Expanding Semiflows on Branched Surfaces and One-Parameter Semigroups of Operators

We consider expanding semiflows on branched surfaces. The family of transfer operators associated to the semiflow is a one-parameter semigroup of operators. The transfer operators may also be viewed as an operator-valued function of time and so, in the appropriate norm, we may consider the vector-valued Laplace transform of this function. We obtain a spectral result on these operators and relate this to the spectrum of the generator of this semigroup. Issues of strong continuity of the semigroup are avoided. The main result is the improvement to the machinery associated with studying semiflows as one-parameter semigroups of operators and the study of the smoothness properties of semiflows defined on branched manifolds, without encoding as a suspension semiflow

Inhomogeneous magnetism in La-doped CaMnO3. (I) Nanometric-scale spin clusters and long-range spin canting

Neutron measurements on Ca{1-x}La{x}MnO3 (0.00 <= x <= 0.20) reveal the development of a liquid-like spatial distribution of magnetic droplets of average size ~10 Angstroms, the concentration of which is proportional to x (one cluster per ~60 doped electrons). In addition, a long-range ordered ferromagnetic component is observed for ~0.05 < x < ~0.14. This component is perpendicularly coupled to the simple G-type antiferromagnetic (G-AFM) structure of the undoped compound, which is a signature of a G-AFM + FM spin-canted state. The possible relationship between cluster formation and the stabilization of a long-range spin-canting for intermediate doping is discussed.Comment: Submitted to Physical Review

Convergence to stable laws for multidimensional stochastic recursions: the case of regular matrices

Given a sequence $(M_{n},Q_{n})_{n\ge 1}$ of i.i.d.\ random variables with generic copy $(M,Q) \in GL(d, \R) \times \R^d$, we consider the random difference equation (RDE) $$R_{n}=M_{n}R_{n-1}+Q_{n},$$ $n\ge 1$, and assume the existence of $\kappa >0$ such that \lim_{n \to \infty}(\E{\norm{M_1 ... M_n}^\kappa})^{\frac{1}{n}} = 1 . We prove, under suitable assumptions, that the sequence $S_n = R_1 + ... + R_n$, appropriately normalized, converges in law to a multidimensional stable distribution with index $\kappa$. As a by-product, we show that the unique stationary solution $R$ of the RDE is regularly varying with index $\kappa$, and give a precise description of its tail measure. This extends the prior work http://arxiv.org/abs/1009.1728v3 .Comment: 15 page

Inhomogeneous Magnetism in La-doped CaMnO3. (II) Mesoscopic Phase Separation due to Lattice-coupled FM Interactions

A detailed investigation of mesoscopic magnetic and crystallographic phase separation in Ca(1-x)La(x)MnO3, 0.00<=x<=0.20, is reported. Neutron powder diffraction and DC-magnetization techniques have been used to isolate the different roles played by electrons doped into the eg level as a function of their concentration x. The presence of multiple low-temperature magnetic and crystallographic phases within individual polycrystalline samples is argued to be an intrinsic feature of the system that follows from the shifting balance between competing FM and AFM interactions as a function of temperature. FM double-exchange interactions associated with doped eg electrons are favored over competing AFM interactions at higher temperatures, and couple more strongly with the lattice via orbital polarization. These FM interactions thereby play a privileged role, even at low eg electron concentrations, by virtue of structural modifications induced above the AFM transition temperatures.Comment: 8 pages, 7 figure

Lattice dynamics of mixed semiconductors (Be,Zn)Se from first-principles calculations

Vibration properties of Zn(1-x)Be(x)Se, a mixed II-VI semiconductor haracterized by a high contrast in elastic properties of its pure constituents, ZnSe and BeSe, are simulated by first-principles calculations of electronic structure, lattice relaxation and frozen phonons. The calculations within the local density approximation has been done with the Siesta method, using norm-conserving pseudopotentials and localized basis functions; the benchmark calculations for pure endsystems were moreover done also by all-electron WIEN2k code. An immediate motivation for the study was to analyze, at the microscopic level, the appearance of anomalous phonon modes early detected in Raman spectra in the intermediate region (20 to 80%) of ZnBe concentration. This was early discussed on the basis of a percolation phenomenon, i.e., the result of the formation of wall-to-wall --Be--Se-- chains throughout the crystal. The presence of such chains was explicitly allowed in our simulation and indeed brought about a softening and splitting off of particular modes, in accordance with experimental observation, due to a relative elongation of Be--Se bonds along the chain as compared to those involving isolated Be atoms. The variation of force constants with interatomic distances shows common trends in relative independence on the short-range order.Comment: 11 pages, 10 figures, to be published in Phys. Rev.

Evidence of anisotropic magnetic polarons in la0.94_{0.94}Sr0.06_{0.06}MnO3_3 by neutron scattering and comparison with Ca-doped manganites

Elastic and inelastic neutron scattering experiments have been performed in a La$_{0.94}$Sr$_{0.06}$MnO$_3$ untwinned crystal, which exhibits an antiferromagnetic canted magnetic structure with ferromagnetic layers. The elastic small q scattering exhibits a modulation with an anisotropic q-dependence. It can be pictured by ferromagnetic inhomogeneities or polarons with a platelike shape, the largest size ($\approx17\AA$) and largest inter-polaron distance ($\approx$ 38$\AA$) being within the ferromagnetic layers. Comparison with observations performed on Ca-doped samples, which show the growth of the magnetic polarons with doping, suggests that this growth is faster for the Sr than for the Ca substitution. Below the gap of the spin wave branch typical of the AF layered magnetic structure, an additional spin wave branch reveals a ferromagnetic and isotropic coupling, already found in Ca-doped samples. Its q-dependent intensity, very anisotropic, closely reflects the ferromagnetic correlations found for the static clusters. All these results agree with a two-phase electronic segregation occurring on a very small scale, although some characteristics of a canted state are also observed suggesting a weakly inhomogeneous state.Comment: 11 pages, 11 figure

High-field AFMR in single-crystalline La_{0.95}Sr_{0.05}MnO_3: Experimental evidence for the existence of a canted magnetic structure

High-field antiferromagnetic-resonance (AFMR) spectra were obtained in the frequency range 60 GHz < \nu < 700 GHz and for magnetic fields up to 8 T in twin-free single crystals of La_{0.95}Sr_{0.05}MnO_3. At low temperatures two antiferromagnetic modes were detected, which reveal different excitation conditions and magnetic field dependencies. No splitting of these modes was observed for any orientation of the static magnetic field excluding the phase-separation scenario for this composition. Instead, the full data set including the anisotropic magnetization can be well described using a two-sublattice model of a canted antiferromagnetic structure.Comment: 4 pages, 3 figure

Approach to the metal-insulator transition in La(1-x)CaxMnO3 (0<x<.2): magnetic inhomogeneity and spin wave anomaly

We describe the evolution of the static and dynamic spin correlations of La$_{1-x}$Ca$_x$MnO$_3$, for x=0.1, 0.125 and 0.2, where the system evolves from the canted magnetic state towards the insulating ferromagnetic state, approaching the metallic transition (x=0.22). In the x=0.1 sample, the observation of two spin wave branches typical of two distinct types of magnetic coupling, and of a modulation in the elastic diffuse scattering characteristic of ferromagnetic inhomogeneities, confirms the static and dynamic inhomogeneous features previously observed at x$<$0.1. The anisotropic q-dependence of the intensity of the low-energy spin wave suggests a bidimensionnal character for the static inhomogeneities. At x=0.125, which corresponds to the occurence of a ferromagnetic and insulating state, the two spin wave branches reduce to a single one, but anisotropic. At this concentration, an anomaly appears at {\bf q$_0$}=(1.25,1.25,0), that could be related to an underlying periodicity, as arising from (1.5,1.5,0) superstructures. At x=0.2, the spin-wave branch is isotropic. In addition to the anomaly observed at q$_0$, extra magnetic excitations are observed at larger q, forming an optical branch. The two dispersion curves suggest an anti-crossing behavior at some {\bf q$_0$'} value, which could be explained by a folding due to an underlying perodicity involving four cubic lattice spacings