Interaction Of Domain Walls Research Articles

Complexes of Domain Walls in Ferromagnetic Stripes

Interaction of domain walls (DWs) in ferromagnetic stripes is studied with relevance to the formation of stable complexes of many domains. Two DW system is described with the Landau-Lifshitz-Gilbert equation including regimes of narrow and wide stripes which correspond the presence of transverse and vortex DWs. The DWs of both kinds are characterized with their chiralities (the direction of the magnetization rotation in the stripe plane) and polarities (the magnetization orientation in the center of a vortex and/or halfvortices), hence, their interactions are analyzed with dependence on these properties. In particular, pairs of the DWs of opposite or like both chiralities and polarities are investigated as well as pairs of opposite (like) chiralities and of like (opposite) polarities. Conditions of the creation of stationary magnetic bubbles built of two interacting DWs are formulated with relevance to the situations of presence and absence of the external magnetic field.

Interaction of Domain Walls and Magnetic Nanoparticles in Giant Magnetoresistive Nanostrips for Biological Applications

Head-to-head domain walls (DW) are formed and detected in U-shaped spin valve nanostrips by a Bitter Method on scanning electron microscope. We find that optimization of the washing technique is critical to proper deposition of magnetic nanoparticles (MNPs). The DW position is monitored electrically with giant magnetoresistance (GMR) similar to a potentiometer. DWs are repeatedly pinned and depinned from a site near the device center using a stage with two axis field. We first confirm the distribution of depinning events from a random sample of devices and obtain a standard deviation of 2.2 Oe. We then obtain an experimental signal of 8 Oe shift in depinning field from just 7 MNPs of 35 nm diameter.

Complexes of Domain Walls in One-Dimensional Ferromagnets Near and Far from Phase Transition

Interactions of domain walls are analyzed with relevance to formation of stationary bubbles (bound state of two domain walls) and bound states of many domains in one-dimensional systems. We investigate the domain structures in ferromagnets which are described with the Landau Lifshitz equation as well as the domains in critical systems described with the Ginzburg Landau equation. Supplementing previous author studies on the creation of hard bubbles [formed by one Bloch domain wall and one Neel (Ising) domain wall] in the presence of an external (magnetic) eld, the soft bubbles consisting of two Bloch domain walls or two Neel (Ising) domain walls are studied in detail. The interactions of two domain walls of the same kind are studied in the framework of a perturbation calculus.

Interactions of defect complexes and domain walls in CuO-doped ferroelectric (K,Na)NbO3

“Lead-free” piezoelectric sodium potassium niobate has been studied with respect to its defect structure when doping with CuO. The results indicate that two kinds of mutually compensating charged defect complexes are formed, (Cu′′′Nb−VO••)′ and (VO••−Cu′′′Nb−VO••)•. Concerning the interplay of these defect complexes with the piezoelectric materials properties, the trimeric (VO••−Cu′′′Nb−VO••)• defect complex primarily has an elastic dipole moment and thus is proposed to impact the electromechanical properties, whereas the dimeric (Cu′′′Nb−VO••)′ defect possesses an electric dipole moment in addition to an elastic distortion. Both types of defect complexes can impede domain-wall motion and may contribute to ferroelectric “hardening.”

Mesoscopic mechanism of the domain wall interaction with elastic defects in uniaxial ferroelectrics

The role of elastic defects on the kinetics of 180° uncharged ferroelectric domain wall motion is explored using continuum time-dependent Landau-Ginzburg-Devonshire equation with elastic dipole coupling. In one dimensional case, ripples, steps, and oscillations of the domain wall velocity appear due to the wall-defect interactions. While the defects do not affect the limiting-wall velocity vs. field dependence, they result in the minimal threshold field required to activate the wall motions. The analytical expressions for the threshold field are derived and the latter is shown to be much smaller than the thermodynamic coercive field. The threshold field is linearly proportional to the concentration of defects and non-monotonically depends on the average distance between them. The obtained results provide the insight into the mesoscopic mechanism of the domain wall pinning by elastic defects in ferroelectrics.

Magnetic micro- and nanostructures of unalloyed steels: Domain wall interactions with cementite precipitates observed by MFM

The morphology and content of a cementite phase controls the macroscopic, mechanical and magnetic properties of steels. The influence of the cementite content on the bulk magnetic properties in unalloyed steels was observed in hysteresis loop and Barkhausen noise signals. Globular cementite embedded in a ferrite matrix is characterized by atomic force microscopy and magnetic force microscopy. Size, shape and orientation of the grains influence the domain configuration. When an external magnetic field is applied, the magnetization process occurs mainly in the ferrite matrix. The Bloch walls in the ferrite matrix move, and they are pinned by the cementite precipitates. This microscopic observation correlates with the macroscopic magnetic properties of the investigated material.

Domain wall interactions at a cross-shaped vertex

The interaction of two domain walls (DWs) at a cross-shaped vertex fabricated from two ferromagnetic nanowires has been experimentally investigated. Both magnetostatically repulsive and attractive interactions have been probed. It is found that in the repulsive case, a passing DW may directly induce the depinning of another that is already pinned at a vertex. This effect can be qualitatively described by considering only simple, magnetostatic-charge-based arguments. In the attractive case, however, asymmetric pinning is found, with complete suppression of depinning possible. This observed effect is contrary to simple charge-based arguments and highlights the need for full micromagnetic characterization of the DW interactions in more complex systems.

Emergent magnetic monopoles in frustrated magnetic systems

Emergent magnetic monopoles in frustrated magnetic systems

DOMAIN BOUNDARIES IN FERROELECTRICS

Present paper is a brief review of the information and existing approaches in the study of domain walls in ferroelectric materials. In the framework of the continuum approach the structure of 180° and 90° domain walls was considered. The results of calculation of width and energy of domain walls were compared with those obtained from ab initio calculations and experimental data. Factors conducive to the broadening of domain boundaries are discussed such as profile temperature fluctuation, capture to nearby defects and surface impact. The structure of charged domain walls was considered under the conditions of screening by free carriers. The structure and characteristics of the moving domain wall are discussed: the local effective mass, the top speed and the mobility. The lateral motion of domain walls in the lattice potential relief in the general case creeping mode is investigated. The factors that control the macroscopic movement of domain walls are studied: an effective quasi-elasticity coefficient and nonlocal effective mass associated with involvement in the movement of the elastic medium surrounding wall. Natural frequency of translational oscillations of domain boundaries and the influence of the size effect were estimated. The interaction of domain walls with different types of defects and their effect on the deformation profile and features of the motion of domain walls are considered.

Indirect interaction of magnetic domain walls

AbstractWe calculate the electron‐mediated exchange interaction between two domain walls in magnetic wires. This corresponds to the equilibrium regime and, therefore, the interaction can be additionally controlled by an electric current. The ex‐ change interaction is long ranged and oscillates as a function of the distance between the walls. It also depends oscillatory on the polarization angle of the walls, having the maximum value for collinear polarization. (© 2011 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

Interaction of Antiparallel Transverse Domain Walls in Ferromagnetic Nanowires

The interaction of antiparallel transverse domain walls in ferromagnetic nanowires was investigated via micromagnetic simulation with systematic variations of the external field strength as well as the wire thickness. The interaction of antiparallel transverse walls after domain wall collision exhibited damped multiple collisions due to the rigid structure of the antiparallel transverse walls. The detailed process during the multiple collisions was analyzed via the Fast Fourier Transform technique, along with a careful examination of the inner spin structures of the colliding domain walls. It was found that a frequency peak of multiple collisions shifted to a higher peak position as the external field strength increases. With a stronger field strength of around a few hundred mT, it was found that two antiparallel transverse walls were finally annihilated with formation of complex antivortex structures.

Spin-density waves and domain wall interactions in nanowires

We investigated how the dynamics of a domain wall are affected by the presence of spin-density waves in a ferromagnetic wire. Domain walls and other scattering centers can cause coherent spin-density waves to propagate through a wire when a current is applied. In some cases, the spin torque due to these scattered electrons can be enhanced such that it is on a par with the exchange and anisotropy energies controlling the shape and dynamics of the domain wall. In such a case, we find that the spin-density waves enhance the current-induced domain-wall motion, allowing for domain-wall motion with smaller current pulses. Here, we consider a system involving two domain walls and focus on how the motion of the second domain wall is modified by the spin-density waves caused by the presence of the first domain wall.

Effects of boundaries and point defects on energetics and dynamics of domain walls

Knowledge about energetics and motions of domain walls is crucial for understanding dynamics in many phase transitions and various properties of domain-wall-based materials. Through direct observation of a surface phase transition, monolayer Pb on Si(111), with a scanning tunneling microscope (STM) and careful sample preparation, the interactions of domain walls with boundaries and point defects are investigated. We observe many local dynamic phenomena near boundaries and defects such as the pinning of domain walls at constrictions and/or by point defects, dependence of transition temperatures with the domain size, enhanced structural fluctuations near boundaries and high defect density areas as well as where high defect density is artificially introduced, etc. A model based on attractive interactions of domain walls with boundaries and point defects can explain our observations qualitatively. We believe phenomena observed and explanations given for this system may be applicable for other domain-wall-rich systems, including three-dimensional systems, of nanometer size.

Effect of Anneal Conditions on Electrical Properties of Mn-Doped (Na0.85K0.15)0.5Bi0.5TiO3 Thin Films Prepared by Sol-Gel Method

Mn-doped (Na0.85K0.15)0.5Bi0.5TiO3 (NKBT-Mn) thin films were fabricated on Pt(111)/Ti/SiO2/Si substrates via an aqueous sol–gel method and annealed at different temperatures from 550° to 800°C. Two different crystallization processes, i.e., single crystallization and multiple crystallizations, were used. The structures of the films were analyzed using X-ray diffraction, which shows that the NKBT-Mn thin film prepared by multiple crystallizations crystallize into the pure perovskite phase, while pyrochlore phase formed in the film prepared by the single crystallization. Ferroelectric and dielectric properties of NKBT-Mn thin films are quite dependent on the anneal temperature. The Pr value was a maximum for the 700oC-annealed thin film and decreased with both decreasing and increasing anneal temperature. The NKBT-Mn thin film annealed at 700°C had the largest ɛr of 426 and the lowest tan δ of 0.061. At the same time, the temperature-dependent ferroelectric property was also investigated from room temperature to −150°C. It is found that Pr of the film sample increases as temperature decreases, which can be well explained by a temperature-dependent charged carriers–domain wall interaction. Current density measurement indicates that the change in morphology with increasing anneal temperature and the volatility of Bi and Na/K at high temperature may responsible for the change in leakage current density and the NKBT-Mn thin film annealed at 700°C has the lowest leakage current of 7.6 × 10−5 A/cm2.

Relaxation stimulated in the domain structure of a triglycine sulfate crystal by an alternating-current electric field

The relaxation of the domain structure in a triglycine sulfate crystal from a nonequilibrium state induced by an alternating-current electric field has been investigated. The distributions of the activation energy of the processes under consideration and the energy of interaction of domain walls with defects over the exciting fields have been obtained.

Influence of uniaxial plastic deformation on surface magnetic field in steel

Under geomagnetic field, surface magnetization measurements were made on 1045 and a3 steels samples uniaxially deformed to differing magnitudes of plastic strain, to study the dependence of surface magnetic field and its distribution on plastic deformation. The results indicated initial increase in surface magnetic field with increasing plastic strain followed by a decrease at higher plastic deformation. At still higher plastic deformation, the surface magnetic field was found to be almost independent of plastic strain. In the middle part of the sample, the uneven plastic deformation interrupted the linear distribution of surface magnetic field. The behavior of surface magnetic field and its distribution with plastic deformation were largely controlled by the different mechanisms of interaction of domain walls with isolated dislocation, dislocation tangles and dislocation cellular structures.

Oxygen Incorporation into Electrodeposited CoFe Films: Consequences for Structure and Magnetic Properties

The nanostructure and magnetic properties of electrodeposited Co40Fe60 alloy films containing varying amounts of oxygen were investigated using transmission electron microscopy (TEM) and diffraction, secondary ion mass spectroscopy (SIMS), and superconducting quantum interference device (SQUID) measurements. Oxygen content in the CoFe deposit was controlled by electrolyte composition. Films were deposited on Si {100} substrates with thin Cu/Ti seed layer. Electron energy loss and x-ray spectroscopies showed that the low oxygen films contained intragranular FeO particles and that the high oxygen films contained Fe2O3 along grain boundaries. The films with oxide present at the grain boundary had increased coercivity and reduced saturation magnetization relative to the lower oxygen content films with intragranular oxide. The differences in magnetic properties between low oxygen and high oxygen concentration films were attributed to stronger mobile domain wall interactions with the grain boundary oxide layers relative to interactions with the intragranular oxide particles in the low oxygen specimens.

Interactions of Defects and Domain Walls in LiNbO3 – Insights from Simulations

The defect formation energies of various possible defect complexes in stoichiometric LiNbO3 are calculated and the dominant defects are predicted based on their relative stabilities. The atomistic structure of one type of ferroelectric domain wall is discussed and the width of the domain wall is identified. Based on the analysis of polarization components normal to and transverse to the domain wall plane, it is found that domain walls exhibit Bloch and Neel like characteristics. Point defects are found to have lower formation energies at domain wall. Therefore, domain walls can be considered as trap sites of point defects.

Simulations of Field Driven Domain Wall Interactions in Ferromagnetic Nanowires

The interaction of domain walls in a single ferromagnetic nanowire has been observed with micromagnetic simulation. Domain walls separating domains of opposite magnetization move towards each other when an external field is applied along the long axis of the wire resulting in a collision. The final magnetic state of the wire after the collision will contain either zero (domain wall annihilation) or two (domain wall conservation) domain walls. Here we explore the behavior that determines the final state, showing that it depends on the initial domain wall configuration, the speed the domain walls are moving with before the collision, and the dimensions of the nanowire. A model is also presented which helps to determine the repulsive force the conserved domain walls exert on each other.

Vortex domain wall chirality rectification due to the interaction with end domain spin structures in permalloy nanowires

The interaction of vortex domain walls with the end domain spin structure present at the rectangular end of a ferromagnetic nanowire is investigated using Lorentz transmission electron microscopy. When vortex walls are moved with short field pulses towards the wire end an end vortex is formed, whose chirality is independent of the original vortex wall chirality but is determined by the spin configuration of the end domain. This acts as a domain wall chirality “rectifier,” which could be useful for applications based on domain walls. The observed chirality transformations are reproduced by micromagnetic simulations showing a complex reversal mechanism.