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.     

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.     

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.     

Model of magnetization in thin magnetic films with one domain and two-domain basic structures

The magnetization processes in thin magnetic films are described by a model analysing the behaviour of one domain and two-domain basic structures (BS) in the applied magnetic field. These structures include the film areas with nearly constant crystal and magnetic parameters. The minimum of BS free energy including the energy in the internal magnetic field, the energy of the induced anisotropy and the domain-wall energy are taken into account. The initial and hysteresis curves of the sample depend on the function of distribution for the BSs are calculated. A good qualitative agreement with the results of other authors is observed if the films consists of one-domain or two-domain BS only. Our experimental data give also some support of the model.     

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.     

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.     

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.     

Interaction of ultrasonic waves with domain walls on nanocrystalline YIG

The nanocrystalline YIG samples with different particle sizes (20–40 nm) has been prepared using microwave–hydrothermal method. As synthesized powders were characterized using XRD and TEM. The powders were pressed and sintered at three different temperatures i.e., 700 °C/30 min, 800 °C/30 min, 900 °C/30 min, using microwave furnace. The sintered samples were characterized using XRD and TEM. The sintered samples are monophasic in nature with average grain size ranging in between 72 nm and 90 nm. The thermal variation of ultrasonic velocities [longitudinal (V_l) and transverse (V_S)] and longitudinal attenuation (α_l) has been measured on sintered samples by the pulse transmissionmethod at 1 MHz, in the temperature range of 300–600 K. The room temperature velocity is found to be grain size dependent and decreases with increasing temperature, except near the Curie temperature, T_C, where a small anomaly is observed. The longitudinal attenuation (α₁) at room temperature is also found to be more sample dependent. The temperature variation of ultrasonic longitudinal attenuation exhibits a sharp maximum just below Curie temperature (T_C). The above observations were carried on in the demagnetized state, on the application of a saturation field of 380 mT, the anomaly observed in the thermal variation of velocities (longitudinal and transverse) and attenuation is found to disappears. The observed interaction of ultrasonic velocity with domain walls has been qualitatively explained with the help oftemperature variation of magneto-crystalline anisotropy constant (k₁) and Landau’s theory.     

Symmetry theory of the flexomagnetoelectric effect in the magnetic domain walls

A local flexomagnetoelectric (A.P. Pyatakov, A.K. Zvezdin, 2009) effect in the magnetic domain walls (DWs) of the cubic hexoctahedral crystal has been investigated on the basis of a symmetry analysis. The strong connection between magnetic symmetry of the DW and the type of the distribution of the electric polarization was shown. Results were systemized in the scope of the DW chirality. It was shown, that new type of the local flexomagnetoelectric coupling corresponds to the presence of the coupled electric charge in the DW. It was found that all time-noninvariant chiral DWs have identical type of spatial distribution of the magnetization and polarization. There are coincidence between the symmetry predictions and results obtaining from the known term of the flexomagnetoelectric coupling for transverse polarization components.     

A model for domain and domain wall NMR signals in magnetic materials

Spin echo NMR signals in magnetic materials (simple metals, alloys or intermetallic compounds) generally result from mixed contributions of distinct magnetic regions of the sample, the magnetic domains and the domain walls. The amplitude of the signal is proportional to the so-called enhancement factor which in most of the cases greatly differs in these two regions, depending upon the wall mobility, the magnetic anisotropy, etc. The experimental access to domain and domain walls is possible, in principle, by a careful control of the RF power applied to the sample. In this paper a simple superposition model is proposed which includes both contributions to the NMR signal. We calculate the amplitude of the spin echo in magnetic powder samples and compare it with experimental situations where it has been possible to separate different contributions to the signal. This has been done in some RCo₂ magnetic rare-earth intermetallic compounds by analyzing the spectral line widths and the curve of the spin echo amplitude versus the applied RF field. Despite its simplicity, the present model allows the understanding of the main features of the NMR spectra and the dependence of the echo amplitude with the RF power in these compounds.     

De Sitter and double irregular domain walls

A new method to obtain thick domain wall solutions to the coupled Einstein scalar field system is presented. The procedure allows the construction of irregular walls from well known ones, such that the spacetime associated to them are physically different. As consequence of the approach, we obtain two irregular geometries corresponding to thick domain walls with dS expansion and topological double kink embedded in AdS spacetime. In particular, the double brane can be derived from a fake superpotential.     

Theoretical study of the relation between interfacial imperfection and transport properties in magnetic tunnel junctions

The ab initio electronic structure of model Co/Al₂O₃ heterojunctions with varying interface quality is investigated. It is evidenced that the metal-induced gap states determine the position of the Fermi level relative to the bottom of the conduction band which defines the effective barrier height for tunnel transport. This introduces a new origin for barrier height fluctuations related to the interfaces.     

Film thickness dependence of the magnetic resonance in Fe–SiO2 nanocomposites

The magnetic properties of Fe–SiO₂ nanogranular composite thin films were studied as a function of film thickness and Fe concentration, f, using ferromagnetic resonance at X-band (9.4 GHz) and Q-band (35 GHz). Films with an Fe volume percent ranging from 17% to 70% were fabricated from a mosaic target using RF sputtering techniques. Film thickness was varied between 10 and 200 nm. From measurements made at room temperature with the external field applied parallel and perpendicular to the film plane, it was possible to determine an almost linear dependence of the effective anisotropy field with Fe concentration. Small differences observed between X- and Q-band, specially at low f, were attributed to the effects that the different fields applied during the experiment cause on the magnetic state of the sample. No systematic change of the effective field or the g value was observed in films of different thickness. The absorption line width, on the other hand, was found to depend on film thickness indicating a larger distribution of particle shape and size with increasing film thickness. A maximum in the line width was observed around f30–35% and is probably caused by the transition from single domain ferromagnetic clusters to superparamagnetic particles.     

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.     

The sandwich domain structure in a Fe-based amorphous ribbon with uniaxial magnetic anisotropy

The formation and motion of two domain walls parallel to the ribbon surface are discovered during its dynamic magnetic reversal. The domain walls form near by the middle plane of a ribbon and move to its opposite main surfaces with different velocities.     

Magneto-optic study of the behavior of magnetic domains walls in ferrimagnetic garnet films placed over samples with in-plane magnetization

Magneto-optic (MO) imaging is based on Faraday rotation of a linearly polarized incident light beam illuminating a sensitive MO layer placed in close contact to the sample. For in-plane magnetized layers of Lu_3−xBi_x Fe_5−yGa_yO₁₂ ferrimagnetic garnet films, zig-zag domain formation occurs whenever the sample stray parallel field component changes sign. In this work we study the behavior of zig-zag domain walls that appear when the garnet is placed over samples with in-plane magnetization like audio tapes recorded with different signals. We describe the zig-zag walls considering the anisotropy, exchange and magnetostatic energies in the Neel tails and the contribution of an applied magnetic field. Using different recorded signals we have been able to control the gradient of stray parallel field component on the garnet, changing the distance between domains and the size of zig-zag walls. We could even avoid the appearance of these zig-zag domain walls and obtain closed domains structures. We also study the behavior of the domain walls when an external magnetic field is applied parallel to the sample.     

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.     

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.     

A study of energy band gap versus temperature for Cu2ZnSnS4 thin films

The temperature dependent band gap energy of Cu₂ZnSnS₄ thin film was studied in the temperature range of 77-410 K. Various relevant parameters, which explain the temperature variation of the fundamental band gap, have been calculated using empirical and semi-empirical models. Amongst the models evaluated, the Varshni and Pässler models show the best agreement with experimental data in the middle temperature range. However, the Bose-Einstein model fits reasonably well over the entire temperature range evaluated. The calculated fitting parameters are in good agreement with the estimated value of the Debye temperature calculated using the Madelung-Einstein approximation and the Hailing method.     

Influence of thickness,width and temperature on critical current density of Nb thin film structures

The density of critical currents j_C in Nb thin films with thickness smaller than 15 nm and width between 100 nm and 10 μm has been measured in a wide temperature range. We have found that the temperature dependencies of j_C in sub-micrometer wide bridges at 0.7T_C < T < T_C are well described by the Ginzburg–Landau de-pairing critical current. In wider bridges already at T < 0.9T_C the j_C value is significantly reduced due to the penetration and de-pinning of magnetic vortices.