Different Types Of Domain Walls Research Articles

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.

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.

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.

Dynamics of Dzyaloshinskii domain walls for ferrimagnets with compensation of angular momentum

Dzyaloshinskii domain walls in chiral ferrimagnets, with a violation of spatial inversion symmetry due to Dzyaloshinskii–Moriya interaction, are studied theoretically. The dynamics of domain walls with non-small velocity is investigated by means of qualitative and numerical analysis of the sigma-model equation, generalized for accounting for chiral interactions and not complete compensation of sublattice angular momenta. Domain wall critical velocity, the maximal velocity that the domain wall can move, its energy and linear momentum are determined. Domain wall dispersion relation, the dependence of the energy on the linear momentum, is constructed. Forced motion of domain walls with accounting for weak dissipation processes is investigated by means of collective variable approach. We found quite a complicated picture of the dynamics of domain walls in chiral ferrimagnet that can be of interest for general theory of magnetic solitons and useful for applications. In addition to the increasing of the critical velocity of the domain wall when approaching angular momentum compensation point, which is the well-known sequence of the exchange enhancement effect, even the qualitative picture of domain wall states is changing. The main difference is that a few different types of domain walls appear, forming a sequence of states with a characteristic complication of the wall structure (formation of cluster domain walls) together with an increase in their energy. Both factors, the exchange enhancement of the limiting domain wall velocity and the destruction of integrability, turn out to be important here. In particular, the critical velocities of cluster domain walls, as well as the maximal values of their linear momenta, appear to be higher (sometimes, a few times higher) than for standard domain walls. This effect is absent for domain walls, known for non-integrable models of ferromagnets. The presence of cluster domain walls can be of interest for the problem, how to increase the maximal velocity of motion for domain walls.

Effects of domain walls in bilayer graphene in an external magnetic field

We investigate bilayer graphene systems with layer switching domain walls separating the two energetically equivalent Bernal stackings in the presence of an external magnetic field. To this end we calculate quantum transport and local densities of three microscopic models for a single domain wall: a hard wall, a defect due to shear, and a defect due to tension. The quantum transport calculations are performed with a recursive Green's function method. Technically, we discuss an explicit algorithm for the separation of a system into subsystems for the recursion and we present an optimization of the well known iteration scheme for lead self-energies for sparse chain couplings. We find strong physical differences for the three different types of domain walls in the integer quantum Hall regime. For a domain wall due to shearing of the upper graphene layer there is a plateau formation in the magnetoconductance for sufficiently wide defect regions. For wide domain walls due to tension in the upper graphene layer there is only an approximate plateau formation with fluctuations of the order of the elementary conuctance quantum $\sigma_0$. A direct transition between stacking regions like for the hard wall domain wall shows no plateau formation and is therefore not a good model for either of the previously mentioned extended domain walls.

Temperature dependence of three-dimensional domain wall arrangement in ferroelectric K0.9Na0.1NbO3 epitaxial thin films

The three-dimensional arrangement and orientation of domain walls in ferroelectric K0.9Na0.1NbO3/(110)NdScO3 epitaxial thin films were investigated at different temperatures both experimentally by means of piezoresponse force microscopy and three-dimensional x-ray diffraction and theoretically by three-dimensional phase-field simulations. At room temperature, a well-ordered herringbone-like domain pattern appears in which there is a periodic arrangement of a1a2/MC monoclinic phases. Four different types of domain walls are observed, which can be characterized by out-of-plane tilt angles of ±45° and in-plane twist angles of ±21°. For the orthorhombic high-temperature phase, a periodic a1/a2 stripe domain pattern with exclusive in-plane polarization is formed. Here, two different types of domain walls are observed, both of them having a fixed out-of-plane domain wall angle of 90° but distinguished by different in-plane twist angles of ±45°. The experimental results are fully consistent with three-dimensional phase-field simulations using anisotropic misfit strains. The qualitative agreement between the experiment and the theory applies, in particular, to the wide phase transition range between about 180 °C and 260 °C. In this temperature range, a complex interplay of coexisting monoclinic a1a2/MC and orthorhombic a1/a2 phases takes place.

Meissner currents induced by topological magnetic textures in hybrid superconductor/ferromagnet structures

Topological spin configurations in proximity to a superconductor have recently attracted great interest due to the potential application of the former in spintronics and also as another platform for realizing non-trivial topological superconductors. Their application in these areas requires precise knowledge of the existing exchange fields and/or the stray-fields which are therefore essential for the study of these systems. Here, we determine the effective stray-field and the Meissner currents in a Superconductor/Ferromagnet/Superconductor (S/F/S) junction produced by various nonhomogenous magnetic textures in the F. The inhomogeneity arises either due to a periodic structure with flat domain walls (DW) or is caused by an isolated chiral magnetic skyrmion (Sk). We consider both Bloch- and N\'{e}el-type Sk and also analyze in detail the periodic structures of different types of DW's-- that is Bloch-type DW (BDW) and N\'{e}el-type DW (NDW) of finite width with in- and out-of-plane magnetization vector. The spatial dependence of the fields and Meissner currents are shown to be qualitatively different for the case of Bloch- and N\'{e}el-type magnetic textures. While the spatial distributions in the upper and lower S are identical for Bloch-type Sk and DW's they are asymmetric for the case of N\'{e}el-type magnetic textures. The depairing factor, which determines the critical temperature and which is related to vector potential of the stray-field, can have its maximum at the center of a magnetic domain but also, as we show, above the DW. For Sk's the maximum is located at a finite distance within the Sk radius. Based on this, we study the nucleation of superconductivity in the presence of DW's. Because of the asymmetry for N\'{e}el-type structures, the critical temperature in the upper and lower S is expected to be different. The obtained results can also be applied to S/F bilayers.

Structural and thermal transport properties of ferroelectric domain walls in GeTe from first principles

Ferroelectric domain walls are boundaries between regions with different polarization orientations in a ferroelectric material. Using first-principles calculations, we characterize all different types of domain walls forming on ($11\overline{1}$), (111), and ($1\overline{1}0$) crystallographic planes in thermoelectric GeTe. We find large structural distortions in the vicinity of most of these domain walls, which are driven by polarization variations. We show that such strong strain-order parameter coupling will considerably reduce the lattice thermal conductivity of GeTe samples containing domain walls with respect to a single crystal. Our results thus suggest that domain engineering is a promising path for enhancing the thermoelectric figure of merit of GeTe.

Coexistence of phases and interphase boundaries in BaTiO3

A theoretical analysis of the internal structure of interphase boundaries separating domains of coexisting phases is presented for the perovskite ferroelectric BaTiO3. The temperature dependence of interphase boundary widths and surface energies are calculated and compared with the corresponding parameters for different types of domain walls existing within the ferroelectric phases of BaTiO3.

Effect of defects, magnetocrystalline anisotropy, and shape anisotropy on magnetic structure of iron thin films by magnetic force microscopy

Microstructures of magnetic materials, including defects and crystallographic orientations, are known to strongly influence magnetic domain structures. Measurement techniques such as magnetic force microscopy (MFM) thus allow study of correlations between microstructural and magnetic properties. The present work probes effects of anisotropy and artificial defects on the evolution of domain structure with applied field. Single crystal iron thin films on MgO substrates were milled by Focused Ion Beam (FIB) to create different magnetically isolated squares and rectangles in [110] crystallographic orientations, having their easy axis 45° from the sample edge. To investigate domain wall response on encountering non-magnetic defects, a 150 nm diameter hole was created in the center of some samples. By simultaneously varying crystal orientation and shape, both magnetocrystalline anisotropy and shape anisotropy, as well as their interaction, could be studied. Shape anisotropy was found to be important primarily for the longer edge of rectangular samples, which exaggerated the FIB edge effects and provided nucleation sites for spike domains in non-easy axis oriented samples. Center holes acted as pinning sites for domain walls until large applied magnetic fields. The present studies are aimed at deepening the understanding of the propagation of different types of domain walls in the presence of defects and different crystal orientations.

Topology breaking of the vortex in multiferroic Y0.67Lu0.33MnO3

Although topological defects, such as domain walls (DWs) or vortices, are naturally protected by topological invariance, yet, we discover an exception that the six-state topology of the vortex with Z2 × Z3 symmetry is broken by a partial edge dislocation (PED) in hexagonal Y0.67Lu0.33MnO3, where the topologies of the four-state vortex or closed DWs emerges. Using aberration-corrected scanning transmission electron microscopy, we found that the PED plays an important role in changing the phase of translation domain. The PED at the vortex core leads to the formation of the four-state vortex, while the ones at closed DWs connect different types of DWs, both corresponding to continuous phase changes. These results indicate that PEDs can change the topology of translation-related domain vortices and more vortices with even domains can be expected.

Selective injection of magnetic domain walls in Permalloy nanostripes

This work explores the conditions that allow the injection and pinning of different magnetic domain walls (DWs) in Permalloy nanostripes with notches of different shapes. The injection is done under a constant external field by applying a 10 ns current pulse through an adjacent current line. The type of DW is identified by its anisotropic magnetoresistance (AMR). We find that, while a quasi-static pinning (nucleating at zero field and propagating the DW to the notch by slowly increasing the external field) would allow to distinguish different types of DWs pinned at the notch, a dynamic pinning (nucleating, propagating, and pinning the DW under a constant non-zero magnetic field) makes the discrimination of different DWs very difficult. Micromagnetic simulations indicate that the AMR of the different types of DWs become quite similar to each other as the injection field increases. This might explain why at large injection fields, usually only one or two values of resistance are detected, depending on the shape of the notch. Therefore, caution should be taken when establishing a one-to-one relationship between a type of DW and a value of resistance, especially if the injection is done under a non-zero external magnetic field.

Effect of magnetic surface anisotropy on domain wall structure in magnetic triaxial films

The influence of the presence of surface anisotropy on the micromagnetic structure of the domain wall in magnetic-triaxial films has been investigated. The investigation method is the numerical minimization of the energy functional of the domain wall used in the two-dimensional model of the distribution of magnetization. Films with different orientations of crystallographic axes with respect to the film surface have been considered. The effect of the surface anisotropy type and surface anisotropy constant K S value on the stability of different types of domain walls has been found.

Phase field simulations of low-dimensional ferroelectrics

This paper reviews the previous work on phase field simulations of low-dimensional ferroelectrics of two-dimensional epitaxial ferroelectric islands, thin films, and nanoparticles. The simulations are conducted in real space with exact boundary conditions of a low-dimensional ferroelectric, but consuming a much longer simulation time in comparison with that conducted in Fourier space. For ferroelectric islands and thin films, the simulations exhibit spatial polarization distributions with different types of domain walls and find two critical thicknesses, at which the simulated material changes from a multidomain state to a single-domain state and from ferroelectric phase to paraelectric phase, respectively. The remanent polarization and the coercive field of the simulated ferroelectric films both decrease with decreasing film thickness. The simulations exhibit vortex patterns of polarizations, which have purely toroidal moments of polarizations and macroscopically negligible averaged polarizations, in stress-free nanoparticles when long-range electrostatic interactions are fully taken into account. However, a single-domain structure without any toroidal moment of polarizations is formed in small nanoparticles with strong long-range elastic interactions.

Domain wall asymmetries in Ni81Fe19/NiO: proof of variable anisotropies in exchange bias systems

Multiple changes in the internal structure of magnetic domain walls due to alterations of the interfacial coupling across the ferromagnetic/antiferromagnetic interface are reported for Ni81Fe19/NiO exchange coupled films. Depending on the antiferromagnetically induced anisotropy, three different types of domain walls are observed. Cross-tie domain wall structures of decreased vortex to anti-vortex spacing develop with the addition of a thin antiferromagnetic layer. For exchange biased samples strong asymmetries in domain wall structure occur for the ascending and descending branch of the magnetization loop. For the descending branch a symmetric 180° Néel wall develops, whereas a folded cross-tie domain wall structure forms during magnetization reversal along the ascending loop branch. The novel type of ‘zig-zagged’ cross-tie wall is characterized by cross-ties reaching differently into the surrounding domain areas. The wall alterations indicate the existence of bi-modal coupling strengths in exchange coupled systems, which is in accordance with models of exchange bias that assume pinned and unpinned spins at the ferromagnetic/antiferromagnetic interface.

Dynamics of Domain Walls in Soft Magnetic Nanostripes: Topological Soliton Approach

The motions of different types of domain walls (DWs) driven by direct current (dc) magnetic field in soft magnetic nanostripes were calculated. The DWs exhibit steady and transient motions in the low fields and oscillations of their internal structure above a critical field. A developed soliton model of the walls explains their dynamics by the motions of a limited number of magnetic topological solitons having nonzero gyrovectors such as vortex and antivortex. The model predicts the reduced DW velocity and critical field in the low-field regime, and increased wall-oscillation frequency in nanostripes, compared to the Walker solution for bulk magnets. The critical field and velocity are determined by the nanostripe thickness and width, whereas the oscillation frequency depends only on the field strength.

Magnetic impurities in a superconductor: Effect of domain walls and interference

We consider the effect of magnetic impurities, modeled by classical spins, in a conventional superconductor. We study their effect on the quasiparticles, specifically on the spin density and local density of states. As previously emphasized, the impurities induce multiple scatterings of the quasiparticle wave functions, leading to complex interference phenomena. Also, the impurities induce quantum phase transitions in the many-body system. Previous authors studied the effect of either a small number of impurities (from 1 to 3) or a finite concentration of impurities, typically in a disordered distribution. In this work, we assume a regular set of spins distributed inside the superconductor in such a way that the spins are oriented, forming different types of domain walls, assumed stable. This situation may be particularly interesting in the context of spin transfer due to polarized currents traversing the material.

Size effects in epitaxial ferroelectric islands and thin films

Size effects on domain configuration and polarization switching in two-dimensional epitaxial ferroelectric islands and in thin films are investigated by using a continuum phase field model that incorporates long-range elastic and electrostatic interactions. The simulations exhibit spatial polarization distributions with different types of domain walls in the epitaxial ferroelectric islands and find two critical thicknesses, at which the simulated material changes from a multidomain state to a single-domain state and from ferroelectric phase to paraelectric phase, respectively. The two critical thicknesses and the domain wall types vary with the length-to-thickness ratio. The simulations show that macroscopic polarization switching in thin films under an external electric field is processed through the nucleation of new domains and domain wall motion. The remanent polarization and the coercive field of the simulated ferroelectric films both decrease with decreasing film thickness.

Magnetostrictive domain walls in antiferromagnetic NiO.

We report high-resolution observations of antiferromagnetic (AF) domain walls at the surface of NiO and determine the typical width of AF walls in this material to be of the order of 150 nm. We observe a number of different types of domain walls, including double walls caused by long-range interaction between walls. We describe the observed wall profiles by a model containing the exchange interaction and magnetostriction as basic ingredients. The good agreement of this model with experiment shows that the formation of walls between antiferromagnetic domains in NiO and their properties are dominated by magnetoelastic interactions.

Landau theory of domain walls for one-dimensional asymmetric potentials

Investigation of a great number of physical systems shows that a Landau free energy of the form F(φ)=Hφ+(A/2)φ2+(B/3)φ3+(C/4)φ4 describes a first-order phase transition in an internal or external field H. To study the formation of static domain walls in these systems we include a spatial gradient (Ginzburg) term of the scalar order parameter φ. From the variational derivative of the total free energy we obtain a static equilibrium condition. By solving this equation exactly for different physical parameters and boundary conditions, we obtained different quasi-one-dimensional soliton-like solutions. These solutions correspond to three different types of domain walls between the two different phases which are created in the system. In addition, we obtain soliton lattice (domain wall array) solutions, calculate their formation energy and the asymptotic interaction between the solitons. By introducing certain transformations, we show that the solutions obtained here can be used to study domain walls in other physical systems such as described by asymmetric double Morse potentials. Finally, we apply our results to the specific cases of liquid crystals and the jam phenomena in traffic flows.