Wetting phenomena are ubiquitous in nature and technology. A solid substrate exposed to the environment is almost invariably covered by a layer of fluid material. In this review, the surface forces that lead to wetting are considered, and the equilibrium surface coverage of a substrate in contact with a drop of liquid. Depending on the nature of the surface forces involved, different scenarios for wetting phase transitions are possible; recent progress allows us to relate the critical exponents directly to the nature of the surface forces which lead to the different wetting scenarios. Thermal fluctuation effects, which can be greatly enhanced for wetting of geometrically or chemically structured substrates, and are much stronger in colloidal suspensions, modify the adsorption singularities. Macroscopic descriptions and microscopic theories have been developed to understand and predict wetting behavior relevant to microfluidics and nanofluidics applications. Then the dynamics of wetting is examined. A drop, placed on a substrate which it wets, spreads out to form a film. Conversely, a nonwetted substrate previously covered by a film dewets upon an appropriate change of system parameters. The hydrodynamics of both wetting and dewetting is influenced by the presence of the three-phase contact line separating "wet" regions from those that are either dry or covered by a microscopic film only. Recent theoretical, experimental, and numerical progress in the description of moving contact line dynamics are reviewed, and its relation to the thermodynamics of wetting is explored. In addition, recent progress on rough surfaces is surveyed. The anchoring of contact lines and contact angle hysteresis are explored resulting from surface inhomogeneities. Further, new ways to mold wetting characteristics according to technological constraints are discussed, for example, the use of patterned surfaces, surfactants, or complex fluids.

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Wetting and Spreading

Domains in ferroelectrics were considered to be well understood by the middle of the last century: They were generally rectilinear, and their walls were Ising-like. Their simplicity stood in stark contrast to the more complex Bloch walls or N\'eel walls in magnets. Only within the past decade and with the introduction of atomic-resolution studies via transmission electron microscopy, electron holography, and atomic force microscopy with polarization sensitivity has their real complexity been revealed. Additional phenomena appear in recent studies, especially of magnetoelectric materials, where functional properties inside domain walls are being directly measured. In this paper these studies are reviewed, focusing attention on ferroelectrics and multiferroics but making comparisons where possible with magnetic domains and domain walls. An important part of this review will concern device applications, with the spotlight on a new paradigm of ferroic devices where the domain walls, rather than the domains, are the active element. Here magnetic wall microelectronics is already in full swing, owing largely to the work of Cowburn and of Parkin and their colleagues. These devices exploit the high domain wall mobilities in magnets and their resulting high velocities, which can be supersonic, as shown by Kreines' and co-workers 30 years ago. By comparison, nanoelectronic devices employing ferroelectric domain walls often have slower domain wall speeds, but may exploit their smaller size as well as their different functional properties. These include domain wall conductivity (metallic or even superconducting in bulk insulating or semiconducting oxides) and the fact that domain walls can be ferromagnetic while the surrounding domains are not.

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Domain wall nanoelectronics

TOPICAL REVIEW: Supermagnetism

Brownian motion is a continuum scaling limit for a wide class of random processes, and there has been great success in developing a theory for its properties (such as distribution functions or regularity) and expanding the breadth of its universality class. Over the past 25 years a new universality class has emerged to describe a host of important physical and probabilistic models (including one-dimensional interface growth processes, interacting particle systems and polymers in random environments) which display characteristic, though unusual, scalings and new statistics. This class is called the Kardar–Parisi–Zhang (KPZ) universality class and underlying it is, again, a continuum object — a non-linear stochastic partial differential equation — known as the KPZ equation. The purpose of this survey is to explain the context for, as well as the content of a number of mathematical breakthroughs which have culminated in the derivation of the exact formula for the distribution function of the KPZ equation started with narrow wedge initial data. In particular we emphasize three topics: (1) The approximation of the KPZ equation through the weakly asymmetric simple exclusion process; (2) The derivation of the exact one-point distribution of the solution to the KPZ equation with narrow wedge initial data; (3) Connections with directed polymers in random media. As the purpose of this article is to survey and review, we make precise statements but provide only heuristic arguments with indications of the technical complexities necessary to make such arguments mathematically rigorous.

The kardar-parisi-zhang equation and universality class

The current status and prospects of research on ferromagnetism in semiconductors are reviewed The question of the origin of ferromagnetism in europium chalcogenides, chromium spinels and, particularly, in diluted magnetic semiconductors is addressed The nature of electronic states derived from 3d of magnetic impurities is discussed in some details Results of a quantitative comparison between experimental and theoretical results, notably for Mn-based III-V and II-VI compounds, are presented This comparison demonstrates that the current theory of the exchange interactions mediated by holes in the valence band describes correctly the values of Curie temperatures T_C magnetic anisotropy, domain structure, and magnetic circular dichroism On this basis, chemical trends are examined and show to lead to the prediction of semiconductor systems with T_C that may exceed room temperature, an expectation that are being confirmed by recent findings Results for materials containing magnetic ions other than Mn are also presented emphasizing that the double exchange involving hoping through d states may operate in those systems

Ferromagnetic semiconductors

We have studied the motion of a magnetic domain wall (MDW) driven by a magnetic field H in a 2D ultrathin Pt/Co/Pt film showing perpendicular anisotropy and quenched disorder. MDW velocity measurements down to the so called creep regime show that the average energy barrier scales as $(1/H{)}^{\ensuremath{\mu}}$ with $\ensuremath{\mu}\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}0.24\ifmmode\pm\else\textpm\fi{}0.04$ and that the correlation function along a MDW is governed by a wandering exponent $\ensuremath{\zeta}\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}0.69\ifmmode\pm\else\textpm\fi{}0.07$, in very good agreement with theories giving $\ensuremath{\mu}\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}0.25$ and $\ensuremath{\zeta}\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}2/3$. This is the first direct measurement of the creep regime for a moving interface in a disordered medium.

Domain wall creep in an ising ultrathin magnetic film

Although crystals are usually quite stable, they are sensitive to a disordered environment: even an infinitesimal amount of impurities can lead to the destruction of crystalline order. The resulting state of matter has been a long-standing puzzle. Until recently it was believed to be an amorphous state in which the crystal would break into 'crystallites'. But a different theory predicts the existence of a novel phase of matter: the so-called Bragg glass, which is a glass and yet nearly as ordered as a perfect crystal. The 'lattice' of vortices that contain magnetic flux in type II superconductors provide a good system to investigate these ideas. Here we show that neutron-diffraction data of the vortex lattice provides unambiguous evidence for a weak, power-law decay of the crystalline order characteristic of a Bragg glass. The theory also predicts accurately the electrical transport properties of superconductors; it naturally explains the observed phase transitions and the dramatic jumps in the critical current associated with the melting of the Bragg glass. Moreover, the model explains experiments as diverse as X-ray scattering in disordered liquid crystals and the conductivity of electronic crystals.

A Bragg glass phase in the vortex lattice of a type II superconductor

We study a D-dimensional interface driven in a disordered medium. We derive finite-temperature and velocity functional renormalization group (FRG) equations, valid in a = 4 − D expansion. These equations allow in principle for a complete study of the velocity v vs. applied force density f characteristics. We focus here on the creep regime at finite temperature and small velocity. We show how the FRG approach gives the form of the v-f characteristics in this regime, and in particular the creep exponent, obtained previously only through phenomenological scaling arguments.

http://iopscience.iop.org/article/10.1209/epl/i1998-00443-7/pdf

Creep via dynamical functional renormalization group

We study the stability of the dislocation-free Bragg glass phase in a layered geometry consisting of coupled parallel planes of d = 1 + 1 vortex lines lying within each plane, in the presence of impurity disorder. Using renormalization group, replica variational calculations and physical arguments, we find that at temperatures T < TG the 3D Bragg glass phase is always stable for weak disorder. It undergoes a weakly first-order transition into a decoupled 2D vortex glass upon increase of disorder.

Stability of the Bragg glass phase in a layered geometry

Using one-loop functional RG we study two problems of pinned elastic systems away from their equilibrium or steady states. The critical regime of the depinning transition is investigated starting from a flat initial condition. It exhibits non-trivial two-time dynamical regimes with exponents and scaling functions obtained in a dimensional expansion. The aging and equilibrium dynamics of the super-rough glass phase of the random Sine-Gordon model at low temperature is found to be characterized by a single dynamical exponent z ≈ c/T, where c compares well with recent numerical work. This agrees with the thermal boundary layer picture of pinned systems.

http://www.th.u-psud.fr/page_perso/Schehr/Sch_LeDou_EPL_05.pdf

P. Le Doussal

Papers

Domain wall creep in an ising ultrathin magnetic film

A Bragg glass phase in the vortex lattice of a type II superconductor

Creep via dynamical functional renormalization group

Stability of the Bragg glass phase in a layered geometry

Functional renormalization for pinned elastic systems away from their steady states