Zigzag Domain Research Articles

Anisotropy of the zigzag order in the Kitaev honeycomb magnet α−RuBr3

Kitaev materials often order magnetically at low temperatures due to the presence of non-Kitaev interactions. Torque magnetometry is a very sensitive technique for probing the magnetic anisotropy, which is critical in understanding the magnetic ground state. In this paper, we report detailed single-crystal torque measurements in the proposed Kitaev candidate honeycomb magnet α−RuBr3, which displays zigzag order below 34 K. Based on angular-dependent torque studies in magnetic fields up to 16 T rotated in the plane normal to the honeycomb layers, we find an easy-plane anisotropy with a temperature dependence of the torque amplitude following closely the behavior of the powder magnetic susceptibility. The torque for the field rotated in the honeycomb plane has a clear sixfold periodicity with a sawtooth shape, reflecting the threefold symmetry of the crystal structure and stabilization of different zigzag domains depending on the field orientation, with a torque amplitude that follows an order parameter form inside the zigzag phase. By comparing experimental data with theoretical calculations we highlight the importance of relevant anisotropic interactions and the role of the competition between different zigzag domains in this candidate Kitaev magnet. Published by the American Physical Society 2024

Observation of Period-Doubling Bloch Oscillations.

Bloch oscillations refer to the periodic oscillation of a wave packet in a lattice under a constant force. Typically, the oscillation has a fundamental period that corresponds to the wave packet traversing the first Brillouin zone once. Here, we demonstrate, both theoretically and experimentally, the optical Bloch oscillations where the wave packet must traverse the first Brillouin zone twice to complete a full cycle, resulting in a period of oscillation that is 2 times longer than that of usual Bloch oscillations. The unusual Bloch oscillations arise due to the band crossing of valley-Hall topological edge states at the Brillouin boundary for zigzag domain walls between two staggered honeycomb lattices with inverted on-site energy detuning, which are protected by the glide-reflection symmetry of the underlying structures. Our work sheds light on the direct detection of band crossings resulting from intrinsic symmetries that extend beyond the fundamental translational symmetry in topological systems.

Observation of zigzag domains in the surface layer of Fe-based microwires by magnetic force microscopy

The magnetic domain structure of the surface layer of Fe-based amorphous microwires with a diameter of 20 µm (after glass removal) was investigated. An approach has been developed to study the domain structure of the curved surface of a microwire by magnetic force microscopy. It was found that in low magnetic fields the domain structure of the surface layer consisted of zigzag-shaped domains elongated along the microwire axis. These domains are inclined to the microwire axis at an angle of 45 degrees. An increase in the magnetic field along the microwire axis resulted in the transformation of the magnetic structure to the structure consisting of ring domains with an opposite orientation of the magnetic moment. The geometric parameters of both types of the domain structure were determined. The width of zigzag-shaped domains was 2 µm. The width of ring domain was 2.5–5 µm.

Investigation of topological valley kink states along zigzag and armchair domain wall in a two-dimensional photonic crystal

This paper provides a numerical analysis of the topological valley kink states along both zigzag and armchair domain walls of a dielectric two-dimensional photonic crystal (PC), considering the photonic energy band folding mechanism. By engineering the side length of triangular holes in a honeycomb PC, we created inequivalent valleys in the momentum space. We utilized two adjacent valley PCs with inverted structures to induce a topological transition of the TE mode energy band as it crossed the interface. Further research into the projected energy bands along both zigzag and armchair directions revealed that topologically protected valley kink states can be supported by both configurations. The zigzag interface enabled valley waveguides to transport chiral optical fields at the 0°, 60°, and 120° bending angles, while maintaining their backscattering immune properties. The armchair interface, on the other hand, supported the straight propagation. By combining both armchair and zigzag interfaces, the valley waveguide can facilitate bending propagation at 90° and 180°, while also enabling the equal splitting of chiral fields at the intersection between these two interfaces. Our analyzation can be helpful to improve the applications of valley waveguides in integrated photonics.

Magnetic ground state of the Kitaev Na2Co2TeO6 spin liquid candidate

As a candidate Kitaev material, Na$_2$Co$_2$TeO$_6$ exhibits intriguing magnetism on a honeycomb lattice that is believed to be $C_3$-symmetric. Here we report a neutron diffraction study of high quality single crystals under $a$-axis magnetic fields. Our data support the less common notion of a magnetic ground state that corresponds to a triple-$\mathbf{q}$ magnetic structure with $C_3$ symmetry, rather than the multi-domain zigzag structure typically assumed in prototype Kitaev spin liquid candidates. In particular, we find that the field is unable to repopulate the supposed zigzag domains, where the only alternative explanation is that the domains are strongly pinned by hitherto unidentified structural reasons. If the triple-$\mathbf{q}$ structure is correct then this requires reevaluation of many candidate Kitaev materials. We also find that fields beyond about 10 Tesla suppress the long range antiferromagnetic order, allowing new magnetic behavior to emerge different from that expected for a spin liquid.

Tuning rotational magnetization for high frequency magnetoimpedance in micro-patterned triangle spiral magnetic systems

Achieving high sensitivity, resolution, and accuracy is desirable and in high demand for magnetic sensor applications. The giant magnetoimpedance (GMI) effect has drawn intensive attention owing to its ultrasensitive response to the magnetic field. Further enhancement of the GMI effect in soft magnetic conductors (wires, ribbons, or films) is essential but represents a big challenge since the experimentally reported highest GMI ratio is still much smaller than its theoretically predicted value. Inspired by the kirigami structures, we propose a new approach for improving the GMI effect by designing triangle spiral magnetic systems. We demonstrate that the GMI ratio can be easily tuned by varying the edge width of the triangle spiral magnetic ribbon. The GMI ratio is enhanced up to 250% and 100% for the Fe 92.5 C 3.5 Si 3.9 ribbon with a 60 μm wide edge when a magnetic field of 100 Oe is aligned along the altitude and edge directions, respectively. Magnetometry indicates that upon reduction of the edge width, the improvement of magnetic susceptibility at low applied fields is correlated with the strengthened shape anisotropy. Micromagnetic simulations suggest that various closure magnetic domain configurations such as stripe and zig-zag domain structures can be formed, depending on the applied magnetic field directions, as a result of the competition of anisotropy and Zeeman energies followed in the Stoner-Wohlfarth model. The simulated results fully support the experimentally observed GMI enhancement and attribute it to the formation of transverse magnetic domains at the critical dimension of the micro-patterned magnetic ribbon system. These superior properties make the triangle-spiral GMI sensor a promising candidate for advanced sensor applications. • Various branch-width triangle spiral magnetic systems have been developed and characterized, at which optimized 60 μm width showing the best GMI effect owing to the strengthened shape anisotropy. • The GMI effect is augmented up to 250% and 100% under an applied magnetic field of 100 Oe aligned along with the altitude and edge directions, respectively. • The GMI enhancement is supported by transverse domain formations approved by OOMMF micromagnetic simulation. • Wide range of magnetic domain configurations can be formed depending on the applied magnetic field directions, originating from the competition of anisotropy and Zeeman energies followed in the Stoner-Wohlfarth model.

Evolution of domain structure with electron doping in ferroelectric thin films

To minimize their electrostatic energy, insulating ferroelectric films tend to break up into nanoscale ``Kittel'' domains of opposite polarization that are separated by uncharged 180$^\circ$ domain walls. Here, I report on self-consistent solutions of coupled Landau-Ginzburg-Devonshire and Schr\"odinger equations for an electron-doped ferroelectric thin film. The model is based on LaAlO$_3$/SrTiO$_3$ interfaces in which the SrTiO$_3$ substrate is made ferroelectric by cation substitution or strain. I find that electron doping destabilizes the Kittel domains. As the two-dimensional electron density $n_\mathrm{2D}$ increases, there is a smooth crossover to a zigzag domain wall configuration. The domain wall is positively charged, but is compensated by the electron gas, which attaches itself to the domain wall and screens depolarizing fields. The domain wall approaches a flat head-to-head configuration in the limit of perfect screening. The polarization profile may be manipulated by an external bias voltage and the electron gas may be switched between surfaces of the ferroelectric film.

Reconstruction of the ferroelectric domain structure morphology in BaTiO3 single crystals using Čerenkov-type second harmonic generation microscopy

Domain structure arising as a result of surface polishing in the bulk of barium titanate BaTiO3 single crystal was imaged by polarized optical microscopy and Čerenkov-type second harmonic generation (ČSHG) microscopy, which allowed distinguishing between 90° and 180° domain walls. 3D-morphology of different domain patterns in the bulk was recovered using ČSHG images. The domain structure represented the stack of the intermitting needlelike a-domains with charged domain walls rarely crossed by the zigzag domain patterns with 180° walls. The used experimental technique can be used for understanding the domain kinetics in the multiaxial crystals.

Zigzag domains caused by strain-induced anisotropy of the Dzyaloshinskii-Moriya interaction

The influence of the anisotropic interfacial Dzyaloshinskii-Moriya interaction (iDMI) on the structure of magnetic domains in thin Co/Pt films is investigated using magnetic force microscopy. The iDMI anisotropy is induced via application of strong (0.08%) in-plane uniaxial mechanical strain. We observe transformation of an isotropic labyrinth domain structure to oriented stripe domains and zigzag domain structures. According to theoretical considerations, such a transformation appears due to strain-induced strong iDMI anisotropy and change of iDMI sign along the direction perpendicular to the deformation axis.

Nonequilibrium dynamics of α-RuCl3 - a time-resolved magneto-optical spectroscopy study.

We present time-resolved magneto-optical spectroscopy on the magnetic Mott-Hubbard-insulating Kitaev spin liquid candidate α-RuCl3 to investigate the nonequilibrium dynamics of its antiferromagnetically ordered zigzag groundstate after photoexcitation. A systematic study of the transient magnetic linear dichroism under different experimental conditions (temperature, external magnetic field, photoexcitation density) gives direct access to the dynamical interplay of charge excitations with the zigzag ordered state on ultrashort time scales. We observe a rather slow initial demagnetization (few to 10s of ps) followed by a long-lived non-thermal antiferromagnetic spin-disordered state (100-1000s of ps), which can be understood in terms of holons and doublons disordering the antiferromagnetic background after photoexcitation. Varying temperature and fluence in the presence of an external magnetic field reveals two distinct photoinduced dynamics associated with the zigzag and quantum paramagnetic disordered phases. The photo-induced non-thermal spin-disordered state shows universal compressed-exponential recovery dynamics related to the growth and propagation of zigzag domains on nanosecond time scales, which is interpreted within the framework of the Fatuzzo-Labrune model for magnetization reversal. The study of nonequilibrium states in strongly correlated materials is a relatively unexplored topic, but our results are expected to be extendable to a large class of Mott-Hubbard insulator materials with strong spin-orbit coupling.

Effect of asymmetry on terahertz transmissions in topological photonic crystals comprising of dielectric rod structures

We numerically demonstrate robust terahertz (THz) transmissions in a topological photonic crystal comprised of dielectric rod structures. Topological edge states (i.e., the vortex states) in the structure are excited via a zig-zag domain boundary at the interface of two nontrivial valley photonic crystals (VPCs). A comprehensive study of the effect of asymmetry (defined as δd=d1−d2) on transmission loss and bandwidth is performed for three different kinds of domain boundaries: straight, Z-shape, and Ω-shape. An increase in the bandwidth of the topological THz transmission is achieved with the increasing asymmetry. The study further demonstrates blue shifting of the topological transmission bandwidth with the increase in asymmetry. An optimized value of the asymmetry parameter is obtained based on the bandwidth as well as the transmission loss. The most robust propagation in terms of the widest bandwidth and low loss transmission is achieved with asymmetry ≥0.25a. The robust THz transmission is attributed to the strong edge modes confinement at the domain boundary of the VPC due to intervalley scattering suppression at this optimal value. Our observations open the path for a strong electromagnetic wave flow in the THz regime with a high transmission, which could be useful in photonic broadband communication and other on-chip applications at THz frequencies, particularly for 6G communications.

Novel optical XOR/OR logic gates based on topologically protected valley photonic crystals edges

Valley photonic crystals (VPCs) have provided a novel topological photonic platform to manipulate light. In this work, we construct zigzag and armchair domain walls using two-dimensional silicon VPCs, the edges between domains of opposite valley indices link to the corresponding topological invariant. We study the light transmission of these edges with defects and sharp bent corners. We design all-optical logic gates at telecommunication wavelength with both XOR and OR functions based on the valley-contrasting edges. Topologically protected waveguides own high transmission and backscattering-immune features, and the coupling process of different edge modes results in interference for logic functions. Compared with traditional photonic crystal logic gates, our device shows outstanding properties, including robust transmission, higher contrast ratio and more compact footprint. Furthermore, our work also shows the potential of topological photonics to be applied in optical logic circuits.

Chirality-induced zigzag domain wall in in-plane magnetized ultrathin films

The domain structure in in-plane magnetized Fe/Ni/W(110) films is investigated using spin-polarized low-energy electron microscopy. A novel transition of the domain wall shape from a zigzaglike pattern to straight is observed as a function of the film thickness, which is triggered by the transition of the domain wall type from the out-of-plane chiral wall to the in-plane Néel wall. The contribution of the Dzyaloshinskii–Moriya interaction to the wall energy is proposed to explain the transition of the domain wall shape, which is supported by Monte Carlo simulations.

Topological valley states in sonic crystals with Willis coupling

Acoustic media with Willis coupling possess intrinsic directionality owing to the vector nature of coupling coefficients in constitutive relations. Here, we report a type of sonic topological insulator that exhibits the valley Hall effect by using an acoustic fluid of the Willis type. We find that the valley Hall phase transition can be triggered by tuning the coupling vector. In addition, the Dirac cones or valley position are displaced away from high symmetry points in the Brillouin zone. The tunability of the valley offset offered by Willis coupling helps to realize equally robust one-way transport for both zigzag and armchair domain walls and for more tortuous wave channels.

Topological edge states in an all-dielectric terahertz photonic crystal

We present an analysis of the robustness of topological edge states in an all-dielectric photonic crystal slab in the terahertz (THz) frequency domain. We initially design a valley photonic crystal (VPC) exhibiting a nontrivial band topology. The excitation of the topological edge states in the structure is facilitated through a zigzag domain wall constructed by interfacing two types of VPCs with distinct band topologies. The robustness of the excited edge states is probed with respect to the magnitude and the sign of the asymmetry in terms of the hole diameters in the VPC, for different domain interfaces. Our study reveals that the topological edge states in the VPC structure are achieved only when the domain walls are formed by the larger air holes (i.e., asymmetry parameter has a positive value). In the case of the domain walls formed by relatively smaller air holes (i.e., asymmetry parameter has a negative value), the topological protection of the edge states is forbidden. For positive asymmetry, we demonstrate that the topological transport of THz becomes more robust with the increasing magnitude of asymmetry in the VPC structure. A robust propagation of topological edge states and strong confinement of electromagnetic fields within the domain wall are observed for asymmetry ranging from 28% to 42% in our structure. We have adopted a generic technique and therefore, the results of our study could be achieved at other frequency regimes by scaling the size parameters of the structure appropriately. At THz frequencies, such extensive analysis on the robustness of the topological edge states could be relevant for the realization of low-loss waveguides for 6G communication and other integrated photonic devices.

Zigzag domain boundaries in magnetostrictive Fe-Ga alloys

A recent development in magnetic materials research on a non-Joulian magnetostriction phenomenon [H. D. Chopra and M. Wuttig, Nature 521, 340 (2015)] highlights peculiar cellular magnetic domains with zigzag boundaries in Fe-Ga alloys. The cause of zigzag boundaries of cellular domains is attributed to hypothetical charge density waves beyond classical magnetic domain theory. In this paper, we report observations in Fe-Ga alloys of zigzag boundaries that form conventional stripe domains. The responses of stripe domains to external magnetic fields are observed, and the behaviors of zigzag boundaries are examined, which are further compared with those in cellular domains. It shows that both cellular and stripe domains and the constituent zigzag boundaries in magnetostrictive Fe-Ga alloys can be explained well by classical magnetic domain theory, without resorting to theory based on hypothetical charge density waves. In particular, our findings provide convincing evidence that zigzag boundaries in Fe-Ga alloys are conventional V lines commonly observed in cubic magnetic crystals like Fe-Si alloys. The intricate cellular domain structure is shown to correlate with the simple stripe domain structure in terms of zigzag V lines and flux-closure surface domains.

$$\Gamma $$-Limit for Two-Dimensional Charged Magnetic Zigzag Domain Walls

Charged domain walls are a type of domain walls in thin ferromagnetic films which appear due to global topological constraints. The non-dimensionalized micromagnetic energy for a uniaxial thin ferromagnetic film with in-plane magnetization $m \in \mathbb{S}^1$ is given by \begin{align*} E_\epsilon[m] \ = \ \epsilon\|\nabla m\|_{L^2}^2 + \frac {1}{\epsilon} \|m \cdot e_2\|_{L^2}^2 + \frac{\pi\lambda}{2|\ln\epsilon|} \|\nabla \cdot (m-M)\|_{\dot H^{-\frac{1}{2}}}^2, \end{align*} where magnetization in $e_1$-direction is globally preferred and where $M$ is an arbitrary fixed background field to ensure global neutrality of magnetic charges. We consider a material in the form a thin strip and enforce a charged domain wall by suitable boundary conditions on $m$. In the limit $\epsilon \to 0$ and for fixed $\lambda> 0$, corresponding to the macroscopic limit, we show that the energy $\Gamma$-converges to a limit energy where jump discontinuities of the magnetization are penalized anisotropically. In particular, in the subcritical regime $\lambda \leq 1$ one-dimensional charged domain walls are favorable, in the supercritical regime $\lambda > 1$ the limit model allows for zigzaging two-dimensional domain walls.

Study of magnetic zigzag domain walls and magnetization reversal process in polycrystalline cobalt thin films: Effect of thickness and crystallographic texturing

The present work reports the effects of crystallographic texturing on the formation of magnetic zigzag domain walls (DWs) and magnetization reversal process in polycrystalline cobalt thin films of different thickness (10 to 91 nm) deposited by magnetron sputtering technique. Grazing incidence x-ray diffraction measurements, carried out in both in-plane and out-of-plane geometry reveals texturing for thinner thickness (≤ 51 nm) films. Magnetic microstructure and magnetization reversal process is studied with Kerr microscopy by utilizing two in-plane orthogonal sensitivities i.e., longitudinal and transverse sensitivity. It is found that with increasing film thickness, the magnetization reversal process changes significantly. Analysis of angular variation of coercivity reveals that for thinner thickness films (≤ 51 nm), the magnetization reversal process follows two-phase model, also substantiated by the observed magnetic domain structure during reversal process. Nevertheless, it is observed that the zigzag DW angle and magnetization ripple microstructure are found to depend on film thickness. The variation of zigzag DWs angle and magnetic ripple variation is explained in terms of the magnetic anisotropy with the thickness of film employing the crystallographic texturing. Further, we have observed crossover in hysteresis loops measured along for angles ≈20∘ away from the hard axis magnetization. The plausible reason could be due to the superposition of the uniaxial anisotropy generated due to magneto-crystalline anisotropy from the hexagonal phase and biaxial anisotropy generated due to the cubic phase of Co.

Orientation and internal structure of domain walls in ferromagnetic films with anisotropic Dzyaloshinskii-Moriya interaction

We present an analytical study of domain-wall internal structure and orientation in a ferromagnetic film with out-of-plane anisotropy and the anisotropic interfacial Dzyaloshinskii-Moriya interaction (iDMI). The term “anisotropic” means that the iDMI constant is different for different in-plane directions. The interplay between the magnetostatic interaction and the iDMI in a domain wall defines both its structure and orientation. In the case of the isotropic iDMI there is no preferable orientation of the DW in the film plane leading to formation of labyrinth domain structure with random shapes of the domains. In the case of the anisotropic iDMI an oriented domain stripe structure and zigzag domains appear. Depending on system parameters, either the Bloch domain walls, or the Néel ones or the hybrid canted walls realize in the magnetic film. The spatial orientation of the DW and the orientation of the magnetization rotation plane in the DW are intimately related by a simple linear ratio. The analytical results are corroborated by micromagnetic simulations.

Local hard and soft pinning of 180° domain walls in BaTiO3 probed by in situ transmission electron microscopy

We report on the electric field response of 180 degree nanodomain walls in BaTiO$_3$ using in situ electrical biasing in transmission electron microscopy (TEM). The sample is biased on a micro-device designed for reliable testing whose key attributes are confirmed by finite element calculations. The presence of weakly charged zig-zag domain walls at room temperature is attributed to the geometric confinement of the device. The motion of the domain walls under the applied electric field allows to extract local P-E loops where distinct domain wall pinning in deep and random energy potential profiles, characteristic for hard and soft ferroelectrics, respectively, are observed. Hard domain wall pinning results in asymmetrical loops typical for "hard" ferroelectrics while the soft domain wall pinning follows Rayleigh-like behaviour. All effects are measured locally and directly from the imaged domain structure.