Domain Width Research Articles

Domain-width model for perpendicularly magnetized systems with Dzyaloshinskii-Moriya interaction

The influence of the Dzyaloshinskii-Moriya interaction (DMI) on stripe domains in perpendicularly magnetized thin ferromagnetic films is theoretically and experimentally investigated. We develop a domain spacing model describing the dependence of the stripe domain width on the magnetic properties of the sample. By including the magnetostatic energy of the domain walls the model correctly describes the transition from Bloch to N\'eel walls with increasing DMI constant. An approach to determine the magnitude of the DMI constant by fitting the stripe domain width as a function of the effective perpendicular anisotropy of wedge-shaped samples is developed and applied to several ultrathin multilayer samples based on Ni/Fe/Cu(001). The magnitude of the DMI constant arising from Fe/Ni and Ni/Fe interfaces is $0.3\ifmmode\pm\else\textpm\fi{}0.14$ meV/atom, indicating that the domain walls are in a pure chiral N\'eel state. Furthermore, phase diagrams of the skyrmionic bubble domain phase are recorded for two samples with different DMI constants, and by scaling the magnetic field a universal phase diagram for perpendicularly magnetized systems is obtained.

The effect of ribbon curvature on the magnetic properties of Fe-based amorphous cores

Coercivity and losses properties of Fe80Si9B11 (at.%) amorphous cores with different radius of curvature have been studied. It shows that coercivity and core loss of the Fe80Si9B11 amorphous alloy increases with the decrement of the winding radius. The domain structure of the ribbons is different for different radius of curvature R. The domain width increases with the decrease of the radius of curvature, since the stress within the ribbon with lower radius of curvature is much stronger. Magnetic-elastic anisotropy energy has also been studied.

Effects of punching process on crystal orientations, magnetic and mechanical properties in non-oriented silicon steel

In an attempt to investigate the effects of punching process on crystal orientations, magnetic and mechanical properties in non-oriented silicon steel, the steel sheet was punched for circular shape of Φ40mm. The crystal orientations and small-angle grain boundaries were characterized by electron backscatter diffraction (EBSD). The results indicated that the initial crystal orientations within a distance of 200μm away from the sheared edge were significantly changed after the punching process. In this area, the fractions of the directions with a high value of magnetocrystalline anisotropy energy Ea, 〈111〉, 〈212〉 and 〈112〉 can reach up to 0.619. However, the fractions of the directions 〈001〉 and 〈113〉 accounts for only 0.096, which have a lower value of Ea. Moreover, the fraction of small-angle grain boundaries markedly increased in the area of about 200μm from the sheared edge, which is mainly attributed to the dislocations multiplication and dislocations motion. The magnetic domain structures were characterized by an optical microscope according to the Bitter method. The results showed that the width of magnetic domain in the sheared edge was much larger than that in the center and the patterns also existed a big difference. The Vickers HV0.1 method was employed to measure the microhardness of the sheared edge. It was found that the values of microhardness within a distance of 400μm away from the sheared edge decreased from 259 to 167 due to the effect of work hardening, which is mainly caused by the dislocations pile-ups near the grain boundaries.

Computational optimization in simulating velocities and water-surface elevations for habitat–flow functions in low-slope rivers

ABSTRACTThe impact of varying computational mesh discretization on the accuracy of simulating velocities and water-surface elevations was investigated using the River2D model and data from 10 study reaches in three low-slope (<0.2%) Canadian rivers. A wide range of computational aspects were examined, including node spacing (1.35 to 60 m), number of mesh nodes (1250 to 58,000) and domain widths (60 to 800 m). Computed values for average cross-sectional velocities and water-surface profiles were compared with corresponding field survey data. The statistical mean absolute and root-mean-square errors were used to evaluate the discrepancy between measured and simulated values due to the mesh discretization characteristics. The results showed that mesh design discretization had a pronounced effect on the precision of the velocity and water-surface elevation predictions. Although the ratio of node spacing to river reach width may be site specific, it was found that optimal values should be <0.022 to obtain the highest accuracy. Regression equations of optimal ratios of node spacing to river reach width and the corresponding minimum mesh resolution errors were estimated. An example is provided that illustrates how the choice of computational mesh properties can affect habitat characterization for fish.

Magnetic shape memory effect in single crystalline Ni-Mn-Ga foil thinned down to 1μm

We report on observation of magnetic-field-induced twin variant reorientation in a thin foil with variable thickness, fabricated from a bulk five-layered Ni49.5Mn28Ga22.5 single crystal. Formation and motion of twinning interfaces in the foil were induced by magnetic fields of 0.6T. The characteristic “labyrinth” magnetic domain structure was fully retained down to 1 μm thickness. Dependence of the characteristic width of magnetic domains on the sample thickness followed a power law with the exponent of 2/3. The reported results indicate that micrometer-scale sized Ni-Mn-Ga devices, fabricated from a bulk, can be actuated by magnetic field.

Nonequilibrium ferroelectric-ferroelastic 10 nm nanodomains: wrinkles, period-doubling, and power-law relaxation

Since the 1935 work of Landau–Lifshitz and of Kittel in 1946 all ferromagnetic, ferroelectric, and ferroelastic domains have been thought to be straight-sided with domain widths proportional to the square root of the sample thickness. We show in the present work that this is not true. We also discover period doubling domains predicted by Metaxas et al (2008 Phys. Rev. Lett. 99 217208) and modeled by Wang and Zhao (2015 Sci. Rep. 5 8887). We examine non-equilibrium ferroic domain structures in perovskite oxides with respect to folding, wrinkling, and relaxation and suggest that structures are kinetically limited and in the viscous flow regime predicted by Metaxas et al in 2008 but never observed experimentally. Comparisons are made with liquid crystals and hydrodynamic instabilities, including chevrons, and fractional power-law relaxation. As Shin et al (2016 Soft Matter 12 3502) recently emphasized: ‘An understanding of how these folds initiate, propagate, and interact with each other is still lacking’. Inside each ferroelastic domain are ferroelectric 90° nano-domains with 10 nm widths and periodicity in agreement with the 10 nm theoretical minima predicted by Feigl et al (2014 Nat. Commun. 5 4677). Evidence is presented for domain-width period doubling, which is common in polymer films but unknown in ferroic domains. A discussion of the folding-to-period doubling phase transition model of Wang and Zhao is included.

Magnetization spin dynamics in a (LuBi)3Fe5O12 (BLIG) epitaxial film

Bismuth substituted lutetium iron garnet (BLIG) films exhibit larger Faraday rotation, and have a higher Curie temperature than yttrium iron garnet. We have observed magnetic stripe domains and measured domain widths of 1.4μm using Fourier domain polarization microscopy, Faraday rotation experiments yield a coercive field of 5Oe. These characterizations form the basis of micromagnetic simulations that allow us to estimate and compare spin wave excitations in BLIG films. We observed that these films support thermal magnons with a precessional frequency of 7GHz with a line width of 400MHz. Further, we studied the dependence of precessional frequency on the externally applied magnetic field. Brillouin light scattering experiments and precession frequencies predicted by simulations show similar trend with increasing field.

Numerical study of thermoacoustic detection of composite materials

In this paper, to study the applicability of thermoacoustic detection of composite materials, the distribution of thermoacoustic waves was numerically calculated when there was a nickel domain inside the silicon domain by applying a sinusoidally varying heat source on the surface of solid silicon domain. By changing the width, thickness and position of the internal nickel domain, the applicable conditions of detecting whether there is another material inside the silicon domain by the distribution of the thermoacoustic waves were studied. In addition, a method of judging the width of the inner nickel domain was given. And the corresponding error was studied.

Magnetic properties of CoPt thin films obtained by electrodeposition from hexachloroplatinate solution. Composition, thickness and substrate dependence

In this paper, magnetic properties of CoPt thin films electrodeposited from an aqueous hexachloroplatinate solution at pH 5.5, in presence of saccharin as an additive, are reported. The electrodeposition was carried out on a sputtered Ru-substrate at controlled potential. X-ray diffraction measurements revealed that CoPt thin films prepared in these specific conditions crystallize in the hexagonal close packing (hcp) phase. The variations of the magnetic properties of 15–500 nm CoPt thin films are explained by taking into account the changes in the elemental composition, thickness, dynamics of the surface roughening during the early stages of deposition, and under-layer structure of the Ru-substrate. The structure and the width of the magnetic domains of electrodeposited CoPt thin films were examined by MFM and found to be thickness dependent.

Accurate model of the stripe domain phase of perpendicularly magnetized multilayers

We develop an accurate analytical model for the stray field energy of parallel stripe domains in multilayer films with perpendicular magnetic anisotropy, taking into account the effects of finite domain wall width and variable domain wall angle. By minimizing the total energy, we predict the domain width, the domain wall width, and the domain wall angle for given material parameters. We show how the domain wall width depends on the film thickness and the domain size. We explore the domain wall angle as a function of Dzyaloshinskii-Moriya interaction (DMI) and derive a threshold value ${D}_{\text{thr}}$ beyond which the system is in a N\'eel state. We find that thicker films require larger values of DMI to stabilize the N\'eel state. Finally, we test the effective medium theory, which allows treating multilayers as effective single layer films, and provide criteria for the applicability of the model in the presence of both surface and volume stray fields. Our results are supported by micromagnetic simulations, which indicate that the predictions are still precise even if the system is in a labyrinthine domain state. Using our model, otherwise inaccessible magnetic parameters, such as the DMI constant or the exchange constant, can now be obtained straightforwardly from static measurements of the stripe domain width in such films.

In Situ variable-Temperature Scanning Tunneling Microscopy Studies of 2D Graphene and Hexagonal Boron Nitride (hBN) Layer Growth Kinetic

The rich physical phenomena and properties associated with two-dimensional (2D) graphene layers have led to a surge in research efforts focused on synthesis, characterization, and, even large-scale production of a variety of 2D crystals. In the newly emergent class of 2D layered materials (and devices), some of the highly exciting developments are a result of leveraging the properties of individual layers via stacking of dissimilar 2D materials held together by van der Waals (vdW) forces. Such vdW-layers exhibit new properties (e.g., valleytronics) and are ideal for ultrathin flexible devices. Graphene is semi-metallic, while its insulating 2D layered analog is hexagonal boron nitride (hBN). Graphene and hBN are isostructural and nearly lattice matched. Composite, lateral, and vertical heterostructures of graphene and hBN layers are expected to exhibit new physical phenomena and properties: tunable bandgap, magnetism, unique electronic and thermal transport properties, robust half-metallic behavior without applied electric fields, and more. Access to such new properties and hence novel applications, hinge on the ability to assemble the 2D materials in desired architecture. This requires fundamental understanding of the mechanisms governing the formation of epitaxial stacks of desired stacking sequences and layer thicknesses, atomically-abrupt graphene-hBN interfaces and domain widths within a single atomic layer, and desired composition within a 2D sheet. As a first step toward this goal, we investigated the chemical vapor deposition (CVD) kinetics of monolayer graphene and hBN on Pd(111) using ultra-high vacuum (UHV) variable-temperature scanning tunneling microscopy (VT-STM). In this talk, we present in situ VT-STM observations of graphene growth using ethylene and hBN growth using borazine on Pd(111) as a function of substrate temperature, borazine flux, and deposition time. We observe the formation of monolayer graphene islands bounded by Pd surface steps. Using scanning tunneling spectroscopy (STS) measurements along with density functional theory (DFT) calculations, we show that graphene/Pd(111) exhibits a bandgap due to the strong interaction between graphene and the Pd substrate. During the CVD of borazine, we observe the nucleation and growth of chemisorbed borazine islands on Pd(111). Using STS, we determined the effect of hBN domain orientation with respect to Pd(111) on its bandgap. From the STM experiments, we identified the growth parameters critical to the formation of single-domain hBN layers on Pd(111). Our studies, which provide new insights into the growth of graphene and hBN monolayers, are useful in developing recipes for the growth of heterostructures of desired architecture.

Ordering of anisotropic nanoparticles in diblock copolymer lamellae: Simulations with dissipative particle dynamics and a molecular theory

Local distribution and orientation of anisotropic nanoparticles in microphase-separated symmetric diblock copolymers has been simulated using dissipative particle dynamics and analyzed with a molecular theory. It has been demonstrated that nanoparticles are characterized by a non-trivial orientational ordering in the lamellar phase due to their anisotropic interactions with isotropic monomer units. In the simulations, the maximum concentration and degree of ordering are attained for non-selective nanorods near the domain boundary. In this case, the nanorods have a certain tendency to align parallel to the interface in the boundary region and perpendicular to it inside the domains. Similar orientation ordering of nanoparticles located at the lamellar interface is predicted by the molecular theory which takes into account that the nanoparticles interact with monomer units via both isotropic and anisotropic potentials. Computer simulations enable one to study the effects of the nanorod concentration, length, stiffness, and selectivity of their interactions with the copolymer components on the phase stability and orientational order of nanoparticles. If the volume fraction of the nanorods is lower than 0.1, they have no effect on the copolymer transition from the disordered state into a lamellar microstructure. Increasing nanorod concentration or nanorod length results in clustering of the nanorods and eventually leads to a macrophase separation, whereas the copolymer preserves its lamellar morphology. Segregated nanorods of length close to the width of the diblock copolymer domains are stacked side by side into smectic layers that fill the domain space. Thus, spontaneous organization and orientation of nanorods leads to a spatial modulation of anisotropic composite properties which may be important for various applications.

Switchable bi-stable multilayer magnetic probes for imaging of soft magnetic structures

We present the use of custom-made multilayer (ML) magnetic probes in magnetic force microscopy (MFM) for imaging soft magnetic structures, i.e. nickel submicron disks of different dimensions. One of the main advantages of a custom-made ML probe is that it can be controllably switched between standard (parallel) and low moment (antiparallel) states. We demonstrate that the predicted vortex and stripe domain states in the disks are observed when using the ML probes both in the antiparallel and parallel states. However, while the phase contrast is significantly larger in the parallel state, the images are dominated by strong sample – probe interactions that obscure the image. By comparison of the stripe domain width observed by MFM with the ML probe and those expected from the Kittel model, we show that the resolution of the probe in the AP and P states is ∼30–40nm, i.e. of the order of the probe geometrical apex and thus approaching the limit of spatial resolution. The ML probes are further compared to the commercial standard and low moment ones, showing that the quality of images obtained with the ML probe is superior to both commercial probes.

Electric-field-driven magnetic domain wall as a microscale magneto-optical shutter

Nowadays, spintronics considers magnetic domain walls as a kind of nanodeviсe that demands for switching much less energy in comparison to homogeneous process. We propose and demonstrate a new concept for the light control via electric field applied locally to a magnetic domain wall playing the role of nanodevice. In detail, we charged a 15-μm-thick metallic tip to generate strong non-uniform electric field in the vicinity of the domain wall in the iron garnet film. The electric field influences the domain wall due to flexomagnetoelectric effect and causes the domain wall shift. The resulting displacement of the domain wall is up to 1/3 of domain width and allows to demonstrate a novel type of the electrically controlled magneto-optical shutter. Polarized laser beam focused on the electric-field-driven domain wall was used to demonstrate the concept of a microscale Faraday modulator. We obtained different regimes of the light modulation – linear, nonlinear and tri-stable – for the same domain wall with corresponding controllable displacement features. Such variability to control of domain wall’s displacement with spatial scale of about 10 μm makes the proposed concept very promising for nanophotonics and spintronics.

Improved block copolymer domain dispersity on chemical patterns via homopolymer-blending and molecular transfer printing

Herein we have investigated the domain width distributions of block copolymers and their ternary blends after directed assembly on chemically patterned surfaces with and without density multiplication. On chemical patterns with density multiplication, the width of the interpolated block copolymer domains was bimodal. Once blended with the corresponding homopolymers, the block copolymers exhibited unimodal distributions of domain width due to the redistribution of homopolymers in the block copolymer domains. When the block copolymers were blended with hydroxyl-terminated homopolymers, the homopolymers with functional end-groups healed the chemical patterns and facilitated the formation of nanostructures with further improved domain width distributions. Lastly, it is demonstrated that the block copolymers achieved the most improved domain width distributions when directed to assemble without density multiplication on one-to-one chemical patterns generated by molecular transfer printing.

Periodical poling of LiNbO3:MgO by electron beam

ABSTRACTWe have studied the features of periodical poling by focused electron beam irradiation of MgO-doped lithium niobate (MgOLN) single crystalline plate covered by the resist layer. We have distinguished the main types of the domain structure depending on the irradiated dose. We have revealed that total domain area and width of the domain stripes depend linearly on the dose and irradiated stripe width. We have observed the highly regular domain structures with duty-cycle close to desirable value of 0.5 on both polar surfaces.

Polarization reversal and domain kinetics in PMN-30PT single crystals

ABSTRACTPolarization reversal process has been studied in [001]-cut lead magnesium niobate-lead titanate single crystals with 30% lead titanate by in situ visualization of domain kinetics and switching current analysis. It has been shown by high-resolution methods that the sample poling leads to partial decay of as-grown domain structure and decrease of the domain width down to 200 nm. Analysis of the switching current by modified Kolmogorov-Avrami approach has shown that the field dependence of the characteristic time follows activation law with activation field value 1040±50 V/mm. In situ visualization has allowed revealing the main stages of domain structure evolution.

Understanding stripe domains in Permalloy films via the angular dependence of permeability spectra

An investigation of the angular dependence of the dynamic permeability spectra has been performed. Three Permalloy films with different thickness were used as the study samples that possess the stripe domains. In order to better understand the magnetization distribution in stripe domains, a theoretical approach was proposed to analyze the variation of the resonance intensity of permeability spectra. By fitting the angular dependence of the μ″max using a theoretical function, a coefficient Λ that can be used to evaluate the average value of the periodic function of the anting angle θ in a periodic stripe is obtained. As the film thickness increases, the decrease of the ratio between domain wall width and stripe domain width is happen. This enables that the coefficient Λ decreases with the increase of film thickness. By deducing this coefficient Λ, one can estimate the maximum canting angle θ0∼8° for the Permalloy films in our experiments.

Tungsten erosion by impurities and redeposition: focus on the magnetised sheath

The effect of the magnetised sheath on the gross erosion and redeposition of tungsten is examined with an insight on impurity impact energy and angle. A complete treatment of the impact energy is performed leading to a scaling that differs from the usual formula. It is found that even if the energy distribution at the sheath entrance strongly differs from this approximation, the discrepancy remains under 20% for the impact energy. The average impact angle of a set of impurities is calculated. The difference between models with and without sheath electric field depends strongly on the charge state and mass of the impurity considered. This can lead, for example in the case of gross sputtering due to impinging , to an underestimation of 3–4 times at for very grazing angles. Scalings for high and low density cases, which correspond for fusion relevant magnetic fields () to m−3 and m−3, respectively, are deduced and provide a good estimation of the average impact angle of all impurities. Finally the magnetised sheath is shown to have an effect on the redeposition through two contributions: it increases the prompt redeposition contribution to the total redeposition and constitutes a potential barrier for the ions leaving the surface. A discussion is provided about the optimal width of the simulation domain to capture these effects.

CFD simulation of a vertical axis wind turbine operating at a moderate tip speed ratio: Guidelines for minimum domain size and azimuthal increment

Accurate prediction of the performance of a vertical-axis wind turbine (VAWT) using Computational Fluid Dynamics (CFD) simulation requires a domain size that is large enough to minimize the effects of blockage and uncertainties in the boundary conditions on the results. It also requires the employment of a sufficiently fine azimuthal increment (dθ) combined with a grid size at which essential flow characteristics can be accurately resolved. The current study systematically investigates the effect of the domain size and azimuthal increment on the performance of a 2-bladed VAWT operating at a moderate tip speed ratio of 4.5 using 2-dimensional and 2.5-dimensional simulations with the unsteady Reynolds-averaged Navier-Stokes (URANS). The grid dependence of the results is studied using three systematically refined grids. The turbine has a low solidity of 0.12 and a swept area of 1 m2. Refining dθ from 10.0° to 0.5° results in a significant (≈43%) increase in the predicted power coefficient (CP) while the effect is negligible (≈0.25%) with further refinement from 0.5° to 0.05° at the given λ. Furthermore, a distance from the turbine center to the domain inlet and outlet of 10D (D: diameter of turbine) each, a domain width of 20D and a diameter of the rotating core of 1.5D are found to be safe choices to minimize the effects of blockage and uncertainty in the boundary conditions on the results.