Statistical convergence in strong topology of probabilistic normed spaces

Following the concept of statistical convergence, we define and study statistical analog concepts of convergence and Cauchy's sequence on a probabilistic normed space that is endowed with a strong topology. Some important properties of statistical convergence have been extended in this new setting

Non-universal results induced by diversity distribution in coupled excitable systems

We consider a system of globally coupled active rotators near the excitable regime. The system displays a transition to a state of collective firing induced by disorder. We show that this transition is found generically for any diversity distribution with well defined moments. Singularly, for the Lorentzian distribution (widely used in Kuramoto-like systems) the transition is not present. This warns about the use of Lorentzian distributions to understand the generic properties of coupled oscillators

High-resolution Mn K-edge x-ray emission and absorption spectroscopy study of the electronic and local structure of the three different phases in Nd0.5Sr0.5MnO3

Nd0.5Sr0.5MnO3 is particularly representative of mixed-valent manganites since their three characteristic macroscopic phases (charge-ordered insulator, ferromagnetic-metallic, and paramagnetic insulator) appear at different temperatures.We here report a complete x-ray emission and absorption spectroscopy (XES-XAS) study of Nd0.5Sr0.5MnO3 as a function of temperature to investigate the electronic and local structure changes of the Mn atom in these three phases. Compared with the differences in the XES-XAS spectra between Nd0.5Sr0.5MnO3 and the single-valent reference compounds NdMnO3 (Mn3+) and Sr/CaMnO3 (Mn4+), only modest changes have been obtained across the magnetoelectrical transitions. The XES spectra, including both the Mn Kα and Kβ emission lines, have mainly shown a subtle decrease in the local spin density accompanying the passage to the ferromagnetic-metallic phase. For the same phase, the small intensity variations in the pre-edge region of the high-resolution XAS spectra reflect an increase of the p-d mixing. The analysis of these XAS spectra imply a charge segregation between the two different Mn sites far from one electron, being in intermediate valences Mn+3.5±δ/2(δ < 0.2 e−) for all the phases. Our results indicate that the spin, charge, and geometrical structure of the Mn atom hardly change among the three macroscopic phases demonstrating the strong competition between the ferromagnetic conductor and the charge-0rdered insulator behaviors in the manganites

Intrinsic electrical properties of LuFe2O4

We here revisit the electrical properties of LuFe2O4, compound candidate for exhibiting multiferroicity. Measurements of dc electrical resistivity as a function of temperature, electric-field polarization measurements at low temperatures with and without magnetic field, and complex impedance as a function of both frequency and temperature were carried out in a LuFe2O4 single crystal, perpendicular and parallel to the hexagonal c axis, and in several ceramic polycrystalline samples. Resistivity measurements reveal that this material is a highly anisotropic semiconductor, being about two orders of magnitude more resistive along the c axis. The temperature dependence of the resistivity indicates a change in the conduction mechanism at TCO ˜ 320 K from thermal activation above TCO to variable range hopping below TCO. The resistivity values at room temperature are relatively small and are below 5000 O¿cm for all samples but we carried out polarization measurements at sufficiently low temperatures, showing that electric-field polarization curves are a straight line as expected for a paraelectric or antiferroelectric material. Furthermore, no differences are found in the polarization curves when a magnetic field is applied either parallel or perpendicular to the electric field. The analysis of the complex impedance data corroborates that the claimed colossal dielectric constant is a spurious effect mainly derived from the capacitance of the electrical contacts. Therefore, our data unequivocally evidence that LuFe2O4 is not ferroelectric

Electronic states of R F e2 O4(R=Lu, Yb, Tm, Y) mixed-valence compounds determined by soft x-ray absorption spectroscopy and x-ray magnetic circular dichroism

We here report an investigation of the electronic states in the RFe2O4(R=Lu,Yb,Tm,Y) mixed-valence ferrites by means of soft x-ray absorption spectroscopy (XAS) and x-ray magnetic circular dichroism (XMCD) measurements together with ab initio theoretical calculations. The presence of Fe+2 and Fe+3 pure ionic species is discarded in the XAS spectra at the OK edge in both experimental data and simulations based on the multiple scattering theory. Similarly, no trace of Fe+2/Fe+3 contributions is detected in the XMCD spectra at the FeK edge. On the other hand, the XAS and XMCD spectra at the FeL2,3 edges can be well described in terms of Fe+2/Fe+3 contributions, and are also supported by multiplet calculations. This finding can be interpreted as the existence of a mixture of 3d5/3d6 configurations at the Fe atoms. Alternative ferrimagnetic spin orderings based on a trimodal Fe valence distribution are also proposed and discussed. Finally, a possible explanation for the strong dependence of the FeL2,3 edges XMCD signal magnitude on both the sample surface preparation and detection method is presented

The collapsed tetragonal phase as a strongly covalent and fully nonmagnetic state: persistent magnetism with interlayer As-As bond formation in Rh-doped Ca0.8_{0.8}Sr0.2_{0.2}Fe2_2As2_2

A well-known feature of CaFe$_{2}$As$_{2}$-based superconductors is the pressure-induced collapsed tetragonal phase that is commonly ascribed to the formation of an interlayer As-As bond. Using detailed X-ray scattering and spectroscopy, we find that Rh-doped Ca$_{0.8}$Sr$_{0.2}$Fe$_{2}$As$_{2}$ does not undergo a first-order phase transition and that local Fe moments persist despite the formation of interlayer As-As bonds. Our density functional theory calculations reveal that the Fe-As bond geometry is critical for stabilizing magnetism and that the pressure-induced drop in the $c$ lattice parameter observed in pure CaFe$_{2}$As$_{2}$ is mostly due to a constriction within the FeAs planes. These phenomena are best understood using an often overlooked explanation for the equilibrium Fe-As bond geometry, which is set by a competition between covalent bonding and exchange splitting between strongly hybridized Fe $3d$ and As $4p$ states. In this framework, the collapsed tetragonal phase emerges when covalent bonding completely wins out over exchange splitting. Thus the collapsed tetragonal phase is properly understood as a strong, covalent phase that is fully nonmagnetic with the As-As bond forming as a byproduct.Comment: 6 pages, 2 figures, and 1 table. Supplemental materials are available by reques

X-ray absorption and emission spectroscopy study of Mn and Co valence and spin states in TbM n1-x C ox O3

The valence and spin state evolution of Mn and Co on TbMn1-xCoxO3 series is precisely determined by means of soft and hard x-ray absorption spectroscopy (XAS) and Kß x-ray emission spectroscopy (XES). Our results show the change from Mn3+ to Mn4+ both high-spin (HS) together with the evolution from Co2+ HS to Co3+ low-spin (LS) with increasing x. In addition, high energy resolution XAS spectra on the K pre-edge region are interpreted in terms of the strong charge transfer and hybridization effects along the series. These results correlate well with the spin values of Mn and Co atoms obtained from the Kß XES data. In this paper, we determine that Co enters into the transition metal sublattice of TbMnO3 as a divalent ion in HS state, destabilizing the Mn long-range magnetic order since very low doping compositions (x=0.1). Samples in the intermediate composition range (0.4=x=0.6) adopt the crystal structure of a double perovskite with long-range ferromagnetic ordering which is due to Mn4+-O-Co2+ superexchange interactions with both cations in HS configuration. Ferromagnetism vanishes for x=0.7 due to the structural disorder that collapses the double perovskite structure. The spectroscopic techniques reveal the occurrence of Mn4+ HS and a fluctuating valence state Co2+ HS/Co3+ LS in this composition range. Disorder and competitive interactions lead to a magnetic glassy behavior in these samples

Role of delay in the stochastic creation process

We develop an approximate theoretical method to study discrete stochastic birth and death models that include a delay time. We analyze the effect of the delay in the fluctuations of the system and obtain that it can qualitatively alter them. We also study the effect of distributed delay. We apply the method to a protein-dynamics model that explicitly includes transcription and translation delays. The theoretical model allows us to understand in a general way the interplay between stochasticity and delay

Effects of A -site ordering on the Mn local structure and polar phases of R Ba Mn 2 O 6 ( R = La , Nd, Sm, and Y)

We have investigated the temperature dependence of the Mn local structure in A-site ordered RBaMn2O6 (R = La, Nd, Sm, and Y) perovskites, in parallel with their disordered counterparts, R0.5Ba0.5MnO3, by means of x-ray emission (XES) and x-ray absorption spectroscopy (XAS) The end member LaBaMn2O6 shows a nearly regular MnO6 octahedron independent of temperature. With decreasing the R ionic radius in the ordered samples, the XAS results indicate that a local distortion develops in the MnO6 octahedron at the low-temperature charge-localized and polar phases. For NdBaMn2O6, this local distortion is tiny, indicating the absence of charge segregation at the Mn site. This is followed by a bigger local distortion anticipated for SmBaMn2O6 in its respective charge-localized and polar phase and finally, the biggest local distortion for the smallest A-site cation ordered compound, YBaMn2O6, for which it even persists above the polar charge-localization transition temperatures. The high-resolution XAS spectra confirm the presence of charge segregation between two nonequivalent Mn sites in the low-temperature polar phase of Sm and Y ordered samples. Thus, our XAS study suggests a displacive mechanism for the charge-localization and polar transitions in the Nd and Sm ordered samples while a combination of displacive and order-disorder contributions is revealed for YBaMn2O6. Besides, calorimetric measurements confirm the combination of the two mechanisms, order-disorder and displacive, for the ordered Sm and Y compounds. On the other hand, the A-site disordered R0.5Ba0.5MnO3 samples with R cations smaller than Nd present a significant static (temperature-independent) local disorder, which explains why polar charge-localization transitions are not developed in these samples. Finally, we correlate our results about the Mn local structure and character of the transitions with the macroscopic magnetic and electric behavior of both A-site ordered and disordered compounds