Zigzag Domain Research Articles

Hard-core bosonic domain walls on a honeycomb lattice

Linelike hard-core bosonic domain walls in a staggered potential on a honeycomb lattice are studied using quantum Monte Carlo simulations. The phase diagrams of ribbons with zigzag and armchair domain walls are mapped, which contain superfluid and insulator phases at various fillings. In the $\ensuremath{\rho}=\frac{1}{2}$ insulator, the domain wall separates two charge-density-wave regions with opposite Berry curvatures. Associated with the change of topological properties, superfluid transport occurs down the domain wall. The superfluid density associated with a zigzag domain wall is much larger than that of an armchair domain wall due to the different arrangements of occupied and unoccupied sites along the domain wall. Our results provide a concrete context to study bosonic topological phenomena, which may be simulated experimentally using bosonic cold atoms trapped in optical lattices.

Structure and domain wall dynamics in lead-free KNN-based ceramics

This paper comprehensively studied the effect of BaHfO3 doping on crystal structure, domain structure, and electrical properties of potassium sodium niobate ceramics, and especially analyzed the intrinsic structural characteristics of the R-O phase boundary, which can be successfully constructed through composition modification. Rietveld refinement and the piezoresponse force microscopy technique were combined to analyze the crystal structure and domain configuration of the material system. Comparative studies indicate that multiple phase coexistence will disturb the zigzag domains of the pure O phase into complex irregular domains, which are easier to switch under an external electric field, thus leading to improved electrical properties. Furthermore, the stabilized polarization state can be maintained under the thermal excitation due to the dominated O phase at high temperatures, which is beneficial for the temperature stability improvement. We believe that the structural analysis can give us a deeper understanding of the relationship among structural symmetry, domain dynamics, and electrical properties of potassium sodium niobate (KNN)-based ceramics.

Rabi-like oscillation of photonic topological valley Hall edge states.

We investigate Rabi-like oscillations of topological valley Hall edge states by introducing two zigzag domain walls in an inversion-symmetry-breaking honeycomb photonic lattice. Such resonant oscillations are stimulated by weak periodic modulation of the lattice depth along the propagation direction that does not affect the overall symmetry and the band topology of the lattice. Oscillations are accompanied by periodic switching between edge states with the same Bloch momentum but located at different domain walls. Switching period and efficiency are the non-monotonic functions of the Bloch momentum in the Brillouin zone. We discuss how the efficiency of this resonant process depends on the detuning of modulation frequency from the resonant value. Switching of nonlinear edge states is also briefly discussed. Our work brings about an effective approach to accomplish resonant oscillations of the valley Hall edge states in time-reversal-invariant topological insulators.

Manipulation of Conductive Domain Walls in Confined Ferroelectric Nanoislands

AbstractConductive ferroelectric domain walls—ultranarrow configurable conduction paths—have been considered as essential building blocks for future programmable domain wall electronics. For applications in high‐density devices, it is imperative to explore the conductive domain walls in small confined systems, while earlier investigations have hitherto focused on thin films or bulk single. Here, an observation and manipulation of conductive domain walls confined within small BiFeO3 nanoislands aligned in high‐density arrays are demonstrated. Using conductive atomic force microscopy, various types of conductive domain walls, including the head‐to‐head charged domain walls (CDWs), zigzag domain walls, and typical 71° head‐to‐tail neutral domain walls (NDWs), are distinctly visualized. The CDWs exhibit remarkably enhanced metallic conductivity with current of ≈nA order in magnitude and 104 times larger than that inside domains (0.01–0.1 pA), while the semiconducting NDWs allow much smaller current (≈10 pA) than the CDWs. The substantial difference in conductivity for dissimilar walls enables manipulations of various wall conduction states for individual addressable nanoislands via electrical tuning of domain structures. A controllable writing of four distinctive states in individual nanoislands can be achieved, showing application potentials for developing multilevel high‐density memories.

Low-Temperature Magnetization Switching of Bilayer FeNi/FeMn Films

A change in the kinetics of magnetization reversal of a bilayer ferromagnet–antiferromagnet film during a decrease in the temperature is experimentally detected. The motion of a zigzag domain wall is typical of high-temperature conditions, and the system undergoes magnetization reversal by irregular rotation at low temperatures. This phenomenon is found to occur only in a coupled system of layers with exchange anisotropy: it is absent when the antiferromagnetic layer is removed. The change in the character of magnetization reversal at low temperatures is related to the appearance of specific pinning of domain walls, which is caused by interface regions with a varying chirality of an interlayer exchange spring and a perpendicular magnetic anisotropy at interface steps.

Topological Defects in Helical Magnets

Helical magnets which violated space inversion symmetry have rather peculiar topological defects. In isotropic helical magnets with exchange and Dzyaloshinskii-Moriya interactions there are only three types of linear defects: $\pm\pi$ and $2\pi$-disclinations. Weak crystal anysotropy suppresses linear defects on large scale. Instead planar defects appear: domain walls that separate domains with different preferential directions of helical wave vectors. The appearance of such domain walls in the bulk helical magnets and some of their properties were predicted in the work \cite{Li 2012}. In a recent work by an international team of experimenters and theorists \cite{Schoenherr 2018} the existence of new types of domain walls on crystal faces of helical magnet FeGe was discovered. They have many features predicted by theory \cite{Li 2012}, but display also unexpected properties, one of them is the possibility of arbitrary angle between helical wave vectors. Depending on this angle the domain walls observed in \cite{Schoenherr 2018} can be divided in two classes: smooth and zig-zag. This article contains a mini-review of the existing theory and experiment. It also contains new results that explain why in a system with continuos orientation of helical wave vectors domain walls are possible. We discuss why and at what conditions smooth and zig-zag domain walls appear, analyze spin textures associated with helical domain walls and find the dependence of their width on angle between helical wave vectors.

Observation of Photonic Topological Valley Hall Edge States.

We experimentally demonstrate topological edge states arising from the valley-Hall effect in two-dimensional honeycomb photonic lattices with broken inversion symmetry. We break the inversion symmetry by detuning the refractive indices of the two honeycomb sublattices, giving rise to a boron nitridelike band structure. The edge states therefore exist along the domain walls between regions of opposite valley Chern numbers. We probe both the armchair and zigzag domain walls and show that the former become gapped for any detuning, whereas the latter remain ungapped until a cutoff is reached. The valley-Hall effect provides a new mechanism for the realization of time-reversal-invariant photonic topological insulators.

Acoustic valley edge states in a graphene-like resonator system

The concept of valley physics, as inspired by the recent development in valleytronic materials, has been extended to acoustic crystals for manipulation of air-borne sound. Many valleytronic materials follow the model of a gapped graphene. Yet the previously demonstrated valley acoustic crystal adopted a mirror-symmetry-breaking mechanism, lacking a direct counterpart in condensed matter systems. In this paper, we investigate a two-dimensional (2D) periodic acoustic resonator system with inversion symmetry breaking, as an analogue of a gapped graphene monolayer. It demonstrates the quantum valley Hall topological phase for sound waves. Similar to a gapped graphene, gapless topological valley edge states can be found at a zigzag domain wall separating different domains with opposite valley Chern numbers, while an armchair domain wall hosts no gapless edge states. Our study offers a route to simulate novel valley phenomena predicted in gapped graphene and other 2D materials with classical acoustic waves.

Domain walls in a chiral d -wave superconductor on the honeycomb lattice

We perform a fully self-consistent study of domain walls between different chiral domains in chiral $d_{x^2-y^2} \pm id_{xy}-wave superconductors with an underlying honeycomb lattice structure. We investigate domain walls along all possible armchair and zigzag directions and with a finite global phase shift across the domain wall, in addition to the change of chirality. For armchair domain walls we find the lowest domain wall energy at zero global phase shift, while the most favorable zigzag domain wall has a finite global phase shift dependent on the doping level. Below the van Hove singularity the armchair domain wall is most favorable, while at even higher doping the zigzag domain wall has the lowest energy. The domain wall causes a local suppression of the superconducting order parameter, with the superconducting recovery length following a universal curve for all domain walls. Moreover, we always find four subgap states crossing zero energy and well localized to the domain wall. However, the details of their energy spectrum vary notably, especially with the global phase shift across the domain wall.

Role of Perpendicular Anisotropy in the Zigzag Domain Wall Structure in Thin Magnetic Films

We investigate apparently zigzag domain walls in ultrathin magnetic films and calculate the total energy in zero applied field considering anisotropies in the second-order approximation. We discuss the change in zigzag wall morphology and scale as a function of the dipolar length and the total energy depend on film parameters exclusively anisotropy constants, crystallographic orientation and film thickness for a given dipolar length. We explain also the role of the second-order anisotropy in the total energy and the dynamics response of the in-plane magnetization for a given dipolar length. We use some constants in connection with experimental data reported for amorphous TbCo films grown in external in-plane magnetic field by high-frequency ion sputtering and for MnAs on GaAs films.

Zigzag Domain Wall Mediated Reversal in Antiferromagnetically Coupled Layers

The Ruderman–Kittel–Kasuya–Yosida (RKKY) coupling between two magnetic layers leads to many important technological applications. Here, the interaction between changing antiferromagnetic RKKY coupling and domain structure is studied in a sample consisting of two 5 nm thick CoFeB layers separated by a wedge of Cu up to 4 nm thick. Magnetic reversal occurs via the propagation of a zigzag domain wall front along the wedge. The modification of domain patterns created in the reversal of a coupled layers in the presence of antiferromagnetic RKKY coupling and coupling gradients is demonstrated. Firstly, the coupling leads to a smaller amplitude of the zigzag wall, which is aligned perpendicular to the easy axis, followed by elongation of the walls at higher coupling strength. The antiferromagnetic RKKY coupling, while not strong enough to cause antiparallel alignment of the layers, is argued to lead to coupling between the spins in the domain walls in the two layers, lowering their energy and driving the reversal behavior of the film.

Two-Dimensional Zigzag Domain Wall Structure in Ultrathin Films

We investigate the zigzag domain wall structure in ultrathin magnetic films, where the easy direction of magnetization is perpendicular to the film. We calculate the dipolar energy as functions of the zigzag period and the film thickness for an equilibrium configuration in absence of external field. Provided that the domain wall size is large compared with the domain size, we find that the zigzag angle, 𝜃, of zigzag domain wall decreases with the film thickness L. We discuss the results in connection with experimental data reported for amorphous TbCo films grown in external in plane magnetic field by high-frequency ion sputtering and for MnAs on GaAs films.

Formation of helical ion chains

We study the nonequilibrium dynamics of the linear to zigzag structural phase transition exhibited by an ion chain confined in a trap with periodic boundary conditions. The transition is driven by reducing the transverse confinement at a finite quench rate, which can be accurately controlled. This results in the formation of zigzag domains oriented along different transverse planes. The twists between different domains can be stabilized by the topology of the trap and under laser cooling the system has a chance to relax to a helical chain with nonzero winding number. Molecular dynamics simulations are used to obtain a large sample of possible trajectories for different quench rates. The scaling of the average winding number with different quench rates is compared to the prediction of the Kibble-Zurek theory, and a good quantitative agreement is found.

Ferroelectric Domain Structures in Low‐Strain BaTiO3

Epitaxial strain in ferroelectric films offers the possibility to enhance the piezoelectric performance utilizing low crystal symmetries and high density of domain walls. Ferroelectric BaTiO3 has been predicted to order in a variety of phases and domain configurations when grown under low strain on low mismatched substrates, but little experimental evidence of that region of the phase diagram exist. Here, epitaxial BaTiO3 thin films are grown on NdScO3 substrates under ≈0.1% strain. A monoclinic ca1/ca2 phase, with 90° periodic in‐plane domain configuration and small additional out‐of‐plane component of polarization, is stabilized at room temperature and investigated using piezoelectric force microscopy and X‐ray diffraction. Above 50 °C, this phase is transformed into an a/c phase with alternating in‐plane and out‐of‐plane polarizations and forming zigzag domain walls between up‐polarized and down‐polarized superdomains. Both types of domain patterns are highly anisotropic, giving rise to very long domain walls. Above 130 °C, the paraelectric phase is observed. The occurrence of a phase transition close to room temperature, a low symmetry ca1/ca2 phase, and the formation of periodic domains make of this material a promising candidate for high piezoelectric response.

Imprinted Magnetic Anisotropy and Zigzag Domain Structure of Amorphous TbCo Films

We investigate the magnetic anisotropy and domain structure of amorphous Tb (x) Co(1-x) films grown in external in-plane magnetic field by high-frequency ion sputtering. Films with different thickn ...

Layer resolved magnetic domain imaging of epitaxial heterostructures in large applied magnetic fields

We use X-ray Excited Luminescence Microscopy to investigate the elemental and layer resolved magnetic reversal in an interlayer exchange coupled (IEC) epitaxial Fe/Cr wedge/Co heterostructure. The transition from strongly coupled parallel Co-Fe reversal for Cr thickness tCr < 0.34 nm to weakly coupled layer independent reversal for tCr > 1.5 nm is punctuated at 0.34 < tCr < 1.5 nm by a combination of IEC guided domain wall motion and stationary zig zag domain walls. Domain walls nucleated at switching field minima are guided by IEC spatial gradients and collapse at switching field maxima.

Microstructure and magnetostrictive behavior of Fe-15 at% Ga alloy with different cooling rates

The main attention of this paper was devoted to the study of the effect of different cooling rates on the magnetic domain configuration and magnetostrictive behavior of heat-treated Fe-15 at% Ga alloy. After annealing at 1,000 °C for 3 h, the samples were subjected to water quenching, air cooling, and furnace cooling treatments. Phase constitution and magnetic domain structures of the samples were studied using X-ray diffraction (XRD) and magnetic force microscopy (MFM). XRD results indicate a single phase of α-Fe with disordered bcc (A2) structure for all samples. MFM results show that both water-quenched (WQ) and air-cooled (AC) samples are mainly made from ordered stripe domain structures, whereas a mixture of irregular stripe, zigzag, and plate domain patterns are observed in furnace-cooled (FC) sample. Magnetostrictive strain was measured in the presence of an externally applied magnetic field. It is found that WQ sample has the highest magnetostriction, while AC and FC samples exhibit moderate and the lowest magnetostriction, respectively, against the applied field. The dependence of initial domain configurations on thermal history is found to be conducive to the change in saturation magnetostrictions of the samples.

Tailoring magnetism at the nanometer scale in SmCo5 amorphous films

The thickness dependence of magnetic properties has been studied in SmCo5 amorphous films with imprinted in-plane anisotropy for thicknesses ranging down to the nanometer scale (2.5–100 nm). The field induced in-plane magnetic anisotropy decreases considerably when the film thickness is below 20 nm. Analysis of the magnetic anisotropy energy shows that the decrease of the induced in-plane anisotropy is accompanied by the development of an out-of-plane interface anisotropy. Two different regimes for the coercivity (Hc) change are found: below 3.75 nm, the Hc decreases continuously with decrease of the film thickness, whereas at above 3.75 nm, the Hc decreases with increase of the film thickness. This change in Hc can be understood by considering the decrease of the short range chemical order for the thinnest films (<3.75 nm) and the relative decrease of the interface contribution with increasing film thickness. The changes in anisotropy have a profound influence on the domain structure, in which the angle of the zigzag domain boundaries decreases with the inverse thickness of the layers.

Current Rectification in Mono- and Bilayer Nanographenes with Different Edges

Graphene nanomaterials are actively used in electronics and materials science as elements of electric circuits and both structural and storage components. Their unique structure and electronic properties allow for a wide variety of applications (i.e., electron and thermal conductivity, ion transport, ion storage, and electric-current rectification). In this work, we investigate the electric-current-rectifying properties of mono- and bilayer two-terminal nanographene devices with the nonequilibrium Green’s function method combined with density functional theory. The diode-like properties are achieved by control of the nanoribbons’ edges. The sequential combination of armchair and zigzag domains leads to nanographene junctions with asymmetric current–voltage characteristics. The rectifying properties of the asymmetric armchair–zigzag carbon materials are derived from the nonequilibrium Green’s function theory. The electric-current rectification is explained by the interaction of the external electric field ...

Magneto-optic study of the behavior of magnetic domains walls in ferrimagnetic garnet films placed over samples with in-plane magnetization

Magneto-optic (MO) imaging is based on Faraday rotation of a linearly polarized incident light beam illuminating a sensitive MO layer placed in close contact to the sample. For in-plane magnetized layers of Lu3−xBix Fe5−yGayO12 ferrimagnetic garnet films, zig-zag domain formation occurs whenever the sample stray parallel field component changes sign. In this work we study the behavior of zig-zag domain walls that appear when the garnet is placed over samples with in-plane magnetization like audio tapes recorded with different signals. We describe the zig-zag walls considering the anisotropy, exchange and magnetostatic energies in the Neel tails and the contribution of an applied magnetic field. Using different recorded signals we have been able to control the gradient of stray parallel field component on the garnet, changing the distance between domains and the size of zig-zag walls. We could even avoid the appearance of these zig-zag domain walls and obtain closed domains structures. We also study the behavior of the domain walls when an external magnetic field is applied parallel to the sample.