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.     

Motion of test particles around domain walls

We present a detailed analysis of the motion of test particles around domain walls. The study of the trajectories of the test particles has been done using the Hamilton-Jacobi formalism. In most of the cases we show that the particles can not be trapped by the walls.     

Theoretical study of the temperature dependence of the width of magnetic domain walls

The temperature dependence of magnetic domain walls in ferromagnetic systems with strong exchange coupling and weak lattice anisotropy is studied assuming that the thermal influence results mainly from the temperature dependence of the magnetization. We obtain that in lattices with an uniaxial symmetry like Co the wall width increases with temperature, but stays finite up to the Curie temperature T_c. In contrary, for a cubic lattice like Fe the wall width diverges for T → T_c, if only the lattice anisotropy is taken into account. The shape of the domain walls is not conserved, since at T_c the wall is determined only by the lowest order of anisotropy. In addition, the temperature dependence of a domain wall width for a thin magnetic film is determined. Using a special symmetry, we obtain a diverging wall width at a temperature markedly lower than T_c. However, the consideration of additional domain wall modes should modify this result.     

Crystallographic orientation dependence of ferroelectric domain walls in antiferroelectric lead zirconate thin films

Domains of antiferroelectric PbZrO₃ have been studied. The (111) PbZrO₃ has lower field transitions due to the reduction of the angle between the ferroelectric polar axis and the applied electric field. The study of the permittivity reveals also that the (111) PbZrO₃ has a higher correlation of dipoles (|S_hf| = 0.007) due to the energy gain associated with their orientation. Therefore, the (111) crystallographic orientation is a better choice for obtaining easily switching domain. The dielectric response of the domain walls in the (100) and (111) PbZrO₃ are identical because they have the same environment (same grain size and similar defects) and interact in the same way. Only the domain wall density is higher in the (111) PbZrO₃ due to its lower crystallographic orientation factor. Different crystallographic directions have more obstacles due to the inhomogeneity of the crystallization and consequently has more nucleation site for domain walls.     

Fast domain wall dynamics in amorphous and nanocrystalline magnetic microwires

We have studied the effect of thermal treatment on the domain wall dynamics of FeSiB and FeCoMoB microwires. It was shown that annealing in transversal magnetic field increases the domain wall mobility as well as the domain wall velocity. Annealing under the tensile stress hinders the appearance of the monodomain structure but application of tensile stress leads to the magnetic bistability having the domain wall mobility twice higher that in as-cast state. Further increase of the tensile stress reduces the domain wall mobility but the domain wall velocity increases as a result of the decrease of critical propagation field. Annealing of the FeCoMoB microwire by Joule heating leads to introduction of the circular anisotropy that favors the vortex domain wall. Such treatment increases the domain wall mobility as well as the maximum domain wall velocity.     

A study of ultrasonic velocity and attenuation on nanocystalline MgCuZn ferrites

The nanocrystalline MgCuZn ferrites with particle size (∼30 nm) have been synthesized by microwave-hydrothermal (M-H) method at 160 °C/45 min. The powders were densified at 750-900 °C/30 min using microwave sintering method. The sintered samples were characterized using X-ray diffraction and scanning electron microscope. The grain sizes of the sintered samples are in the range of 60-80 nm. The ultrasonic velocities have been measured on MgCuZn ferrites using the pulse transmission method at 1 MHz. The ultrasonic velocity is found to decrease with an increase of temperature. A small anomaly is observed around the Curie temperature, 520 K. The anomaly observed in the thermal variation of longitudinal velocity and attenuation is explained with the help of magneto-crystalline anisotropy constant.     

Accurate calibration of the velocity-dependent one-scale model for domain walls

We study the asymptotic scaling properties of standard domain wall networks in several cosmological epochs. We carry out the largest field theory simulations achieved to date, with simulation boxes of size 2048³, and confirm that a scale-invariant evolution of the network is indeed the attractor solution. The simulations are also used to obtain an accurate calibration for the velocity-dependent one-scale model for domain walls: we numerically determine the two free model parameters to have the values _cw=0.34±0.16$c_w=0.34\pm 0.16$ and _kw=0.98±0.07$k_w=0.98\pm 0.07$, which are of higher precision than (but in agreement with) earlier estimates.     

The influence of wire width on the charge distribution of transverse domain walls and their stray field interactions

We present here a numerical study of the magnetostatic charge distribution of transverse Néel type domain wall in permalloy nanowires. The calculations indicate that not only is the distribution highly non-uniform within a given transverse wall but it also varies dramatically with respect to the wire width. The implications of this for magnetostatic domain wall pinning are analyzed by considering the stray field interaction between a wall and another extended magnetic body for a particular domain wall chirality, where two distinct depinning mechanisms are observed depending on the wire width.     

Propagation of ultrasonic waves in neptunium monochalcogenides

The ultrasonic attenuation and acoustic coupling constants due to phonon–phonon interaction and thermoelastic relaxation mechanisms have been studied for longitudinal and shear waves in B₁ structured neptunium monochalcogenides NpX (X: S, Se, Te) along 〈1 0 0〉 direction in the temperature range 100–300 K. The second and third order elastic constants (SOEC and TOEC) of the chosen monochalcogenides are also computed for the evaluation of ultrasonic parameters. The ultrasonic attenuation due to phonon–phonon interaction process is predominant over thermoelastic relaxation process in these materials. The ultrasonic attenuation in NpTe has been found lesser than other materials NpS, NpSe and GdY (Y: P, As, Sb and Bi). The semiconducting or semimetallic nature of neptunium monochalcogenides can be well understood with the study of thermal relaxation time. Total ultrasonic attenuation in these materials is found to be quadratic function of temperature. The nature of NpTe is very similar to semimetallic GdP. The mechanical and ultrasonic study indicates that NpTe is more reliable, perfect, flawless material.     

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.     

Magnetic symmetry of the plain domain walls in ferro- and ferrimagnets

Magnetic symmetry of all possible plane domain walls in ferro- and ferrimagnets is considered. Magnetic symmetry classes of non 180° (including 0°) domain walls are obtained. The domain walls degeneracy is investigated. The symmetry classification is applied for research of all possible plane domain walls in crystals of the hexoctahedral crystallographic class.     

Magnetic properties of ferrocholesterics with soft particle anchoring

The influence of the external magnetic field on the orientational structure and magnetic properties of the ferrocholesteric is analyzed. A soft homeotropic coupling between the magnetic particles and the cholesteric molecules is assumed. The diamagnetic anisotropy of the matrix is chosen to be positive. In this case, the dipolar and quadrupolar mechanisms of orientational interaction with the external field compete with each other. The field being applied normal to the helix. Using the continuum theory, the occurrence of magnetic-field-induced ferrocholesteric–ferronematic transition is studied. The transition field as a function of the material parameters of a ferrocholesteric is found. It is shown that rising the field strength in the ferronematic phase leads to a change in the coupling between the particles and the director from homeotropic to planar one. A study on the structure of the domain walls in ferronematic phase is undertaken.     

Domain walls confined in magnetic nanotubes with uniaxial anisotropy

We present calculations of the different domain wall structures confined in magnetic nanotubes, such as transverse wall, asymmetric vortex wall, branch fashion wall, and horse-saddle wall. The wall structures were calculated by micromagnetic simulations. The tube radii R=50 nm and 100 nm, and aspect ratios length/radius L/R≤15 were considered. The magnetic phase diagrams of the stability of different kinds of the domain walls were plotted as function of the tube aspect ratio L/R and the tube thickness (difference of the outer and inner tube radii).     

Influence of the measurement frequency on the magnetic disaccommodation spectra of YIG samples

Magnetic aftereffect phenomena in yttrium iron garnets and their relationship to the dynamics of domain walls are analyzed by means of the magnetic disaccommodation (DA) technique. The samples have been prepared using a standard ceramic technique in CO₂ atmosphere in order to enhance the formation of ferrous ions in the lattice. The results reveal the presence of the well-known process II around 130 K and a process at higher temperatures (187 K). Furthermore, accommodation (or negative DA) processes have been detected at temperatures just below process II. The features of these phenomena are strongly related to the measurement frequency and, hence, they are more noticeable as this frequency is increased. Such behavior is associated with the resonance of the domain wall motion at frequencies around the measurement frequency. The characteristic parameters that define this resonance depends upon time due to the presence of an induced anisotropy relaxation process that occurs after demagnetization.     

An investigation of generalized lamb waves using ultrasonic reflectivity measurements

Ultrasonic critical angle reflectivity method is used to measure the phase velocity of generalized Lamb waves in cadmium and zinc platings. In addition to the free propagating modes, leaky-wave modes are also observed. Leaky waves are considered using principles familiar from the discussion of surface waves in anisotropic media and a relatively good agreement is obtained between the theoretical computations and measured data.     

Size dependent ultrasonic properties of InN nanowires

The ultrasonic properties of single crystalline indium nitride nanowires (InN NWs) are studied for wire size (diameter) 6–100 nm at 300 K following the interaction potential model. Ultrasonic attenuation, ultrasonic velocity, acoustic coupling constant and thermal relaxation time are calculated using higher order elastic constants and thermal conductivity of the nanowires. The analysis of size dependent thermal relaxation time and ultrasonic properties shows that above the 20 nm diameter, InN nanowire tends towards its bulk material property. The third order polynomial is found to be best fit for size variation of thermal relaxation time. The ultrasonic attenuation as a function of size of the nanowires is found to be mainly affected by the thermal conductivity of the nanowires of different sizes.     

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.     

Low-scale leptogenesis and the domain wall problem in models with discrete flavor symmetries

We propose a new mechanism for leptogenesis, which is naturally realized in models with a flavor symmetry based on the discrete group A₄$A_4$, where the symmetry breaking parameter also controls the Majorana masses for the heavy right-handed (RH) neutrinos. During the early universe, for T?TeV$T?\text{TeV}$, part of the symmetry is restored, due to finite temperature contributions, and the RH neutrinos remain massless and can be produced in thermal equilibrium even at temperatures well below the most conservative gravitino bounds. Below this temperature the phase transition occurs and they become massive, decaying out of equilibrium and producing the necessary lepton asymmetry. Unless the symmetry is broken explicitly by Planck-suppressed terms, the domain walls generated by the symmetry breaking survive till the quark–hadron phase transition, where they disappear due to a small energy splitting between the A₄$A_4$ vacua caused by the QCD anomaly.     

Elastic and ultrasonic properties of single crystalline nickel nanowires

In the present paper, we have theoretically calculated the non linear elastic constants of single crystalline Ni NWs at very broad temperature range 20–300 K validating simple interaction potential model. The temperature dependent ultrasonic attenuation and other related properties are determined using their second and third order elastic constants (SOECs/TOECs). Where possible, the results are compared with experiments from literature. There is a correlation between the thermal conductivity and ultrasonic attenuation in the temperature range 100–300 K. Also, a correlation between the resistivity and ultrasonic attenuation in the temperature range 40–100 K has been established validating the theoretical approach.     

Effect of reaction condition on microstructure and properties of (NiCuZn)Fe2O4 nanoparticles synthesized via co-precipitation with ultrasonic irradiation

Nano-spinel ferrites synthesized via chemical co-precipitation method are small in size and have serious agglomeration phenomenon, which makes separation difficult in the subsequent process. Ni_0.4Cu_0.2Zn_0.4Fe₂O₄ ferrites nanoparticles were synthesized via co-precipitation assisted with ultrasonic irradiation produced by ultrasonic cleaner with 20 kHz frequency using chlorinated salts and KOH as initial materials. The effects of ultrasonic power (0, 40 W, 60 W, 80 W) and reaction temperature on the microstructure and magnetic properties of ferrite nanoparticles were investigated. The structure analyses via XRD revealed the successful formation of pure (NiCuZn)Fe₂O₄ ferrites nanospinel without any impurity. The crystallites sizes were less than 40 nm and the lattice constant was near 8.39 Å. The TEM showed ferrite particle polygonal. M−H analyses performed the saturation magnetization and coercivity of ferrite nanoparticles obtained at the reaction temperature of 25℃ were higher than at 50℃ with same power. The samples exhibited the highest values of Ms 55.67 emu/g at 25℃ and 47.77 emu/g at 50℃ for 60 W and the lowest values of Hc 71.23 Oe at 25℃ for 40 W and 52.85 Oe at 50℃ for 60 W. The squareness ratio (SQR) were found to be lower than 0.5, which revealed the single magnetic domain nature (NiCuZn)Fe₂O₄ nanoparticles. All the outcomes show the ultrasonic irradiation has positive effects on improving the microstructure and increasing magnetic properties.