Energy exponents of avalanches and Hausdorff dimensions of collapse patterns.

A simple numerical model to simulate athermal avalanches is presented. The model is inspired by the "porous collapse" process where the compression of porous materials generates collapse cascades, leading to power law distributed avalanches. The energy (E), amplitude (A_{max}), and size (S) exponents are derived by computer simulation in two approximations. Time-dependent "jerk" spectra are calculated in a single avalanche model where each avalanche is simulated separately from other avalanches. The average avalanche profile is parabolic, the scaling between energy and amplitude follows E∼A_{max}^{2}, and the energy exponent is ε = 1.33. Adding a general noise term in a continuous event model generates infinite avalanche sequences which allow the evaluation of waiting time distributions and pattern formation. We find the validity of the Omori law and the same exponents as in the single avalanche model. We then add spatial correlations by stipulating the ratio G/N between growth processes G (linked to a previous event location) and nucleation processes N (with new, randomly chosen nucleation sites). We found, in good approximation, a power law correlation between the energy exponent ε and the Hausdorff dimension H_{D} of the resulting collapse pattern H_{D}-1∼ɛ^{-3}. The evolving patterns depend strongly on G/N with the distribution of collapse sites equally power law distributed. Its exponent ɛ_{topo} would be linked to the dynamical exponent ε if each collapse carried an energy equivalent to the size of the collapse. A complex correlation between ɛ,ɛ_{topo}, and H_{D} emerges, depending strongly on the relative occupancy of the collapse sites in the simulation box

Avalanches from charged domain wall motion in BaTiO3 during ferroelectric switching

We report two methods for direct observations of avalanches in ferroelectric materials during the motion of domain walls. In the first method, we use optical imaging techniques to derive changes in domain structures under an electric field. All changes occur through small jumps (jerks) that obey avalanche statistics. In the second method, we analyze jerks by their displacement current. Both methods reveal a power law distribution with an energy exponent of 1.6, in agreement with previous acoustic emission measurements, and integrated mean field theory. This new combination of methods allows us to probe both polarization and strain variations during the motion of domain walls and can be used for a much wider class of ferroelectrics, including ceramic samples, than acoustic emission

Avalanche criticality during ferroelectric/ferroelastic switching

Abstract: Field induced domain wall displacements define ferroelectric/ferroelastic hysteresis loops, which are at the core of piezoelectric, magnetoelectric and memristive devices. These collective displacements are scale invariant jumps with avalanche characteristics. Here, we analyse the spatial distribution of avalanches in ferroelectrics with different domain and transformation patterns: Pb(Mg1/3Nb2/3)O3–PbTiO3 contains complex domains with needles and junction patterns, while BaTiO3 has parallel straight domains. Nevertheless, their avalanche characteristics are indistinguishable. The energies, areas and perimeters of the switched regions are power law distributed with exponents close to predicted mean field values. At the coercive field, the area exponent decreases, while the fractal dimension increases. This fine structure of the switching process has not been detected before and suggests that switching occurs via criticality at the coercive field with fundamentally different switching geometries at and near this critical point. We conjecture that the domain switching process in ferroelectrics is universal at the coercive field

Avalanche criticality during ferroelectric/ferroelastic switching

Abstract: Field induced domain wall displacements define ferroelectric/ferroelastic hysteresis loops, which are at the core of piezoelectric, magnetoelectric and memristive devices. These collective displacements are scale invariant jumps with avalanche characteristics. Here, we analyse the spatial distribution of avalanches in ferroelectrics with different domain and transformation patterns: Pb(Mg1/3Nb2/3)O3–PbTiO3 contains complex domains with needles and junction patterns, while BaTiO3 has parallel straight domains. Nevertheless, their avalanche characteristics are indistinguishable. The energies, areas and perimeters of the switched regions are power law distributed with exponents close to predicted mean field values. At the coercive field, the area exponent decreases, while the fractal dimension increases. This fine structure of the switching process has not been detected before and suggests that switching occurs via criticality at the coercive field with fundamentally different switching geometries at and near this critical point. We conjecture that the domain switching process in ferroelectrics is universal at the coercive field

Untangling the contributions of cerium and iron to the magnetism of Ce-doped yttrium iron garnet

The remarkable magnetic properties of yttrium iron garnets (YIGs) underpin the use of these materials in a broad scope of spintronic and photonic applications. In particular, the addition of rare earth metals in the structure enhances to a great extent the magneto-optical activity, which is beneficial for the development of nonreciprocal optical devices. Exploiting the wavelength selectivity of magneto-optics, we have identified a range of frequencies at which one can unravel the individual contributions to the magnetism and gyrotropic response arising from cerium and iron. We envision that this outcome may pave the way to further experiments to assess quantitatively the effect on the optical properties of rare earth incorporation into YIG.This work was supported by the Spanish Government by the MAT2011-29269-C03, MAT2014-56063-C2-1-R, and the Severo Ochoa SEV-2015-0496 Projects and the Generalitat de Catalunya (2014 SGR 734 Project). B.C. acknowledges his grant FPI BES-2012-059023 and R.C. acknowledges his fellowship from CNPq - Brazil. S.G., M.O., and R.G. thank T. Brenninger and E. Zamburg for technical support. We also acknowledge the contribution of C. Rubio in preliminary structural and magnetic characterization of thin films as well as Dr. F. Sanchez for scientific guiding and discussions on materials issues.Peer Reviewe

Avalanche criticality during ferroelectric/ferroelastic switching

Field induced domain wall displacements define ferroelectric/ferroelastic hysteresis loops, which are at the core of piezoelectric, magnetoelectric and memristive devices. These collective displacements are scale invariant jumps with avalanche characteristics. Here, we analyse the spatial distribution of avalanches in ferroelectrics with different domain and transformation patterns: Pb(Mg1/3Nb2/3)O3–PbTiO3 contains complex domains with needles and junction patterns, while BaTiO3 has parallel straight domains. Nevertheless, their avalanche characteristics are indistinguishable. The energies, areas and perimeters of the switched regions are power law distributed with exponents close to predicted mean field values. At the coercive field, the area exponent decreases, while the fractal dimension increases. This fine structure of the switching process has not been detected before and suggests that switching occurs via criticality at the coercive field with fundamentally different switching geometries at and near this critical point. We conjecture that the domain switching process in ferroelectrics is universal at the coercive field

A Novel chip for cyclic stretch and intermittent hypoxia cell exposures mimicking obstructive sleep apnea

Intermittent hypoxia (IH), a hallmark of obstructive sleep apnea (OSA), plays a critical role in the pathogenesis of OSA-associated morbidities, especially in the cardiovascular and respiratory systems. Oxidative stress and inflammation induced by IH are suggested as main contributors of end-organ dysfunction in OSA patients and animal models. Since the molecular mechanisms underlying these in vivo pathological responses remain poorly understood, implementation of experimental in vitro cell-based systems capable of inducing high-frequency IH would be highly desirable. Here, we describe the design, fabrication, and validation of a versatile chip for subjecting cultured cells to fast changes in gas partial pressure and to cyclic stretch. The chip is fabricated with polydimethylsiloxane (PDMS) and consists of a cylindrical well-covered by a thin membrane. Cells cultured on top of the membrane can be subjected to fast changes in oxygen concentration (equilibrium time similar to 6 s). Moreover, cells can be subjected to cyclic stretch at cardiac or respiratory frequencies independently or simultaneously. Rat bone marrow-derived mesenchymal stem cells (MSCs) exposed to IH mimicking OSA and cyclic stretch at cardiac frequencies revealed that hypoxia-inducible factor 1 alpha (HIF-1 alpha) expression was increased in response to both stimuli. Thus, the chip provides a versatile tool for the study of cellular responses to cyclical hypoxia and stretch

The duration-energy-size enigma for acoustic emission

Abstract: Acoustic emission (AE) measurements of avalanches in different systems, such as domain movements in ferroics or the collapse of voids in porous materials, cannot be compared with model predictions without a detailed analysis of the AE process. In particular, most AE experiments scale the avalanche energy E, maximum amplitude Amax and duration D as E ~ Amaxx and Amax ~ Dχ with x = 2 and a poorly defined power law distribution for the duration. In contrast, simple mean field theory (MFT) predicts that x = 3 and χ = 2. The disagreement is due to details of the AE measurements: the initial acoustic strain signal of an avalanche is modified by the propagation of the acoustic wave, which is then measured by the detector. We demonstrate, by simple model simulations, that typical avalanches follow the observed AE results with x = 2 and ‘half-moon’ shapes for the cross-correlation. Furthermore, the size S of an avalanche does not always scale as the square of the maximum AE avalanche amplitude Amax as predicted by MFT but scales linearly S ~ Amax. We propose that the AE rise time reflects the atomistic avalanche time profile better than the duration of the AE signal

Qu­antification of propagating and standing surface acoustic waves by stroboscopic X-ray photoemission electron microscopy

The quantification of surface acoustic waves (SAWs) in LiNbO3 piezoelectric crystals by stroboscopic X-ray photoemission electron microscopy (XPEEM), with a temporal smearing below 80 ps and a spatial resolution below 100 nm, is reported. The contrast mechanism is the varying piezoelectric surface potential associated with the SAW phase. Thus, kinetic energy spectra of photoemitted secondary electrons measure directly the SAW electrical amplitude and allow for the quantification of the associated strain. The stroboscopic imaging combined with a deliberate detuning allows resolving and quantifying the respective standing and propagating components of SAWs from a superposition of waves. Furthermore, standing-wave components can also be imaged by low-energy electron microscopy (LEEM). Our method opens the door to studies that quantitatively correlate SAWs excitation with a variety of sample electronic, magnetic and chemical properties

The duration-energy-size enigma for acoustic emission

Abstract: Acoustic emission (AE) measurements of avalanches in different systems, such as domain movements in ferroics or the collapse of voids in porous materials, cannot be compared with model predictions without a detailed analysis of the AE process. In particular, most AE experiments scale the avalanche energy E, maximum amplitude Amax and duration D as E ~ Amaxx and Amax ~ Dχ with x = 2 and a poorly defined power law distribution for the duration. In contrast, simple mean field theory (MFT) predicts that x = 3 and χ = 2. The disagreement is due to details of the AE measurements: the initial acoustic strain signal of an avalanche is modified by the propagation of the acoustic wave, which is then measured by the detector. We demonstrate, by simple model simulations, that typical avalanches follow the observed AE results with x = 2 and ‘half-moon’ shapes for the cross-correlation. Furthermore, the size S of an avalanche does not always scale as the square of the maximum AE avalanche amplitude Amax as predicted by MFT but scales linearly S ~ Amax. We propose that the AE rise time reflects the atomistic avalanche time profile better than the duration of the AE signal