Evolution Of Domain Walls Research Articles

Electroweak Baryogenesis with Embedded Domain Walls

We consider electroweak baryogenesis mediated by embedded domain walls. Embedded domain walls originating from a symmetry breaking phase transition are stabilized by thermal plasma effects, so that the electroweak symmetry is unbroken in their cores. For this reason, the cosmological evolution of such domain walls can generate a sufficiently large baryon asymmetry, irrespective of the order of the electroweak phase transition. For embedded domain walls, the condition that the energy of the universe not be dominated by the energy of the domain walls is relaxed significantly, and it is shown to be compatible with our scenario of electroweak baryogenesis.

Aging of the field-induced asymmetry in a disordered ferroelectric

The isothermal aging of the asymmetry induced in the disordered dielectric crystal \(\mbox{KTa}_{1-x} \mbox{Nb}_{x} \mbox{O}_{3} \) (x=0.027) submitted to the biasing electric field E, is investigated. To this end, the response of the complex dielectric constant to infinitesimal field changes \(\delta{\bf E}\), applied to the sample after a variable aging delay, has been measured for different magnitudes of E and after different aging delays. Two different experimental procedures have been used: in both cases the response strongly depends on the time spent under field. For short aging delays, the response has a strong contribution proportional to δE and a weak quadratic contribution proportional to \(\left({\delta E}\right)^2\). As time elapses, the linear and the quadratic contributions age in opposite ways: the former decreases whereas the latter increases. This paradoxical behaviour is analyzed in the framework of a model which attributes aging and the related effects (rejuvenation, memory) to the evolution of polarization domain walls: the decrease of the linear contribution is related to the decrease of the total wall area, while the increase of the quadratic term is attributed to wall reconformations.

Ground state and constrained domain walls in Gd∕Fe multilayers

The magnetic ground state of antiferromagnetically coupled Gd∕Fe multilayers and the evolution of in-plane domain walls is modeled with micromagnetics. The twisted state is characterized by a rapid decrease of the interface angle with increasing magnetic field. We found that for certain ratios MFe:MGd, the twisted state is already present at low fields. However, the magnetic ground state is not only determined by the ratio MFe:MGd but also by the thicknesses of the layers; that is by the total moments of the layer. The dependence of the magnetic ground state is explained by the amount of overlap of the domain walls at the interface. Thicker layers suppress the Fe-aligned and the Gd-aligned state in favor of the twisted state. On the other hand, ultrathin layers exclude the twisted state, since wider domain walls cannot form in these ultrathin layers.

A Meso-Electro-Mechanical Model for PMN-PT-BT Ceramics Behavior

A three-dimensional, meso-electro-mechanical model has been formulated for description of PMN-PT-BT ceramics. Unlike the experimentally fit models and phenomenological models which are based on state variables and/or empirical relationships, this fully coupled, computational mesomechanics model for polycrystalline PMN-PT-BT ceramics is developed based on considerations of constitutive behavior of single crystals. Specifically, domain wall nucleation and evolution rate equations are proposed in this work to describe the nonlinear hysteresis behavior of these ceramics near the phase transition temperature with maximum permittivity. Comparisons of hysteresis loops under different temperature conditions between testing results and the present simulation show good agreement. Effects of compressive stresses on relationships of strain versus electric field are also discussed.

Dependence of domain wall dynamics on background wave number.

We report on the growth of domains of standing waves in electroconvection in a nematic liquid crystal, focusing on the evolution of domain walls. An ac voltage is applied to the system, forming an initial state that consists of traveling striped patterns with two different orientations, zig and zag rolls. The standing waves are generated by suddenly applying a periodic modulation of the amplitude of the applied voltage that is approximately resonant with the traveling frequency of the pattern. By varying the modulation frequency, we are able to vary the steady-state, average wave number. We characterize the evolution of the domain walls as a function of the average background wave number by measuring the total area and length of domain walls present in the system as a function of time. We find that as the background wave number is varied away from the "natural" wave number for the pattern, the evolution of the domain walls occurs at a faster rate.

Ground state and constrained domain walls in Gd/Fe multilayers

The magnetic ground state of Gd/Fe multilayers and the evolution of domain walls is modelled with micromagnetics. The ground state is determined not only by the ratio M s Fe: M s Gd but also by the thickness of the layers. Thicker layers can prevent the Fe aligned state.

Differentiability breaking and Schwarz theorem violation in an aging material

Dielectric constant measurements are performed in the frequency range from 1 kHz to 1 MHz on a disordered material with ferroelectric properties $({\mathrm{KTa}}_{1\ensuremath{-}x}{\mathrm{Nb}}_{x}{\mathrm{O}}_{3}$ crystals) after isothermal aging at the plateau temperature ${T}_{\mathrm{pl}}\ensuremath{\cong}10\mathrm{K}.$ They show that the derivatives of the complex capacitance with respect to temperature and time present two very peculiar behaviors. The first point is that the first and second derivatives against temperature are not equal on the two sides of ${T}_{\mathrm{pl}};$ this is differentiability breaking. The second point is that the two crossed second derivatives against temperature and time are not equal (indeed they have opposite signs); this is a violation of Schwarz theorem. These results are obtained on both the real part and the imaginary part of the capacitance. A model, initially imagined for aging and memory of aging, attributes the time-dependent properties to the evolution (growth and reconformations) of the polarization domain walls. It is shown that it can also explain the observed differentiability breaking (and in particular its logarithmic increase with the plateau duration ${t}_{\mathrm{pl}})$ and the violation of Schwarz theorem.

Evolution of domain walls in 6H- and 4H-SiC single crystals

From the study of 6H and 4H single crystals, grown under various conditions on Si- and C- terminated seed surfaces, two types of defects with different slit length are discussed. Short slits with a length in the submillimetre range are spread between micropipes in an advanced growth stage. Their generation is correlated to micropipe agglomeration. The long slits up to some millimetres, which are associated with dislocation bundles in the basal plane, are correlated to polytype domain walls. In this region the slit formation seems to be favourable similar to the Frank mechanism of micropipe generation (Acta Crystallogr. 4 (1951) 479).

30 MHz ultrasonic attenuation of TiNi single crystal associated with B2-B19' martensitic transformation and twin boundaries

Ultrasonic attenuation was measured for the first time at megahertz range (30MHz) for a TiNi single crystal, which undergoes B2-B19' (cubic-monoclinic) martensitic transformation. A sharp attenuation peak was found at transformation temperature region (two-phase region), which was associated with the structural transformation and drastic domain wall evolution in the two-phase region. Besides, a very broad peak below the transformation temperature (i.e., in martensite state) was also found, which can be ascribed to twin boundary motion at megahertz range. This broad peak has a high internal friction level of 0.0027. Considering that this alloy also has a high damping capacity at low frequency, we can deduce that TiNi martensite is an excellent high damping material in an extremely wide frequency range and wide temperature range.

Scaling properties of magnetic domain walls in Pt/Co/Pt trilayers on MgO (1 1 1)

We present a scaling analysis of the time evolution of domain walls in ultrathin magnetic films that are subject to different forms of uncorrelated and correlated disorder caused by the microstructure of the underlying template. The study is performed on ultrafine modulated Pt/Co/Pt trilayers grown on as-supplied and structured MgO (1 1 1) substrates employing polar Kerr microscopy for the imaging of the magnetic domains.

Evolution of domain walls in ferroelectric solids

The evolution of domain walls in ferroelectrics is analyzed. The placement field and the polarization vector field accounting for the microstructure of ferroelectric domains describe the body. Measures of interaction are associated to the polarization field. They have electromechanical nature and are balanced by appropriate equations. The deduction of the evolution equations for strongly anisotropic domain walls and corners (junctions among domain walls) is the main result of this paper. The model is applied to typical cases and the explicit solutions obtained fit the available experimental results on Barium Titanate. An analogous agreement is found also at the junctions.

Formation and evolution of charged domain walls in congruent lithium niobate

We present experimental evidence of the formation of stable charged domain walls (CDWs) in congruent lithium niobate during switching. CDW evolution under the action of field pulses was in situ visualized. CDW boundary motion velocity is about 60 μm/s at 20 kV/mm. Relief of CDW strongly depends on applied field. Dielectric response in the presence of CDW demonstrates the pronounced frequency dependence in the range 50–150 °C. We propose the mechanism of CDW self-maintained propagation governed by self-consistent electrostatic interaction between the wall’s steps.

Topological defects: Fossils of an anisotropic era?

We consider the evolution of domain walls produced during an anisotropic phase in the very early universe, showing that the resulting network can be very anisotropic. If the domain walls are produced during an inflationary era, the network will soon freeze-out in comoving coordinates retaining the imprints of the anisotropic regime, even though inflation makes the universe isotropic. Only at late times, when the typical size of the major axis of the domain walls becomes smaller than the Hubble radius, does the network evolve rapidly towards isotropy. Hence, we may hope to see imprints of the anisotropic era if by today the typical size of the major axis of the domain walls is of the order of the Hubble radius or if the walls reentered it only very recently. Depending on the mass scale of the domain walls, there is also the possibility that they reenter at earlier times, but their evolution remained friction dominated until recently, in which case the signatures of the anisotropic era will be much better preserved. These effects are expected to occur in generic topological defect models.

Analytic solutions for the evolution of domain walls

We introduce an unusual asymmetric double well potential, a piecewise parabolic one, and we show that the solutions for the evolution of its domain walls can be found analytically, in contrast with the case of the standard ${\ensuremath{\varphi}}^{4}$ field theory. We find exact solutions for the critical bubble, for the motion of domain walls in one, two and three spatial dimensions, and for the Euclidean O(4) bounce that determines the decay rate of the false vacuum.

Unusual magnetization process in haematite investigated by synchrotron radiation diffraction imaging

The magnetization process of a nearly perfect crystal of haematite is investigated through the observation of domain wall evolution in an applied magnetic field, by white-beam X-ray section topography. The sample is a (111) platelet. The walls are nearly parallel to its main surface. Their contrast changes dramatically with increasing field, but their locations are not altered very much during most of this process. These experimental facts are interpreted as corresponding to a magnetization process which occurs mainly by spin rotation within the domains. The very small basal plane anisotropy of haematite and the pinning of the walls by defects results in this unusual magnetization process, which differs from the standard process for ferromagnets.

Analytic Scaling Solutions for Cosmic Domain Walls.

A relativistic generalisation of a well-known method for approximating the dynamics of topological defects in condensed matter is constructed, and applied to the evolution of domain walls in a cosmological context. It is shown that there are self-similar ``scaling'' solutions, for which one can in principle calculate many quantities of interest without recourse to numerical simulations. Here, the area density in the scaling regime is calculated in various backgrounds. Remarkably good agreement with numerical simulations is obtained.

Erratum: Dynamics of topological defects and inflation

We study the dynamics of topological defects in the context of ``topological inflation" proposed by Vilenkin and Linde independently. Analysing the time evolution of planar domain walls and of global monopoles, we find that the defects undergo inflationary expansion if $\eta\stackrel{>}{\sim}0.33m_{Pl}$, where $\eta$ is the vacuum expectation value of the Higgs field and $m_{Pl}$ is the Planck mass. This result confirms the estimates by Vilenkin and Linde. The critical value of $\eta$ is independent of the coupling constant $\lambda$ and the initial size of the defect. Even for defects with an initial size much greater than the horizon scale, inflation does not occur at all if $\eta$ is smaller than the critical value. We also examine the effect of gauge fields for static monopole solutions and find that the spacetime with a gauge monopole has an attractive nature, contrary to the spacetime with a global monopole. It suggests that gauge fields affect the onset of inflation.

Dynamics of topological defects and inflation.

We study the dynamics of topological defects in the context of ``topological inflation'' proposed by Vilenkin and Linde independently. Analyzing the time evolution of planar domain walls and of global monopoles, we find that the defects undergo inflationary expansion if \ensuremath{\eta}\ensuremath{\gtrsim}0.33${\mathit{m}}_{\mathrm{Pl}}$, where \ensuremath{\eta} is the vacuum expectation value of the Higgs field and ${\mathit{m}}_{\mathrm{Pl}}$ is the Planck mass. This result confirms the estimates by Vilenkin and Linde. The critical value of \ensuremath{\eta} is independent of the coupling constant \ensuremath{\lambda} and the initial size of the defect. Even for defects with an initial size much greater than the horizon scale, inflation does not occur at all if \ensuremath{\eta} is smaller than the critical value. We also examine the effect of gauge fields for static monopole solutions and find that the spacetime with a gauge monopole has an attractive nature, contrary to the spacetime with a global monopole. It suggests that gauge fields affect the onset of inflation. \textcopyright{} 1996 The American Physical Society.

Cosmological domain wall evolution and spontaneous CP violation from a gauge singlet scalar sector

We consider the evolution of domains of different spontaneous CP violating phase which form during a cosmological phase transition in a simple model of gauge singlet scalars. This model can in principle be coupled to the Standard Model in order to provide the additional CP violation necessary during the electroweak phase transition in order to allow for a successful electroweak baryogenesis scenario, provided that the domains resulting in negative baryon number, which would be produced in the limit of purely spontaneous CP violation in equal numbers along with the domains resulting in positive baryon number, are eliminated prior to the electroweak phase transition. We show that it is possible to eliminate the negative baryon number domains by the introduction of an explicit CP violating phase in the singlet scalar potential, which can be as small as O(10 −15) in the case where the singlet scalars have a mass scale ≲ 1 TeV. The possibility that such a small explicit phase could have a gravitational origin is briefly discussed.

Biased discrete symmetry and domain wall problem

We reconsider the cosmological evolution of domain walls produced by the spontaneous breaking of an approximate discrete symmetry. We show that domain walls may never collapse, even if the standard bound on the vacuum energy asymmetry is satisfied. Instead of disappearing, these defects may form stable “bound states”-double wall systems. Possible stability of such a wall is a dynamical question and consequently restricts the allowed range of parameters. In particular, in the two Higgs doublet standard model with an anomalous Z 2 symmetry, the above restriction suggests the mass of the pseudoscalar Higgs (would be axion) being close to the mass of the scalar one.