Accelerating random walks by disorder

We investigate the dynamic impact of heterogeneous environments on superdiffusive random walks known as L\'evy flights. We devote particular attention to the relative weight of source and target locations on the rates for spatial displacements of the random walk. Unlike ordinary random walks which are slowed down for all values of the relative weight of source and target, non-local superdiffusive processes show distinct regimes of attenuation and acceleration for increased source and target weight, respectively. Consequently, spatial inhomogeneities can facilitate the spread of superdiffusive processes, in contrast to common belief that external disorder generally slows down stochastic processes. Our results are based on a novel type of fractional Fokker-Planck equation which we investigate numerically and by perturbation theory for weak disorder.Comment: 8 pages, 5 figure

L\'evy-like behavior in deterministic models of intelligent agents exploring heterogeneous environments

Many studies on animal and human movement patterns report the existence of scaling laws and power-law distributions. Whereas a number of random walk models have been proposed to explain observations, in many situations individuals actually rely on mental maps to explore strongly heterogeneous environments. In this work we study a model of a deterministic walker, visiting sites randomly distributed on the plane and with varying weight or attractiveness. At each step, the walker minimizes a function that depends on the distance to the next unvisited target (cost) and on the weight of that target (gain). If the target weight distribution is a power-law, $p(k)\sim k^{-\beta}$, in some range of the exponent $\beta$, the foraging medium induces movements that are similar to L\'evy flights and are characterized by non-trivial exponents. We explore variations of the choice rule in order to test the robustness of the model and argue that the addition of noise has a limited impact on the dynamics in strongly disordered media.Comment: 15 pages, 7 figures. One section adde

Universal magneto-orbital ordering in the divalent AA-site quadruple perovskite manganites AAMn7_7O12_{12} (AA = Ca, Sr, Cd, and Pb)

Through analysis of variable temperature neutron powder diffraction data, we present solutions for the magnetic structures of SrMn$_7$O$_{12}$, CdMn$_7$O$_{12}$, and PbMn$_7$O$_{12}$ in all long-range ordered phases. The three compounds were found to have magnetic structures analogous to that reported for CaMn$_7$O$_{12}$. They all feature a higher temperature lock-in phase with \emph{commensurate} magneto-orbital coupling, and a delocked, multi-\textbf{k} magnetic ground state where \emph{incommensurate} magneto-orbital coupling gives rise to a constant-moment magnetic helix with modulated spin helicity. CdMn$_7$O$_{12}$ represents a special case in which the orbital modulation is commensurate with the crystal lattice and involves stacking of fully and partially polarized orbital states. Our results provide a robust confirmation of the phenomenological model for magneto-orbital coupling previously presented for CaMn$_7$O$_{12}$. Furthermore, we show that the model is universal to the $A^{2+}$ quadruple perovskite manganites synthesised to date, and that it is tunable by selection of the $A$-site ionic radius

Magnetic ground state and multiferroicity in BiMnO3_3

We argue that the centrosymmetric $C2/c$ symmetry in BiMnO$_3$ is spontaneously broken by antiferromagnetic (AFM) interactions existing in the system. The true symmetry is expected to be $Cc$, which is compatible with the noncollinear magnetic ground state, where the ferromagnetic order along one crystallographic axis coexists with the the hidden AFM order and related to it ferroelectric polarization along two other axes. The $C2/c$ symmetry can be restored by the magnetic field $B \sim 35$ Tesla, which switches off the ferroelectric polarization. Our analysis is based on the solution of the low-energy model constructed for the 3d-bands of BiMnO$_3$, where all the parameters have been derived from the first-principles calculations. Test calculations for isostructural BiCrO$_3$ reveal an excellent agreement with experimental data.Comment: 5 pages, 5 figure

High-Pressure Synthesis, Crystal Structures, and Properties of A-Site Columnar-Ordered Quadruple Perovskites NaRMn2Ti4O12 with R = Sm, Eu, Gd, Dy, Ho, Y

The formation of NaRMn2Ti4O12 compounds (R = rare earth) under high pressure (about 6 GPa) and high temperature (about 1750 K) conditions was studied. Such compounds with R = Sm, Eu, Gd, Dy, Ho, Y adopt an A-site columnar-ordered quadruple-perovskite structure with the generic chemical formula A2A′A″B4O12. Their crystal structures were studied by powder synchrotron X-ray and neutron diffraction between 1.5 and 300 K. They maintain a paraelectric structure with centrosymmetric space group P42/nmc (No. 137) at all temperatures, in comparison with the related CaMnTi2O6 perovskite, in which a ferroelectric transition occurs at 630 K. The centrosymmetric structure was also confirmed by second-harmonic generation. It has a cation distribution of [Na+R3+]A[Mn2+]A′[Mn2+]A″[Ti4+4]BO12 (to match with the generic chemical formula) with statistical distributions of Na+ and R3+ at the large A site and a strongly split position of Mn2+ at the square-planar A′ site. We found a C-type long-range antiferromagnetic structure of Mn2+ ions at the A′ and A″ sites below TN = 12 K for R = Dy and found that the presence of Dy3+ disturbs the long-range ordering of Mn2+ below a second transition at lower temperatures. The first magnetic transition occurs below 8–13 K in all compounds, but the second magnetic transition occurs only for R = Dy, Sm, Eu. All compounds show large dielectric constants of a possible extrinsic origin similar to that of CaCu3Ti4O12. NaRMn2Ti4O12 with R = Er–Lu crystallized in the GdFeO3-type Pnma perovskite structure, and NaRMn2Ti4O12 with R = La, Nd contained two perovskite phases: an AA′3B4O12-type Im3̅ phase and a GdFeO3-type Pnma phase

Observation of persistent centrosymmetricity in the hexagonal manganite family

The controversy regarding the ferroelectric behavior of hexagonal InMnO$_3$ is resolved by using a combination of x-ray diffraction (XRD), piezoresponse force microscopy (PFM), second harmonic generation (SHG), and density functional theory (DFT). While XRD data show a symmetry-lowering unit-cell tripling, which is also found in the multiferroic hexagonal manganites of $P6_3cm$ symmetry, PFM and SHG do not detect ferroelectricity at ambient or low temperature, in striking contrast to the behavior in the multiferroic counterparts. We propose instead a centrosymmetric $P\bar{3}c$ phase as the ground state structure. Our DFT calculations reveal that the relative energy of the ferroelectric and nonferroelectric structures is determined by a competition between electrostatics and oxygen-$R$-site covalency, with an absence of covalency favoring the ferroelectric phase.Comment: 8 pages, 9 figure

Antiferrodistortive phase transition in EuTiO3

X-ray diffraction, dynamical mechanical analysis and infrared reflectivity studies revealed an antiferrodistortive phase transition in EuTiO3 ceramics. Near 300K the perovskite structure changes from cubic Pm-3m to tetragonal I4/mcm due to antiphase tilting of oxygen octahedra along the c axis (a0a0c- in Glazer notation). The phase transition is analogous to SrTiO3. However, some ceramics as well as single crystals of EuTiO3 show different infrared reflectivity spectra bringing evidence of a different crystal structure. In such samples electron diffraction revealed an incommensurate tetragonal structure with modulation wavevector q ~ 0.38 a*. Extra phonons in samples with modulated structure are activated in the IR spectra due to folding of the Brillouin zone. We propose that defects like Eu3+ and oxygen vacancies strongly influence the temperature of the phase transition to antiferrodistortive phase as well as the tendency to incommensurate modulation in EuTiO3.Comment: PRB, in pres