Modern Physics Letters B

So far tens of multiferroic materials, with various chemical compositions and crystal structures, have been discovered in the past years. Among these multiferroics, some perovskite manganites with ferroelectricity driven by magnetic orders are of particular interest. In these multiferroic perovskite manganites, the multiferroic phenomena are not only quite prominent, but the involved physical mechanisms are also very plenty and representative. In this brief review, we will introduce some recent theoretical and experimental progress on multiferroic manganites, including the fascinating microscopic physics and very recently addressed experimental findings with attractive multiferroicity.

The quantum dynamics of a driven single-band tight-binding model with infinite and Dirichlet boundary conditions is considered. The polynomial algebra for the above model but with periodic boundary conditions (quantum ring) is constructed. Based on analyzing the algebraic structures of Hamiltonian, the solution of the time-dependent Schrödinger equation is also obtained exactly.

We introduce a new method to generate three-dimensional structures, with mixed topologies. We focus on Multilayered Regular Hyperbranched Fractals (MRHF), three-dimensional networks constructed as a set of identical generalized Vicsek fractals, known as Regular Hyperbranched Fractals (RHF), layered on top of each other. Every node of any layer is directly connected only to copies of itself from nearest-neighbor layers. We found out that also for MRHF the eigenvalue spectrum of the connectivity matrix is determined through a semi-analytical method, which gives the opportunity to analyze very large structures. This fact allows us to study in detail the crossover effects of two basic topologies: linear, corresponding to the way we connect the layers and fractal due to the layers' topology. From the wealth of applications which depends on the eigenvalue spectrum we choose the return-to-the-origin probability. The results show the expected short-time and long-time behaviors. In the intermediate time domain we obtained two different power-law exponents: the first one is given by the combination linear-RHF, while the second one is peculiar either of a single RHF or of a single linear chain.

The structural, ferroelectric and magnetic properties of bulk perovskite Fe-doped BaTiO₃ (BFTO) prepared by standard solid-state reaction have been investigated. X-ray diffraction (XRD) identifies the tetragonal structure of BFTO samples. Rietveld refinements of XRD data indicates that the doping ions led to ab-plane expansion and out-of-ab-plane shrinkage of the BFTO phases. X-ray photoelectron spectroscopy (XPS) measurements for the prepared samples reveals that Fe³⁺ and Fe⁴⁺ ions replaces Ti⁴⁺ ions in the crystal lattice to form single-phase BFTO solids. The results of the temperature-dependent dielectric properties and magnetic hysteresis loops for the BFTO solids show simultaneously the ferroelectric order and ferromagnetic order at room temperature. The doping of magnetic element Fe brings about ferromagnetic order for the samples, and the measured magnetic moment for each Fe atom increases from 0.70 μ_B to 1.55 μ_B in BFTO samples. The origin of ferromagnetism of the BFTO samples should be attributed to the double exchange interactions of Fe³⁺–O₂–Fe⁴⁺ ions.

The structural, electronic and magnetic properties of icosahedral bimetallic Ti_nMn_13-n (n = 1–12) clusters were investigated by the density-functional method. The results show that the central position is occupied by a manganese atom in the most stable structures. The total magnetic moment decreases with the increase of Ti atoms. It is interesting and important to note that, from the local magnetic moment, all Ti atoms are ferromagnetic coupling in various clusters, and most Mn atoms have the same feature. However, the spins between Ti and Mn atoms except for Ti₁₂Mn₁ are anti-parallel, i.e. an antiferromagnetic couple on magnetic structure. All the above are discussed in terms of magnetic ordering theory.

In this paper, mesoscopic RLC circuit with source is studied with Feynman's path integral method. Resistance and source in the circuits make the quantization process rather complicated. To solve the problem, fluctuation analysis method is proposed to calculate the path integral propagator. Furthermore, the wave function and quantum fluctuation of the system are obtained, and time evolution characters of the system are discussed. The methods used in the paper would be helpful to the application of mesoscopic quantum theory.