On the thickness of domain walls in ferroelectrics and ferroelastics

Ferroelastic and ferroelectric domain walls are commonly described by wall profiles of the tanh(x/w)-type. We argue that this profile is still a good approximation if higher-order gradient energies are considered. Such energies are relevant for phase transitions close to structural incommensurations and also for phase transitions with dominant elastic interactions. Their effect on the wall profile is to influence the effective wall thickness. Positive gradient energies tend to widen domain walls beyond the values predicted in classic Landau-Ginzburg theory.     

Microscopic and macroscopic signatures of antiferromagnetic domain walls

Magnetotransport measurements on small single crystals of Cr, the elemental antiferromagnet, reveal the hysteretic thermodynamics of the domain structure. The temperature dependence of the transport coefficients is directly correlated with the real-space evolution of the domain configuration as recorded by x-ray microprobe imaging, revealing the effect of antiferromagnetic domain walls on electron transport. A single antiferromagnetic domain wall interface resistance is deduced to be of order 5 x 10(-5) mu Omega cm(2) at a temperature of 100 K.     

Macroscopic quantum resonance tunneling of domain walls

Results are presented of a theoretical investigation of the tunneling of magnetic domain walls, taking account of the interaction of the walls with the thermal system of the crystal. It is shown that thermal stimulation increases considerably the transmittance of the potential barriers during propagation of walls through a crystal. Fiz. Tverd. Tela (St. Petersburg) 40, 1855–1860 (October 1998)     

Microscopic insight into temperature-graded ferroelectrics

A microscopic approach based on the first-principles effective Hamiltonian is developed to study the polarization response in temperature-graded ferroelectrics. This approach has been applied to the case of (Ba(0.75)Sr(0.25))TiO? alloy. A comparison of the computational results with available experimental data attests to the remarkable accuracy of the present approach. Our computations reveal a strong anisotropy in the response of polarization to the temperature gradient (TG). In particular, the polarization offset along the direction of TG is an order of magnitude lower than in the perpendicular direction. The large as well as the small TGs are considered and found to yield qualitatively different polarization field responses. Among other striking findings are (i) the coexistence of different phases in chemically homogeneous regions, (ii) formation of low-symmetry phases, and (iii) thermally controlled polarization rotation.     

Lattice-scale domain wall dynamics in ferroelectrics

Ferroelectric domain walls are atomically thin, and consequently their dynamics are sensitive to the periodic potential of the underlying lattice. Despite their central role in domain dynamics, lattice-scale effects have never been directly observed. We investigate local domain dynamics in thin film ferroelectrics using atomic-force microscopy. Upon combined dc and ac electric driving, fluctuations in the local piezoresponse are observed. Fourier analysis of the fluctuations reveals the presence of narrow band and broad band noise, and Barkhausen jumps. The narrow band noise is attributed to dynamics associated with lattice-scale pinning and is reproduced by a simple physical model.     

Surface electromagnetic waves on the domain boundaries in ferroelectrics

It is argued that low-frequency surface electromagnetic waves can propagate along the domain boundary in ferroelectrics. These waves cause the oscillatory motion of the boundary.     

Minkowski domain walls in hyperbolic metamaterials

Minkowski domain walls are being actively considered in gravitation theory. They may form during a vacuum phase transition, or as a result of braneworld collision. Despite having interesting physical properties, Minkowski domain walls had remained in the theoretical domain only since their first introduction a few decades ago. Here we demonstrate how to make an electromagnetic analogue of a Minkowski domain wall using hyperbolic metamaterials. We analyze electromagnetic field behavior at the wall, and present a simple experimental model of “Minkowski domain wall” formation due to “collision” of two Minkowski spaces.     

Electromechanical cracking in ferroelectrics driven by large scale domain switching

Experimental results indicate three regimes for cracking in a ferroelectric double cantilever beam (DCB) under combined electromechanical loading. In the loading, the maximum amplitude of the applied electric field reaches almost twice the coercive field of ferroelectrics. Thus, the model of small scale domain switching is not applicable any more, which is dictated only by the singular term of the crack tip field. In the DCB test, a large or global scale domain switching takes place instead, which is driven...     

Giant domain walls in a ferromagnet

Giant domain walls with a width of ∼7 μm are observed on the surface of a ferromagnet — an amorphous magnetically soft alloy. A magnetooptic investigation shows that the walls have a Néel structure in the subsurface region. The subsurface structure of these walls differs substantially from that of the narrower walls previously observed in iron, Permalloy, and amorphous materials. According to the theoretical model of Scheinfein and co-workers, which relates the width of an asymmetric Bloch wall in the bulk with the width at the surface, the width of the wall in the bulk is estimated to be 3–4 μm. Pis’ma Zh. éksp. Teor. Fiz. 70, No. 8, 528–530 (25 October 1999)     

Magnetostrictive domain walls in antiferromagnetic NiO

We report high-resolution observations of antiferromagnetic (AF) domain walls at the surface of NiO and determine the typical width of AF walls in this material to be of the order of 150 nm. We observe a number of different types of domain walls, including double walls caused by long-range interaction between walls. We describe the observed wall profiles by a model containing the exchange interaction and magnetostriction as basic ingredients. The good agreement of this model with experiment shows that the formation of walls between antiferromagnetic domains in NiO and their properties are dominated by magnetoelastic interactions.     

Vortex domain walls in helical magnets

We show that helical magnets exhibit a nontrivial type of domain wall consisting of a regular array of vortex lines, except for a few distinguished orientations. This result follows from topological consideration and is independent of the microscopic models. We used simple models to calculate the shape and energetics of vortex walls in centrosymmetric and noncentrosymmetric crystals. Vortices are strongly anisotropic, deviating from the conventional Berezinskii-Kosterlitz-Thouless form. The width of the domain walls depend only weakly on the magnetic anisotropy, in contrast to ferromagnets and antiferromagnets. We show that vortex walls can be driven by external currents and in multiferroics also by electric fields.     

Zero modes in nonlocal domain walls

We generalize the Callan–Harvey mechanism to the case of actions with a nonlocal mass term for the fermions. Using a (2+1)-dimensional model as a concrete example, we show that both the existence and properties of localized zero modes can also be consistently studied when the mass is nonlocal. We derive some general properties from a study of the resulting integral equations, and consider their realization in a concrete example.     

A model of elastic and relaxation polarization of ferroelectrics with a distribution of domain walls over relaxation times and natural frequencies

A model that takes into account the distribution of domain walls over natural frequencies and relaxation times (or activation energies) is proposed. It is demonstrated that the function of the distribution of domain walls over natural frequencies and relaxation times ?(ω₀, τ) (or potential barriers ?(ω₀, W ₀)) can be calculated from the spectral-temperature dependence of the complex permittivity ?*(ω, T).     

Domains and domain walls in multiferroics

Multiferroics are gathering solid-state matter in which several types of orders are simultaneously allowed, as ferroelectricity, ferromagnetism (or antiferromagnetism), ferroelasticity, or ferrotoroidicity. Among all, the ferroelectric/ferromagnetic couple is the most intensively studied because of potential applications in novel low-power magnetoelectric devices. Switching of one order thanks to the other necessarily proceeds via the nucleation and growth of coupled domains. This review is an introduction to the basics of ferroelectric/ferromagnetic domain formation and to the recent microscopy techniques devoted to domains imaging, providing new insights into the archetypal multiferroic domain morphologies. Some relevant examples are also given to illustrate some of the unexpected properties of domain walls, as well as the way these domain walls can be manipulated altogether thanks to various types of magnetoelectric coupling.     

Permissible domain walls in ferroelectric species

A previously developed method makes it possible to determine the orientations of domain walls in ferroelectrics which are permissible under the condition that neighbouring domains must be mechanically compatible. In this paper, the method has been applied to all 88 ferroelectric species in which the polarization is the parameter of the transition. Types of permissible walls and their orientations are listed in form of tables. Cases where no walls fulfil the compatibility conditions are shown.     

Leptogenesis with left-right domain walls

The presence of domain walls separating regions of unbrokenSU(2)_L andSU(2)_R is shown to provide necessary conditions for leptogenesis which converts later to the observed baryon asymmetry. The strength of lepton number violation is related to the Majorana neutrino mass and hence related to current bounds on light neutrino masses. Thus the observed neutrino masses and the baryon asymmetry can be used to constrain the scale of left-right symmetry breaking.     

Cosmic strings and domain walls

Phase transitions in the early universe can give rise to microscopic topological defects: vacuum domain walls, strings, walls bounded by strings, and monopoles connected by strings. This article reviews the formation, physical properties and the cosmological evolution of various defects. A particular attention is paid to strings and their cosmological consequences, including the string scenario of galaxy formation and possible observational effects of strings.