Straight Domain Research Articles

Deep supercooling solidification towards tuned amorphous/nanocrystalline dual phases for superior magnetic nanocrystalline alloys

Nanocrystalline soft magnetic alloys featuring with amorphous-nanocrystalline dual-phase structure are critical for energy conversion and transportation at elevated frequencies. Their applications however, are refrained by limited saturation magnetic flux density (Bs) due to unavoidable addition of a considerable quantity of non-magnetic elements for glass forming ability (GFA). Furthermore, engineering of the amorphous-nanocrystalline microstructure is critical for the coercivity (Hc), which urges development of advanced approach. In this study, a deep supercooling solidification has been proposed, which not only promotes the formation of short-range packing and icosahedron/icosahedron-like structures for enhanced GFA, but also induces an optimized microstructure consisting of highly disordered amorphous matrix to facilitate nanograin refinement. Based on such strategy, Finemet-based nanocrystalline alloy with superior magnetic properties (Bs = 1.71 T, Hc = 5.0 A/m) has been achieved without additional glass forming element. Such superior performance is correlated to the unique magnetic domain structure involving straight domain walls and smooth movement. The deep supercooling strategy not only breaks the trade-off between the Bs and GFA to allow the design of nanocrystalline alloys with large ferromagnetic content, but also serves as an effective method for microstructure optimization for nanocrystalline alloys.

A molecular ferroelectric thin film of imidazolium perchlorate on silicon

Molecular ferroelectrics have garnered significant attention due to their structural tunability, low synthesis temperature, and high flexibility. Herein, we successfully synthesized imidazole perchlorate (ImClO4) single crystals and high-quality, highly-oriented thin films on Si substrates. These films demonstrated a high inverse piezoelectric coefficient of 55.7 pm/V. Two types of domain bands were observed: type-I bands tilted ~60° relative to the horizontal axis, and type-II bands positioned perpendicular to the horizontal axis. Under a + 20 V bias, type-I bands showed a reduction and detachment of 180° domain walls to form a needle-like domain. It extended toward the band boundary after applying −20 V bias, which grew along the boundary upon contact. In contrast, type-II bands showed straight domain wall motion and displayed a higher piezoresponse than type-I bands. The growth of high quality molecular ferroelectric thin films on Si substrates paves the way for the development of on-chip devices.

Evidence of the Monopolar-Dipolar Crossover Regime: A Multiscale Study of Ferroelastic Domains by In Situ Microscopy Techniques.

The elastic interaction between kinks (and antikinks) within domain walls plays a pivotal role in shaping the domain structure, and their dynamics. In bulk materials, kinks interact as elastic monopoles, dependent on the distance between walls (d-1) and typically characterized by a rigid and straight domain configuration. In this work the evolution of the domain structure is investigated, as the sample size decreases, by the means of in situ heating microscopy techniques on free-standing samples. As the sample size decreases, a significant transformation is observed: domain walls exhibit pronounced curvature, accompanied by an increase in both domain wall and junction density. This transformation is attributed to the pronounced influence of kinks, inducing sample warping, where "dipole-dipole" interactions are dominant (d-2). Moreover, a critical thickness range that delineates a crossover between the monopolar and dipolar regimens is experimentally identified and corroborated by atomic simulations. These findings are relevant for in situ TEM studies and for the development of novel devices based on free-standing ferroic thin films and nanomaterials.

Straight domains are locally divided

We present a proof that all straight domains are locally divided—thereby answering two open problems posed by Dobbs and Picavet, which appeared in the survey “Open Problems in Commutative Ring Theory” written by Cahen, Fontana, Frisch, and Glaz. In fact, we are able to prove a stronger result: a prime ideal of a domain is straight if and only if it is locally divided.

Spontaneous Topological (Anti)meron Chains in the Domain Walls of Centrosymmetric Rare‐Earth Magnet

AbstractExploration and manipulation of topological protected magnetic swirls, such as skyrmion, antiskyrmion, meron, and vortex, holds significance for fundamental research and practical applications in high‐density magnetic information storage and spintronics because of their high storage density and low driven current. This study unveils the existence of field‐free spontaneous (anti)meron chains with a topological charge of ±1/2 in the centrosymmetric rare‐earth magnet Tb6Co2.17Si2.5 via in situ real‐space observation. The spin reorientation transition from in‐plane to uniaxial anisotropy contributes to the spontaneous transformation from straight domain walls to topological (anti)meron chains and to stripe domains along the [110] zone axis during in situ cooling. The study further confirms the critical role of the noncollinear magnetic structure of Tb atoms in the formation of topological (anti)meron chains via real‐space observations, first‐principles calculations, and micromagnetic simulations. The spontaneous topological magnetic texture is strongly correlated with the 4f electrons of rare‐earth atoms, enriching and stimulating alternative generation mechanisms of topological spin textures from emerging rare‐earth magnets, and further applications in spintronics.

Nanoscopic spin-wave channeling along programmable magnetic domain walls in a CoFeB/BaTiO3 multiferroic heterostructure

We report a micromagnetic study on spin-wave propagation along magnetic domain walls in a ferromagnetic/ferroelectric bilayer. In our system, strain coupling between the two ferroic materials and inverse magnetostriction produce a fully correlated domain pattern wherein straight and narrow ferroelectric domain walls pin the magnetic domain walls. Consequently, an external magnetic field does tailor the spin structure of the magnetic domain walls instead of moving them. We use experimental parameters from a previously studied CoFeB/BaTiO3 material system to investigate the potential of artificial multiferroics for programmable nanoscopic spin-wave channeling. We show that spin waves are transported along the pinned magnetic domain walls at zero magnetic field and low frequency due to a local demagnetizing field. Further, switching of the domain wall spin structure from a head-to-tail to a head-to-head configuration abruptly changes the propagating spin-wave mode. We study the effect of magnetic field strength on the localized modes and discuss reversible control of spin-wave channeling via electric-field-driven magnetic domain wall motion. Nanoscopic guiding of propagating spin waves by an electric field, in combination with positional robustness to and mode programming by an external magnetic field, offers prospects for low-power and reconfigurable domain-wall-based magnonic devices.

A phase-field model for ferroelectrics with general kinetics, Part I: Model formulation

When subjected to electro-mechanical loading, ferroelectrics see their polarization evolve through the nucleation and evolution of domains. Existing mesoscale phase-field models for ferroelectrics are typically based on a gradient-descent law for the evolution of the order parameter. While this implicitly assumes that domain walls evolve with linear kinetics, experiments instead indicate that domain wall kinetics is nonlinear. This, in turn, is an important feature for the modeling of rate-dependent effects in polarization switching. We propose a new multiple-phase-field model for ferroelectrics, which permits domain wall motion with nonlinear kinetics, with applications in other solid–solid phase transformation problems. By means of analytical traveling wave solutions, we characterize the interfacial properties (energy and width) and the interface kinetics of straight domain walls, as furnished by the general kinetics model, and compare them to those of the classical Allen–Cahn model. We show that the proposed model propagates domain walls with arbitrarily chosen nonlinear kinetic relations, which can be tuned to differ for the different types of domain walls in accordance with experimental evidence.

Anomalous domain wall dynamics in Ir50Mn50/Fe2CoSi bilayers

We report on the evidenced anomalous saw-tooth and curved domains in the Si/SiO2/IrMn/Fe2CoSi/Ta bilayers. The existence of saw-tooth domains is attributed to higher magnetic charge density at the domain boundary induced by the IrMn layer, while curved domains are apparent due to Dzyaloshinskii-Morya interaction (DMI). On the other hand, straight domain walls are apparent as a result of uni–axial anisotropy and four-fold anisotropy along the easy axis. The curvature for the domain walls decreases upon changing the angle between sample edge and the magnetic field. We believe that the present results would indeed be helpful for the development of the domain wall motion devices.

Plasmon-induced transparency in a reconfigurable composite valley photonic crystal.

We propose a new kind of reconfigurable topological valley photonic crystal (TVPC), and a novel topological waveguide can be formed by constructing a domain wall between two TVPCs with opposite valley-Chern indices. The topological waveguide mode in the composite TVPC has large group refractive index. A topologically protected coupled waveguide cavity system is then designed by introducing a hexagonal ring cavity at the center of the straight domain wall of a combined TVPC, in which a narrow plasmon induced transparency window rises at 3.8848 GHz with a Q-factor of 1387 and a maximum group refractive index as high as 186. We propose a notch filter with a resonant frequency of 3.8852 GHz and a very high Q-factor of 10224. By changing the refractive index of liquid crystals via an external voltage applied between two parallel metal plates, the filter can be switched between band-pass and band-stop based on the reconfigurable topological interface state.

Mixed finite element formulation for bending of laminated beams using the refined zigzag theory

This study presents a mixed finite element formulation for the stress analysis of laminated composite beams based on the refined zigzag theory. The Hellinger–Reissner variational principle is employed to obtain the first variation of the functional that is expressed in terms of displacements and stress resultants. Due to C0 continuity requirements of the formulation, linear shape functions are adopted to discretize the straight beam domain with two-noded finite elements. The proposed formulation is shear locking free from nature since it introduces displacement and stress resultant terms as independent field variables. A monolithic solution of the global finite element equations is preferred, hence the stress resultants are directly obtained from the solution of these equations. The in-plane strain measures of the beam are obtained directly at the nodes over the compliance matrix and stress resultants by avoiding error-prone spatial derivatives. Following, transverse shear stresses are calculated from the equilibrium equations at the post-processing level. This simple but effective finite element formulation is first verified and tested for convergence behavior. The robustness of the approach is shown through some examples and its accuracy in predicting the displacement and stress components is revealed.

Avalanche criticality during ferroelectric/ferroelastic switching

Field induced domain wall displacements define ferroelectric/ferroelastic hysteresis loops, which are at the core of piezoelectric, magnetoelectric and memristive devices. These collective displacements are scale invariant jumps with avalanche characteristics. Here, we analyse the spatial distribution of avalanches in ferroelectrics with different domain and transformation patterns: Pb(Mg1/3Nb2/3)O3–PbTiO3 contains complex domains with needles and junction patterns, while BaTiO3 has parallel straight domains. Nevertheless, their avalanche characteristics are indistinguishable. The energies, areas and perimeters of the switched regions are power law distributed with exponents close to predicted mean field values. At the coercive field, the area exponent decreases, while the fractal dimension increases. This fine structure of the switching process has not been detected before and suggests that switching occurs via criticality at the coercive field with fundamentally different switching geometries at and near this critical point. We conjecture that the domain switching process in ferroelectrics is universal at the coercive field.

Magnetic Domain With Straight Domain Walls Passing Through a Ferromagnetic Insulator for a Continuously Looped Racetrack Memory

We demonstrate via micromagnetic simulations that a magnetic domain, which has two straight domain walls (DWs) and is formed in a perpendicularly magnetized ferromagnetic metal (FM), moves through a perpendicularly magnetized ferromagnetic insulator (FI) because of the spin-transfer torque arising from a spin-polarized current flowing in the FM. This phenomenon could be used for realizing racetrack memory with a continuous loop structure built from a nanowire comprising an FM/FI junction. We employ two nanowire structures in which two FMs are separated by a rectangular or a zigzag FI. In the system with a rectangular FI, the domain passes through the insulator when the length of the insulator is shorter than the DW length. However, the domain transforms into an unstable structure with current-induced domain motion after it passes through the insulator. In the system with a zigzag FI, the domain passes through the insulator irrespective of the length of the insulator. When passing through the zigzag FI, the velocity of the domain increases.

Direct measure of crystalline domain size, distribution, and orientation in polyethylene fibers

High performance ultra high molecular weight polyethylene (UHMWPE) fibers are primarily composed of extended chain (shish) and lamellae (kebab) crystalline domains. Characterization of these architectures commonly utilizes x-ray scattering techniques, which rely upon models to transform from inverse scattering space to real space. Scattering models for lamellae and straight chain crystalline domains were developed and intended for use in ideal scattering scenarios; ie. purely extended chain or purely lamellae. Simultaneous implementation of both models with real (non-ideal) fibers takes for granted the validity of either model in the presence of the other crystalline feature. In this work, we utilize atomic force microscopy (AFM) to directly couple real space stiffness measurements to the analysis of scattering data. The validity of scattering models is tested against real space image analysis and conclusions are drawn regarding the analysis of scattering data to quantify crystalline domain sizes. We find that the lamellae long spacing estimated from scattering data is consistent with real space image analysis. Whereas significant differences are observed for the analysis of lamellae diameter. The characteristic size of extended chain crystalline domains is measured via the streak analysis method on both SAXS 2D scattering data and the Fast Fourier Transform (FFT) of AFM stiffness maps. The streak analysis results in comparable length scales when applied to SAXS and FFT AFM images. A comparison of the streak analysis with novel filtered AFM images suggest that the streak analysis is capturing continuity of straight chain crystalline domains.

Chiral Magnonics: Reprogrammable Nanoscale Spin Wave Networks Based on Chiral Domain Walls.

SummarySpin waves offer promising perspectives as information carriers for future computational architectures beyond conventional complementary metal-oxide-semiconductor (CMOS) technology, owing to their benefits for device minimizations and low-ohmic losses. Although plenty of magnonic devices have been proposed previously, scalable nanoscale networks based on spin waves are still missing. Here, we demonstrate a reprogrammable two-dimensional spin wave network by combining the chiral exchange spin waves and chiral domain walls. The spin-wave network can be extended to two dimensions and offers unprecedented control of exchange spin waves. Each cell in the network can excite, transmit, and detect spin waves independently in the chiral domain wall, and spin-wave logics are also demonstrated. Our results open up perspectives for integrating spin waves into future logic and computing circuits and networks.

Analytical computation of the demagnetizing energy of thin-film domain walls

Due to its non-local nature, calculating the demagnetizing field remains the biggest challenge in understanding domain structures in ferromagnetic materials. Analytical descriptions of demagnetizing effects typically approximate domain walls as uniformly magnetized ellipsoids, neglecting both the smooth rotation of magnetization from one domain to the other and the interaction between the two domains. Here, instead of the demagnetizing field, we compute analytically the demagnetizing energy of a straight domain wall described by the classical $\tanh$ magnetization profile in a thin film with perpendicular magnetic anisotropy. We then use our expression for the demagnetizing energy to derive an improved version of the 1D model of field-driven domain wall motion, resulting in accurate expressions for important properties of the domain wall such as the domain wall width and the Walker breakdown field. We verify the accuracy of our analytical results by micromagnetic simulations.

Structure and Dynamics of Ferroelectric Domains in Polycrystalline Pb(Fe1/2Nb1/2)O3.

A complex domain structure with variations in the morphology is observed at ambient temperature in monoclinic Pb(Fe1/2Nb1/2)O3. Using electron microscopy and piezoresponse force microscopy, it is possible to reveal micrometre-sized wedge, lamellar-like, and irregularly shaped domains. By increasing the temperature, the domain structure persists up to 80 °C, and then starts to disappear at around 100 °C due to the proximity of the ferroelectric–paraelectric phase transition, in agreement with macroscopic dielectric measurements. In order to understand to what degree domain switching can occur in the ceramic, the mobility of the domain walls was studied at ambient temperature. The in situ poling experiment performed using piezoresponse force microscopy resulted in an almost perfectly poled area, providing evidence that all types of domains can be easily switched. By poling half an area with 20 V and the other half with −20 V, two domains separated by a straight domain wall were created, indicating that Pb(Fe1/2Nb1/2)O3 is a promising material for domain-wall engineering.

δ′-interaction as a limit of a thin Neumann waveguide with transversal window

We consider a waveguide-like domain consisting of two thin straight tubular domains connected through a tiny window. The perpendicular size of this waveguide is of order ε . Under the assumption that the window is appropriately scaled we prove that the Neumann Laplacian on this domain converges in (a kind of) norm resolvent sense as ε → 0 to a one-dimensional Schrödinger operator corresponding to a δ ′ -interaction of a non-negative strength. We estimate the rate of this convergence, also we prove the convergence of spectra.

Current-induced motion of bubble domains stabilised in nanowires with edge defects

Bubble domain (BD) motion is expected to be useful for domain motion magnetic memory. We investigate the current-induced motion of BDs produced in a perpendicularly magnetised thin wire with edge defects by using micro-magnetic simulation. We produce a stable BD in the wire and find that its size increases with the wire width. Upon application of a spin-polarised current, the BD both with and without Bloch points moves with a velocity similar to the theoretical velocity of domain wall motion while maintaining its structure. In the presence of edge defects in the wire, the motion of the BD is slightly affected by the magnetisation of the uneven edge structure, whereas a straight domain wall is pinned strongly by the edge defects. The effect of edge defects on BD motion is much smaller than that in straight domain wall motion.

Millimeter-sized magnetic domains in perpendicularly magnetized ferrimagnetic Mn4N thin films grown on SrTiO3

The use of epitaxial layers for domain wall-based spintronic applications is often hampered by the presence of pinning sites. Here, we show that when depositing Mn4N (10 nm) epitaxial films, the replacement of MgO(001) by SrTiO3(001) substrates allows minimizing the misfit, and to obtain an improved crystalline quality, a sharper switching, a full remanence, a high anisotropy and remarkable millimeter-sized magnetic domains, with straight and smooth domain walls. In a context of rising interest for current-induced domain wall motion in rare-earth ferrimagnets, we show that Mn4N/SrTiO3, which is rare-earth free, constitutes a very promising ferrimagnetic system for current-induced domain wall motion.

Three-dimensional fluid topology optimization for heat transfer

In this work, an in house topology optimization (TO) solver is developed to optimize a conjugate heat transfer problem: realizing more complex and efficient coolant systems by minimizing pressure losses and maximizing the heat transfer. The TO method consists in an idealized sedimentation process in which a design variable, in this case impermeability, is iteratively updated across the domain. The optimal solution is the solidified region uniquely defined by the final distribution of impermeability. Due to the geometrical complexity of the optimal solutions obtained, this design method is not always suitable for classic manufacturing methods (molding, stamping....) On the contrary, it can be thought as an approach to better and fully exploit the flexibility offered by additive manufacturing (AM), still often used on old and less efficient design techniques. In the present article, the proposed method is developed using a Lagrangian optimization approach to minimize stagnation pressure dissipation while maximizing heat transfer between fluid and solid region. An impermeability dependent thermal conductivity is included and a smoother operator is adopted to bound thermal diffusivity gradients across solid and fluid. Simulations are performed on a straight squared duct domain. The variability of the results is shown on the basis of different weights of the objective functions. The solver builds automatically three-dimensional structures enhancing the heat transfer level between the walls and the flow through the generation of pairs of counter rotating vortices. This is consistent to solution proposed in literature like v-shaped ribs, even if the geometry generated is more complex and more efficient. It is possible to define the desired level of heat transfer and losses and obtain the closest optimal solution. It is the first time that a conjugate heat transfer optimization problem, with these constraints, has been tackled with this approach for three-dimensional geometries.