Domain reversal behavior in perpendicular magnetic nanothin films

We report domain reversal behavior in perpendicular ferromagnetic nanothin films investigated by means of a novel magneto-optical microscope magnetometer, capable of grabbing domain reversal patterns in real time under an applied field as well as simultaneous measurements of 8000 local hysteresis loops with 400-nm special resolution. Three contrasting domain reversal behaviors are found to exist: wall-motion dominant, dendritic-growth dominant, and nucleation dominant reversal. Quantitative analysis reveals that the contrasting reversal behavior is mainly caused by a sensitive change in wall-motion speed and that the reversal ratio of wall-motion speed over nucleation rate is a governing parameter for the contrasting domain reversal dynamics. The activation volumes of the wall-motion and nucleation processes are found generally unequal, and the inequality is closely related with the domain dynamics. The domain reversal pattern is truly coincident with submicron-scale local coercivity variation and local switching time of domain evolution is exponentially dependent on local coercivity governed by a thermal activation relaxation process. The observed domain reversal behavior could be well predicted by a Monte Carlo simulation of a micromagnetic model based on the uniaxial magnetic anisotropy of nanothin films.     

Nonlinear dynamic structure rearrangement of vortexlike domain walls in magnetic films with in-plane anisotropy

The nonlinear dynamic behavior of vortexlike domain walls in magnetic uniaxial films having an in-plane anisotropy was investigated within a rigorous micromagnetic approach in the framework of a two-dimensional magnetization distribution by numerically solving the Landau–Lifshitz equations (with the Gilbert damping parameter) with allowance for all the main interactions, including the dipole–dipole one. The studies were carried out on magnetic soft films with an anisotropy axis lying in their plane in a dc magnetic field parallel to an easy axis and a pulsed magnetic field normal to it. New possibilities for controlling the nonlinear dynamic rearrangement of the internal structure of domain walls and their velocities in fields both above and below the critical field are established. The wall motion in the field above the critical one is nonstationary.     

Model for domain wall avalanches in ferromagnetic thin films

The Barkhausen jumps or avalanches in magnetic domain-walls motion between successive pinned configurations, due the competition among magnetic external driving force and substrum quenched disorder, appear in bulk materials and thin films. We introduce a model based in rules for the domain wall evolution of ferromagnetic media with exchange or short-range interactions, that include disorder and driving force effects. We simulate in 2-dimensions with Monte Carlo dynamics, calculate numerically distributions of sizes and durations of the jumps and find power-law critical behavior. The avalanche-size exponent is in excellent agreement with experimental results for thin films and is close to predictions of the other models, such as like random-field and random-bond disorder, or functional renormalization group. The model allows us to review current issues in the study of avalanches motion of the magnetic domain walls in thin films with ferromagnetic interactions and opens a new approach to describe these materials with dipolar or long-range interactions.     

Domain wall creep in epitaxial ferroelectric Pb(Zr(0.2)Ti(0.08)O(3) thin films

Ferroelectric switching and nanoscale domain dynamics were investigated using atomic force microscopy on monocrystalline Pb(Zr(0.2)Ti(0.8))O(3) thin films. Measurements of domain size versus writing time reveal a two-step domain growth mechanism, in which initial nucleation is followed by radial domain wall motion perpendicular to the polarization direction. The electric field dependence of the domain wall velocity demonstrates that domain wall motion in ferroelectric thin films is a creep process, with the critical exponent mu close to 1. The dimensionality of the films suggests that disorder is at the origin of the observed creep behavior.     

The stochastic nature of the domain wall motion along high perpendicular anisotropy strips with surface roughness

The domain wall dynamics along thin ferromagnetic strips with high perpendicular magnetocrystalline anisotropy driven by either magnetic fields or spin-polarized currents is theoretically analyzed by means of full micromagnetic simulations and a one-dimensional model, including both surface roughness and thermal effects. At finite temperature, the results show a field dependence of the domain wall velocity in good qualitative agreement with available experimental measurements, indicating a low field, low velocity creep regime, and a high field, linear regime separated by a smeared depinning region. Similar behaviors were also observed under applied currents. In the low current creep regime the velocity-current characteristic does not depend significantly on the non-adiabaticity. At high currents, where the domain wall velocity becomes insensitive to surface pinning, the domain wall shows a precessional behavior even when the non-adiabatic parameter is equal to the Gilbert damping. These analyses confirm the relevance of both thermal fluctuations and surface roughness for the domain wall dynamics, and that complete micromagnetic modeling and one-dimensional studies taking into account these effects are required to interpret the experimental measurements in order to get a better understanding of the origin, the role and the magnitude of the non-adiabaticity.     

Nonlinear structural mechanics based modeling of carbon nanotube deformation

A nonlinear structural mechanics based approach for modeling the structure and the deformation of single-wall and multiwall carbon nanotubes (CNTs) is presented. Individual tubes are modeled using shell finite elements, where a specific pairing of elastic properties and mechanical thickness of the tube wall is identified to enable successful modeling with shell theory. The effects of van der Waals forces are simulated with special interaction elements. This new CNT modeling approach is verified by comparison with molecular dynamics simulations and high-resolution micrographs available in the literature. The mechanics of wrinkling of multiwall CNTs are studied, demonstrating the role of the multiwalled shell structure and interwall van der Waals interactions in governing buckling and postbuckling behavior.     

Domain wall roughness in epitaxial ferroelectric PbZr0.2Ti0.8O3 thin films

The static configuration of ferroelectric domain walls was investigated using atomic force microscopy on epitaxial PbZr(0.2)Ti(0.8)O(3) thin films. Measurements of domain wall roughness reveal a power-law growth of the correlation function of relative displacements B(L) alpha L(2zeta) with zeta approximately 0.26 at short length scales L, followed by an apparent saturation at large L. In the same films, the dynamic exponent mu was found to be approximately 0.6 from independent measurements of domain wall creep. These results give an effective domain wall dimensionality of d = 2.5, in good agreement with theoretical calculations for a two-dimensional elastic interface in the presence of random-bond disorder and long-range dipolar interactions.     

Domain wall solitons in quantum electron plasmas

We show the existence of new stationary solutions in the form of domain wall soliton in the nonlinear Schrödinger-Poisson equations describing the dynamics of quantum electron plasmas. It is found that the domain wall soliton exists at strong coupling constant regime and shows a different dynamical behavior in comparison with the previously found dark and gray solitons. The robustness and the conservation of the energy of the domain wall solitons is demonstrated by numerical simulations.     

Domain wall dynamics in ferromagnets

The main results of studying the linear and nonlinear dynamics of a domain wall in ferromagnets are presented beginning with the first publications. The experimental data obtained on polycrystals, single crystals, and films differing in terms of their anisotropy, as well as on magnetic nanostructures, are compared with theoretical results obtained by various methods.     

Editorial: Ecological complex systems

Main aim of this topical issue is to report recent advances in noisy nonequilibrium processes useful to describe the dynamics of ecological systems and to address the mechanisms of spatio-temporal pattern formation in ecology both from the experimental and theoretical points of view. This is in order to understand the dynamical behaviour of ecological complex systems through the interplay between nonlinearity, noise, random and periodic environmental interactions. Discovering the microscopic rules and the local interactions which lead to the emergence of specific global patterns or global dynamical behaviour and the noise’s role in the nonlinear dynamics is an important, key aspect to understand and then to model ecological complex systems.     

Dynamics of vortexlike domain walls in triaxial magnetic films with the Goss orientation of the surface

The stationary dynamics of vortexlike domain walls in films with three magnetic axes and Goss orientation of the surface is studied for the first time with a micromagnetic method that exactly takes into account all basic types of interaction (including dipole-dipole interaction). Consideration is carried out using a 2D model of magnetization distribution by numerically solving Landau and Lifshitz’s nonlinear equations with attenuation in the Gilbert form. Dynamic configurations of domain walls are established, and the dependences of the domain wall velocity on an applied magnetic field, damping parameter, and magnetic film thickness are found.     

Effect of the potential function and strain rate on mechanical behavior of the single crystal Ni-based alloys: A molecular dynamics study

Molecular dynamics has been widely used to study the fundamental mechanism of Ni-based superalloys. However, the effect of the potential function and strain rate on mechanical behavior has rarely been mentioned in the previous molecular dynamics studies. In the present work, we show that the potential function of molecular dynamics can dramatically influence the simulation results of single crystal Ni-based superalloys. The microstructure and mechanical behavior of single crystal Ni-based superalloys under four commonly used potential functions are systematically compared. A most suitable potential function for the mechanical deformation is critically selected, and based on it, the role of strain rate on the mechanical deformation is investigated.     

Domain dynamics and magneto-electronics in magnetic thin films and nanowires

Recent theoretical results are highlighted that illustrate some of the interesting phenomena associated with magnetic domain boundary walls. Two problems will be discussed: dynamics associated with domain wall propagation, and effects related to spin transport through domain walls. For the first problem, an example of wall interaction and motion through a random potential will be discussed with reference to the general problem of roughening transitions. Images of domain dynamics in thin films of ion irradiated Co reveal a de-roughening transition associated with long range magnetostatic interactions between pairs of domain walls. A scaling theory of this transition is described in which a curious type of dynamic hysteresis can occur. For the second problem, results from calculations of ballistic charge and spin transport through domain boundary walls are discussed in terms of an effective circuit model.     

Microstructural and domain effects in epitaxial CoFe2O4 films on MgO with perpendicular magnetic anisotropy

CoFe₂O₄ (CFO) epitaxial thin films of various thicknesses were grown on MgO substrates using the pulsed electron-beam deposition technique. The films have excellent in-plane coherence with the substrate, exhibit layer-by-layer growth and have well-defined thickness fringes in x-ray diffraction measurements. Atomic force microscopy (AFM) measurements indicate that misfit dislocations form in thicker films and the critical thickness for the dislocation formation is estimated. Perpendicular magnetic anisotropy in CFO due to epitaxial in-plane tensile strain from the substrate was found. A stripe-like domain structure in the demagnetized state is demonstrated using magnetic force microscopy (MFM), in agreement with previous predictions. Coercivity increased in thicker films, which is explained by domain wall pinning due to misfit dislocations at the CFO/MgO interface.     

Automatic ridgelet image enhancement algorithm for road crack image based on fuzzy entropy and fuzzy divergence

True estimation of the boundary of a road crack and its size is a major task for its automatic detection. The improvement of visual effects of a road image is necessary for such a task. Therefore, we propose an automatic ridgelet image enhancement algorithm. A nonlinear function plays an important role in the enhancement algorithm in the ridgelet domain of an image. However, it is difficult to adjust the parameters of the nonlinear function adaptively with the variation of the road crack image input. Based on the fuzzy entropy criterion, we introduce two fuzzy divergences and two supplementary linear combinations between the fuzzy entropy and two fuzzy divergences as new measurements to solve the threshold segmentation problem in the ridgelet domain. According to the distribution histogram of magnitudes of the ridgelet high-frequency coefficients, we obtain the optimal segmentation thresholds that act as the parameters of the nonlinear function by using the maximum or minimum measurements of fuzzy entropy and fuzzy divergence, respectively. The self-adaptive nonlinear function makes it possible to realize the automatic enhancement of a road crack image. Experimental results show that our image enhancement algorithm can effectively enhance the global and local contrastive effects on road crack images.     

Effect of a pulsed magnetic field on the nonlinear dynamics of vortexlike domain walls in magnetic films

The Landau-Lifshitz equation is numerically solved to study the nonlinear dynamic behavior of domain walls with the 2D vortexlike magnetization distribution in magnetically uniaxial films that have in-plane anisotropy and are exposed to a pulsed magnetic field. It is shown that a pulsed magnetic field H _p may induce transitions between various steady wall motions that differ in magnetization distribution. Solitary rectangular pulses, as well as a regular train of rectangular pulses, may be used to control the period of nonlinear dynamic transformations of the wall internal structure and the related period of variation of the wall velocity.     

Mechanically driven domain wall movement in magnetoelastic nanomagnets

Magnetic domain walls are fundamental objects arising in ferromagnetic materials, largely investigated both through micromagnetic simulations and experiments. While current- and field-based techniques for inducing domain wall propagation have been widely studied for fundamental understanding and application-oriented purposes, the possibility to manipulate domain walls using mechanical stress in magnetoelastic materials has only recently drawn interest. Here, a complete analytical model describing stress-induced transverse domain wall movement in ferromagnetic nanostripe with variable cross-section is presented. This approach yields a nonlinear integro-differential equation describing the magnetization field. Its numerical implementation, based on the nonlinear relaxation method, demonstrates the possibility to precisely control the position of a domain wall through mechanical action.     

Theory of giant electromechanical response from ferroelectric bilayers with polydomain structures due to interlayer and interdomain coupling

The effect of interdomain ferroelastic coupling in ferroic multilayers is investigated theoretically. Specifically, we use nonlinear thermodynamics to analyze a heteroepitaxial ferroelectric PbZrxTi1-xO3 (PZT) bilayer consisting of (001) tetragonal (T) PZT and (001) rhombohedral (R) PZT films. We predict for certain misfit strain regimes that interlayer and interdomain interactions lead to an adaptive domain structure in both the T and R layers and result in significant enhancements in the piezoelectricity compared to single-layer films. Our results demonstrate that electrostatic, magnetostatic, and elastic interactions in ferroic multilayers can be a generic route to generate ultrahigh susceptibilities.     

Agreement dynamics on interaction networks with diverse topologies

We review the behavior of a recently introduced model of agreement dynamics, called the "Naming Game." This model describes the self-organized emergence of linguistic conventions and the establishment of simple communication systems in a population of agents with pairwise local interactions. The mechanisms of convergence towards agreement strongly depend on the network of possible interactions between the agents. In particular, the mean-field case in which all agents communicate with all the others is not efficient, since a large temporary memory is requested for the agents. On the other hand, regular lattice topologies lead to a fast local convergence but to a slow global dynamics similar to coarsening phenomena. The embedding of the agents in a small-world network represents an interesting tradeoff: a local consensus is easily reached, while the long-range links allow to bypass coarsening-like convergence. We also consider alternative adaptive strategies which can lead to faster global convergence.     

Anomalous magnetization processes and non-symmetrical domain wall displacements in L10 FePt particulate films

Anomalous magnetization processes and non-symmetrical domain wall displacements in the minor loop of L1₀ FePt particulate films were investigated by magnetization measurements and in situ magnetic force microscopy. Magnetization (M) decreases dramatically on increasing the magnetic field to ∼3 kOe after which M becomes small and constant in the range of 5–20 kOe as observed in the successive measurement of minor loops. The domain wall displacement is non-symmetrical with respect to the field direction. The anomalous magnetization behavior was attributed to the non-symmetrical domain wall displacement and large magnetic field required for domain wall nucleation. Energy calculations from modeling suggest that non-symmetrical domain wall displacement is caused by the existence of metastable domains in which the domain edges are stuck to the particle boundaries.