Types Of Domain Walls Research Articles

Generation of dark pulses in mode-locked erbium-doped fiber ring laser using Ti2SnC absorber

Abstract We report the experimental observation of domain-wall type dark solitons in an all-fiber ring cavity erbium-doped fiber laser (EDFL) mode-locked with a Titanium Tin Carbide (Ti2SnC) saturable absorber (SA). The SA, featuring a modulation depth of 8.2%, was created by incorporating Ti2SnC particles into a polyvinyl film. Dark pulse formation is attributed to cross-phase coupling resulting from cavity birefringence. The mode-locked laser operates at 1559 nm with pump power ranging from 30.9 mW to 90.0 mW, achieving a maximum pulse energy of 1.73 nJ, a repetition rate of 1.78 MHz, and a pulse width of 261.2 ns.

Localized Flexoelectric Effect Around Ba(CuNb) Nano‐Clusters in Epitaxial BiFeO3 Films for Enhancement of Electric and Multiferroic Properties

AbstractRoom‐temperature (RT) multiferroic materials have received significant research attention for various potential applications; however, their properties are not suitable for real‐world implementation. In this study, a nano‐scale localized flexoelectric effect is introduced to enhance the RT multiferroic performance of epitaxial bismuth iron oxide (BiFeO3; BFO) thin films by embedding 10 mol% Ba(Cu1/3Nb2/3)O3 (BCN) nano‐clusters into the host BFO film, which originally has a rhombohedral crystal structure. By utilizing nano‐clustering, a large out‐of‐plane coherent strain is localized around the nano‐clusters, resulting in a highly strained tetragonality of the BFO structure; subsequently, the films exhibit peculiar types of domains and domain walls, such as nano‐scale rotational vortices and antiparallel dipole configurations. These peculiar domain structures, which originate from the localized flexoelectric effect at the nano‐scale, enable excellent ferroelectric, ferromagnetic, and RT multiferroic magnetoelectric coupling. This study reveals that the local variation in the localized flexoelectric field around nano‐clusters considerably impacts the formation of unusual domain‐wall structures. This suggests that the controlled introduction of nano‐clusters with different crystal structures is promising for achieving the desired multiferroic properties.

Frequency-selective valley-edge transmission and channeling in phononic-crystal plates with dual topological modulations

In this numerical study, we propose dual-modulated topological pillared phononic crystal (PnC) plates and demonstrate their application in achieving frequency-selective waveguiding of Lamb-wave valley-edge states. We show that both the radius and the height of the pillars in the honeycomb unit cell can be varied, allowing a generalized parameter space to obtain the complete topological bandgaps and two groups of distinct valley Hall phases for designing topological waveguides operating in different frequency ranges. Accordingly, we construct different types of phase domain walls to support valley-edge states using the dual-modulated PnC plates with a lattice constant of 2000 μm and with topological bandgaps opened around the Dirac cone frequency of 426 kHz. The numerical results show that the valley-edge states emerge to cover different frequency ranges and exhibit robust backscattering immunity when propagating along zigzag paths with sharp corners. Furthermore, the transport path of the valley-edge states can be designed to be highly dependent on the operating frequency in different domain walls. Consequently, we design a straight waveguide and three multichannel waveguides to demonstrate frequency-dependent switchable transmission and selective channeling of valley-edge states, respectively. The results of this study pave the way for the development and optimization of topological acoustic circuits using the generalized parameter space approaches and are expected to find promising applications in frequency-controlled and signal-division devices.

Topological solitons in charge-[formula omitted] flux quantized state of Kagome superconductors

A recent Little-Parks experiment on the new Kagome superconductor CsV3Sb5 demonstrated resistance oscillation with a period of ϕ0/3=hc/6e. This observation of charge-6e flux quantization is effectively explained by a three-component Ginzburg–Landau (GL) model that incorporates second-order Josephson-type couplings. Here, we numerically solve the GL model to present stable topological solitons. We reveal the structures of these solitons, characterized by closed domain walls with attached vortices. We identify two types of domain walls. These solitons possess multiple flux quanta and exhibit a ringlike geometry. Furthermore, we present the characteristic magnetic field distributions of these solitons, enabling their identification in, e.g., scanning Hall probe and scanning SQUID experiments.

Estimation of the interfacial Dzyaloshinskii–Moriya interaction in all-metallic multilayer with perpendicular magnetic anisotropy

The interfacial Dzyaloshinskii–Moriya (iDMI) interaction which arises at the interface between a heavy metal (HM) and a ferromagnet (FM) can stabilize chiral Néel type domain walls in ultrathin perpendicularly magnetized multilayers. Dissimilar HMs are required on both bottom and top sides of the FM layer in order to introduce the structural inversion asymmetry which ensures an effective iDMI in the FM layer. HMs like Pt, Ir, Ta etc are very well known for developing large iDMI in the interface with Co, whereas noble metals like Au can produce negligible iDMI. Therefore, a multilayer Pt/Co/Au is chosen to determine the individual iDMI in the Pt/Co interface. Some procedures like field-induced domain wall motion study, spin–orbit torque efficiency estimation study are well established to quantify the effective field due to the iDMI ( HDMI ) which in turn gives the strength of the iDMI ( Deff ). Besides these procedures, a current-induced switching of magnetization was studied to construct a switching phase diagram where the critical current density of magnetization switching has been plotted as a function of the applied in-plane magnetic field. The experimentally constructed diagram and the simulated diagram using a micromagnetic study have revealed the possibility to quantify HDMI . Thus, a systematic and unified estimation of Deff has been done on all-metallic Ta/Pt/Co/Au multilayers.

Dynamics of chiral domain walls in bent cylindrical magnetic nanowires

Cylindrical magnetic nanowires (NWs) constitute a viable component of 3D nanoscale magnetic devices and engineering their response to external stimuli is necessary for their future functionalization. Here, by means of micromagnetic simulations, we study the dynamical response of vortex–antivortex and Bloch point domain walls under the action of an applied magnetic field in curved arc-shaped NWs varying the saturation magnetization value. Our results provide evidence that, in the range considered in this work, the curvature has no influence on the critical diameters, delimiting different domain wall types. However, it has a relevant effect on the domain wall dynamics. Specifically, the vortex–antivortex domain wall oscillates back and forth while rotating around the nanowire, and the frequency and amplitude can be tuned by curvature and applied field. On the contrary, Bloch point domain wall dynamics does not show any oscillatory behavior, and the domain wall is rapidly expelled from the nanowire with velocities similar to that of the straight cylindrical nanowires. These results allow engineering magnetic response of cylindrical nanowires with curvature.

Modified rational six vertex model on the rectangular lattice

We consider a rational six vertex model on a rectangular lattice with boundary conditions that generalize the usual domain wall type. We find that the partition function of the inhomogeneous version of this model is given by a modified Izergin determinant. The proofs are based on the quantum inverse scattering method and its representation theory together with elementary linear algebra.

Domain walls and vector solitons in the coupled nonlinear Schrödinger equation

We outline a program to classify domain walls (DWs) and vector solitons in the 1D two-component coupled nonlinear Schrödinger (CNLS) equation without restricting the signs or magnitudes of any coefficients. The CNLS equation is reduced first to a complex ordinary differential equation (ODE), and then to a real ODE after imposing a restriction. In the real ODE, we identify four possible equilibria including ZZ, ZN, NZ, and NN, with Z(N) denoting a zero (nonzero) value in a component, and analyze their spatial stability. We identify two types of DWs including asymmetric DWs between ZZ and NN and symmetric DWs between ZN and NZ. We identify three codimension-1 mechanisms for generating vector solitons in the real ODE including heteroclinic cycles, local bifurcations, and exact solutions. Heteroclinic cycles are formed by assembling two DWs back-to-back and generate extended bright-bright (BB), dark-dark (DD), and dark-bright (DB) solitons. Local bifurcations include the Turing (Hamiltonian–Hopf) bifurcation that generates Turing solitons with oscillatory tails and the pitchfork bifurcation that generates DB, bright-antidark, DD, and dark-antidark solitons with monotonic tails. Exact solutions include scalar bright and dark solitons with vector amplitudes. Any codimension-1 real vector soliton can be numerically continued into a codimension-0 family. Complex vector solitons have two more parameters: a dark or antidark component can be numerically continued in the wavenumber, while a bright component can be multiplied by a constant phase factor. We introduce a numerical continuation method to find real and complex vector solitons and show that DWs and DB solitons in the immiscible regime can be related by varying bifurcation parameters. We show that collisions between two DB solitons with a nonzero phase difference in their bright components typically feature a mass exchange that changes the frequencies and phases of the two bright components and the two soliton velocities.

Permissible domain walls in monoclinic MAB ferroelectric phases.

The concept of monoclinic ferroelectric phases has been extensively used over recent decades for the understanding of crystallographic structures of ferroelectric materials. Monoclinic phases have been actively invoked to describe the phase boundaries such as the so-called morphotropic phase boundary in functional perovskite oxides. These phases are believed to play a major role in the enhancement of such functional properties as dielectricity and electromechanical coupling through rotation of spontaneous polarization and/or modification of the rich domain microstructures. Unfortunately, such microstructures remain poorly understood due to the complexity of the subject. The goal of this work is to formulate the geometrical laws behind the monoclinic domain microstructures. Specifically, the result of previous work [Gorfman et al. (2022). Acta Cryst. A78, 158-171] is implemented to catalog and outline some properties of permissible domain walls that connect `strain' domains with monoclinic (MA/MB type) symmetry, occurring in ferroelectric perovskite oxides. The term `permissible' [Fousek & Janovec (1969). J. Appl. Phys. 40, 135-142] pertains to the domain walls connecting a pair of `strain' domains without a lattice mismatch. It was found that 12 monoclinic domains may form pairs connected along 84 types of permissible domain walls. These contain 48 domain walls with fixed Miller indices (known as W-walls) and 36 domain walls whose Miller indices may change when free lattice parameters change as well (known as S-walls). Simple and intuitive analytical expressions are provided that describe the orientation of these domain walls, the matrices of transformation between crystallographic basis vectors and, most importantly, the separation between Bragg peaks, diffracted from each of the 84 pairs of domains, connected along a permissible domain wall. It is shown that the orientation of a domain wall may be described by the specific combination of the monoclinic distortion parameters r = [2/(γ - α)][(c/a) - 1], f = (π - 2γ)/(π - 2α) and p = [2/(π - α - γ)] [(c/a) - 1]. The results of this work will enhance understanding and facilitate investigation (e.g. using single-crystal X-ray diffraction) of complex monoclinic domain microstructures in both crystals and thin films.

Influence of an external electric field on the structure and properties of domain walls in a (111)-oriented ferrite-garnet film

In this study, the features of the manifestation of the flexomagnetoelectric effect in a (111)-oriented ferrite garnet film were investigated. It has been shown that, in such magnets, two types of domain walls with magnetization in domains with are possible: a Bloch-type domain wall and a wall with a quasi-Bloch structure. The evolution of each type of domain wall in an increasing electric field with is revealed, and the characteristic stages of transformation of their structures were determined. Critical fields for their rearrangement and the corresponding values of differential and integral polarizations were found. It has been established that the presence of cubic anisotropy in a (111)-oriented film weakens the degree of manifestation of the flexomagnetoelectric effect in it.

Domain pattern formation in tetragonal ferroelectric ceramics

We present the results of high-resolution simulations of the ferroelectric domain evolution in polycrystalline lead zirconate titanate (PZT), using a phase-field framework that accounts for thermal fluctuations. Leveraging the parallel efficiency of a Fourier spectral scheme, we model micron-sized ceramic samples with thousands of grains at atomic-unit-cell spatial resolution. We introduce a method to automatically identify and track different types of domain walls from phase-field data, which we exploit to study their role during polarization reversal under applied electric fields. Results indicate that the density of domain walls and the domain width obey the Kittel-Mitsui-Furuichi-Roitburd square-root law with implications on the macroscopically observable piezo- and dielectric material properties. Moreover, analyzing the statistics of the domain pattern formation in simulated samples reveals correlations between the average polarization and strain within a grain and its crystallographic orientation, which is in agreement with high-energy x-ray diffraction experiments. Furthermore, we study the occurrence of the two predominant types of domain patterns – monodomain and laminate/twin domain structures – whose emergence within gains of a polycrystal is traced back to the grain orientation. Phase-field statistics are supported by a simple analytical model, which is based on minimizing the electric enthalpy and accurately predicts some of the reported correlations and allows us to further study the behavior of monodomains vs. laminate patterns in ferroelectric ceramics.

Ferroelastic twin domain patterns and polar domain walls of BiVO4 thin films via phase-field simulations

Polar domain walls in centrosymmetric ferroelastics (e.g., BiVO4 films) give rise to inhomogeneity and offer promises for solar energy conversion applications via expediting charge-carrier separation. However, the origin of polar domain walls and the relationship between them and spontaneous strain from structural phase transition remain elusive at the mesoscale in BiVO4 films. Here, from the perspective of phenomenological thermodynamics, the relationship between four variants of monoclinic (M) phase and the corresponding lattice parameters during the tetragonal-monoclinic (T-M) phase transition is revealed. Using phase-field simulations, it suggests that the formation of four variants of ferroelastic twin domains arises from spontaneous strain from T-M phase transition. Moreover, it is demonstrated that (i) polar domain walls in BiVO4 films originate from the flexoelectric effect induced by strain gradient across the domain walls during phase transition process; (ii) shear strain gradient dominates the contribution to the polarization vectors at the domain walls; (iii) 180° head-to-head or tail-to-tail in-plane polarization configurations emerge at the adjacent domain walls. The stability of several types of ferroelastic domain walls is also analyzed from the point of view of total free energy. These results not only provide a fundamental understanding of the origin of polar domain walls and the formation mechanisms of ferroelastic twin patterns, but also stimulate potential applications of polar domain walls of non-polar BiVO4 films in energy conversion.

Direct observation of Néel-type skyrmions and domain walls in a ferrimagnetic DyCo3 thin film

Isolated magnetic skyrmions are stable, topologically protected spin textures that are at the forefront of research interests today due to their potential applications in information technology. A distinct class of skyrmion hosts are rare earth - transition metal (RE-TM) ferrimagnetic materials. To date, the nature and the control of basic traits of skyrmions in these materials are not fully understood. We show that for an archetypal ferrimagnetic material DyCo3 that exhibits a strong perpendicular anisotropy, the ferrimagnetic skyrmion size can be tuned by an external magnetic field. Moreover, by taking advantage of the high spatial resolution of scanning transmission X-ray microscopy (STXM) and utilizing a large x-ray magnetic linear dichroism (XMLD) contrast that occurs naturally at the RE resonant edges, we resolve the nature of the magnetic domain walls of ferrimagnetic skyrmions. We demonstrate that through this method one can easily discriminate between Bloch and Néel type domain walls for each individual skyrmion. For all isolated ferrimagnetic skyrmions, we observe that the domain walls are of Néel-type. This key information is corroborated with results of micromagnetic simulations and allows us to conclude on the nature of the Dzyaloshinskii-Moriya interaction (DMI) which concurs to the stabilisation of skyrmions in this ferrimagnetic system. Establishing that an intrinsic DMI occurs in RE-TM materials will also be beneficial towards a deeper understanding of chiral spin texture control in ferrimagnetic materials.

Multichannel valley topological beam splitter based on different types of domain walls

Topological photonics has made great progress from physical concept verification to new technical applications, and valley topological photonic crystal (TPCs) are one of the most important candidates for future applications in functional devices because of large bandwidth and lossless optical transport. However, due to the limitations of the design method and structure arrangement, the multichannel valley topological beam splitter (BS) has not yet been much explored. Here, we reveal the different robustness of four types of domain walls in valley TPCs. Benefiting from the differences in domain walls, we numerically present and experimentally demonstrate a highly integrated multichannel valley topological BS in the microwave regime. Compared with traditional BSs, it has the advantages of being more robust and compact and having more output ports and higher integration. The reported multichannel topological BS opens an avenue to engineer the flow of light and offers effective design approaches for integrated photonic device miniaturization.

Chiral Interlayer Exchange Coupling for Asymmetric Domain Wall Propagation in Field-Free Magnetization Switching

The discovery of chiral spin texture has unveiled many unusual yet extraordinary physical phenomena, such as the Néel type domain walls and magnetic skyrmions. A recent theoretical study suggests that a chiral exchange interaction is not limited to a single ferromagnetic layer; instead, three-dimensional spin textures can arise from an interlayer Dzyaloshinskii-Moriya interaction. However, the influence of chiral interlayer exchange coupling on the electrical manipulation of magnetization has rarely been addressed. Here, the coexistence of both symmetric and chiral interlayer exchange coupling between two orthogonally magnetized CoFeB layers in PtMn/CoFeB/W/CoFeB/MgO is demonstrated. Images from polar magneto-optical Kerr effect microscopy indicate that the two types of coupling act concurrently to induce asymmetric domain wall propagation, where the velocities of domain walls with opposite chiralities are substantially different. Based on this microscopic mechanism, field-free switching of the perpendicularly magnetized CoFeB is achieved with a wide range of W thicknesses of 0.6-4.5 nm. This work enriches the understanding of interlayer exchange coupling for spintronic applications.

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.

60∘ and 120∘ domain walls in epitaxial BaTiO3 (111)/Co multiferroic heterostructures

We report on domain pattern transfer from a ferroelectric ${\mathrm{BaTiO}}_{3}$ substrate with a (111) orientation of the surface to an epitaxial Co film grown on a Pd buffer layer. Spatially modulated interfacial strain transfer from ferroelectric/ferroelastic domains and inverse magnetostriction in the ferromagnetic film induce stripe regions with a modulation of the in-plane uniaxial magnetic anisotropy direction. Using spin-polarized low-energy electron microscopy, we observe the formation of two distinct anisotropy configurations between stripe regions, leading to angles of ${60}^{\ensuremath{\circ}}$ or ${120}^{\ensuremath{\circ}}$ between the magnetizations of adjacent domains. Moreover, through application of a magnetic field parallel or perpendicular to these stripes, head-to-head or head-to-tail magnetization configurations are initialized. This results in four distinct magnetic domain-wall types associated with different energies and domain widths, which, in turn, affects whether domain pattern transfer can be achieved.

Persistent modification of magnetotransport properties in LaAlO3/SrTiO3 by gate-induced modification of structural domains

We investigate the influence of large electric fields on the transport properties of nanostructures patterned into the electron gas at the interface between ${\mathrm{LaAlO}}_{3}$ and ${\mathrm{SrTiO}}_{3}$ (100). In these nanostructures, the transport is largely dominated by domain walls between structural domains in the ${\mathrm{SrTiO}}_{3}$ appearing below a structural phase transition temperature. We find that both positive and negative gate voltages applied in a side-gate configuration can induce persistent changes in the sample that are only reversed by warming through the phase transition. These changes include a resistance increase and a change in magnetoresistance in magnitude and sign. Furthermore, a resistance anomaly during warm-up that has been observed in the past can be further increased by briefly applying a side-gate voltage. These effects are typically observed in nanostructures below a certain size limit. The electric fields also increase this size limit from a few-hundred nm to more than 1 $\ensuremath{\mu}\mathrm{m}$. All these observations can be consistently explained by a field-induced removal of specific domain-wall types accompanied by an increasing domain size and a reduced number of domain walls in the structures. The results not only show that under certain conditions domain walls can dominate the transport properties even of micron-sized structures, but they also provide an additional tuning knob to induce nonvolatile changes in the transport properties of ${\mathrm{LaAlO}}_{3}\text{/}{\mathrm{SrTiO}}_{3}$ interfaces at low temperatures.

Competition between exchange and magnetostatic energies in domain pattern transfer from BaTiO3 (111) to a Ni thin film

We use spin-polarized low-energy electron microscopy to investigate domain pattern transfer in a multiferroic heterostructure consisting of a (111)-oriented ${\mathrm{BaTiO}}_{3}$ substrate and an epitaxial Ni film. After in situ thick-film deposition and annealing through the ferroelectric phase transition, interfacial strain transfer from ferroelastic domains in the substrate and inverse magnetostriction in the magnetic thick film introduce a uniaxial in-plane magnetic anisotropy that rotates by ${60}^{\ensuremath{\circ}}$ between alternating stripe regions. We show that two types of magnetic domain wall can be initialized in principle. Combining experimental results with micromagnetic simulations, we show that a competition between the exchange and magnetostatic energies in these domain walls has a strong influence on the magnetic domain configuration.

Intersecting multiaxial domain walls in plastic ferroelectric crystal films

Plastic ferroelectrics comprise a class of solution-processable molecular ferroelectrics, in which spherical polar molecules can rotate and/or freeze within crystal lattices. Some compounds exhibit superior multiaxial ferroelectricity and very sharp ferroelectric switching characteristics, although the domain wall (DW) characteristics have not yet been explored. Here, we report distinctive DW characteristics in drop-casted monocrystalline thin films of a typical plastic/ferroelectric $[\mathrm{AH}][\mathrm{Re}{\mathrm{O}}_{4}]$. We demonstrate that the films form ${71}^{\ensuremath{\circ}}, {109}^{\ensuremath{\circ}}$, and ${180}^{\ensuremath{\circ}}$ DWs, unique to the pseudocubic rhombohedral lattice, that emerge and compete with each other, depending on the crystallographic orientation of the films. Particularly, it is observed that all three types of DWs intersect at several single points, whose unique nature should be ascribed to the small elastic deformation. The observed domains and ${180}^{\ensuremath{\circ}}$ DWs also comprise much larger periodicity and scaling than those of conventional inorganic ferroelectric films, which should be associated with the unique polarization reversal mechanism in the compound films. These observed features reveal the exotic multiaxial ferroelectricity of soft plastic/ferroelectrics, paving the way for developing printable ferroelectronics.