magnetotransport due to broken conservation laws. Here, we analyze the magnetotransport of WSM in the presence of the time-reversal symmetry-breaking tilt parameter. The analytical expression for the magnetoconductivity is derived in the small tilt limit using the semiclassical Boltzmann equation. We predict a planar Hall current which flows transverse to the electric field and in the plane containing magnetic and electric fields and scales linearly with the tilt parameter. A tilt-induced transverse conductivity is also present in the case where the electric and magnetic fields are parallel to each other, a scenario where the conventional Hall current completely vanishes., Comment: 6 pages, 10 figures

We adopt the tight-binding mode-matching method to study the strain effect on silicene heterojunctions. It is found that valley- and spin-dependent separation of electrons cannot be achieved by the electric field only. When a strain and an electric field are simultaneously applied to the central scattering region, not only are the electrons of valleys K and K' separated into two distinct transmission lobes in opposite transverse directions, but the up-spin and down-spin electrons will also move in the two opposite transverse directions. Therefore, one can realize an effective modulation of valley- and spin-dependent transport by changing the amplitude and the stretch direction of the strain. The phenomenon of the strain-induced valley and spin deflection can be exploited for silicene-based valleytronics devices., Comment: 6 pages, 6 figures

In this investigation, undoped BiFeO$_3$, Gd doped Bi$_{0.9}$Gd$_{0.1}$FeO$_3$, and Gd-Ti co-doped Bi$_{0.9}$Gd$_{0.1}$Fe$_{1-x}$Ti$_x$O$_3$ (x = 0.10, 0.20) materials were synthesized to report their multiferroic properties. The structural analysis and phase identification of these multiferroic ceramics were performed using Rietveld refinement. The Rietveld analysis has confirmed the high phase purity of the 10% Gd-Ti co-doped Bi$_{0.9}$Gd$_{0.1}$Fe$_{0.9}$Ti$_{0.1}$O$_3$ sample compared to that of other compositions under investigation. The major phase of this particular composition is of rhombohedral \textit{R3c} type structure (wt% $>99\%$) with negligible amount of impurity phases. In terms of characterization, we address magnetic properties of this co-doped ceramic system by applying substantially higher magnetic fields than that applied in previously reported investigations. The dependence of temperature and maximum applied magnetic fields on their magnetization behavior have also been investigated. Additionally, the leakage current density has been measured to explore its effect on the ferroelectric properties of this multiferroic system. The outcome of this investigation suggests that the substitution of 10% Gd and Ti in place of Bi and Fe, respectively, in BiFeO$_3$ significantly enhances its multiferroic properties. The improved properties of this specific composition is associated with homogeneous reduced grain size, significant suppression of impurity phases and reduction in leakage current density which is further asserted by polarization vs. electric field hysteresis loop measurements., Comment: 7 figures, Journal of Alloys and Compounds,October 2016

The ceramic pellets of the nominal compositions Bi$_{0.7}$Ba$_{0.3}$Fe$_{1-x}$Ti$_x$O$_3$ (x = 0.00-0.20) were prepared initially by standard solid state reaction technique. The pellets were then ground into micrometer-sized powders and mixed with isopropanol in an ultrasonic bath to prepare nanoparticles. The X-ray diffraction patterns demonstrate the presence of a significant number of impurity phases in bulk powder materials. Interestingly, these secondary phases were completely removed due to the sonication of these bulk powder materials for 60 minutes. The field and temperature dependent magnetization measurements exhibited significant difference between the magnetic properties of the bulk materials and their corresponding nanoparticles. We anticipate that the large difference in the magnetic behavior may be associated with the presence and absence of secondary impurity phases in the bulk materials and their corresponding nanoparticles, respectively. The leakage current density of the bulk materials was also found to suppress in the ultrasonically prepared nanoparticles compared to that of bulk counterparts., Comment: 9 pages in Journal of Physics D: Applied Physics, 2016

Let $G=(V,E)$ be a simple graph. A set $I\subseteq V$ is an independent set, if no two of its members are adjacent in $G$. The $k$-independent graph of $G$, $I_k (G)$, is defined to be the graph whose vertices correspond to the independent sets of $G$ that have cardinality at most $k$. Two vertices in $I_k(G)$ are adjacent if and only if the corresponding independent sets of $G$ differ by either adding or deleting a single vertex. In this paper, we obtain some properties of $I_k(G)$ and compute it for some graphs., Comment: 10 pages, 4 Figures......This is updated version of paper in arXiv:1510.05360 which the name of co-author "Abdul Jalil M. Khalaf" added

We obtain the lowest energy solutions for the skymion field equations and their corresponding vortex structures. Two nondegenerate solutions emerge with their vortex swirls in opposite directions. The solutions are associated with an extremum property, which favors an array of almost hexagonal shape. We predict that a regular hexagonal lattice must have a mix of skyrmions of both swirls. Although our solutions could not keep the norm of the magnetization constant at unity, their greatest deviation from unity occurred in regions where the spins are far from planar; we show how to improve this situation., Comment: 12 pages, 5 figures

We study the Thiele equation for current-induced motion in a skyrmion lattice through two soluble models of the pinning potential. Comprised by a Magnus term, a dissipative term and a pinning force, Thiele's equation resembles Newton's law but in virtue of the topological character of the first two, it differs significantly from Newtonian mechanics and because the Magnus force is dominant, unlike its mechanical counterpart, the Coriolis force, skyrmion trajectories do not necessarily have mechanical counterparts. This is important if we are to understand skykrmion dynamics and tap into its potential for data-storage technology. We identify a pinning threshold velocity for the one-dimensional potential and for a two-dimensional potential we find a pinning point and the skyrmion trajectories toward the point are spirals whose frequency (compare Kepler's second law) and amplitude decay depends only on the Gilbert constant and potential at the pinning point., Comment: 14 pages, 5 figures