Properties Of Domain Walls Research Articles

Signatures of polarity in ferroelastic domain walls and antiphase boundaries of SrTiO3 and other perovskites

In the present work we study the polar properties of domain walls using a recently developed method of combining layer group analysis with order parameter symmetry [Schranz et al. PRB 100 (2019) 184105]. Using this method we obtain a detailed overview on the microscopic and macroscopic properties of domain walls which we can quantify with results from Landau-Ginzburg-Devonshire theory. Recently, we have applied [Schranz et al. PRB 102 (2020) 184101] the method to analyse the symmetry and polar properties of ferroelastic twin walls and antiphase boundaries in SrTiO3. Here we discuss the elastic anomalies observed in SrTiO3 at various temperatures in the light of these findings.

Observation of 90° domain walls in relaxor ferroelectrics PMN-28.6%PT by focusing upon the CTR scattering

Rod-shaped scattering has been observed in the tetragonal phase of Pb(Mg1/3Nb2/3)O3–28.7%PbTiO3 by use of the backscattering setting. We attribute it to crystal truncation rod (CTR) scattering associated with the boundary of 90° domains. The CTR scattering shows a characteristic temperature evolution, which enables us to discuss the properties of the domain walls, especially their temperature dependence on the domain wall widths. Though it is necessary to have a situation where the crystal coherence is suddenly truncated, like the 90° domain wall, CTR scattering can be expected to be a powerful tool for examining the domain wall properties.

Postquench entropy growth in a chiral clock model

We numerically study quenches from a fully ordered state to the ferromagnetic regime of the chiral $\mathbb{Z}_3$ clock model, where the physics can be understood in terms of sparse domain walls of six flavors. As in the previously studied models, the spread of entangled domain wall pairs generated by the quench lead to a linear growth of entropy with time, upto a time $\ell/2v_g$ in size-$\ell$ subsystems in the bulk where $v_g$ is the maximal group velocity of domain walls. In small subsystems located in the bulk, the entropy continues to further grow towards $\ln 3$, as domain walls traverse the subsystem and increment the population of the two oppositely ordered states, restoring the $\mathbb{Z}_3$ symmetry. The latter growth in entropy is seen also in small subsystems near an open boundary in a non-chiral clock model. In contrast to this, in the case of the chiral model, the entropy of small subsystems near an open boundary saturates. We rationalize the difference in behavior in terms of qualitatively different scattering properties of domain walls at the open boundary in the chiral model. We also present empirical results for entropy growth, correlation spread, and energies of longitudinal-field-induced bound states of domain wall pairs in the chiral model.

Criticality and conformality in the random dimer model.

In critical systems, the effect of a localized perturbation affects points that are arbitrarily far from the perturbation location. In this paper, we study the effect of localized perturbations on the solution of the random dimer problem in two dimensions. By means of an accurate numerical analysis, we show that a local perturbation of the optimal covering induces an excitation whose size is extensive with finite probability. We compute the fractal dimension of the excitations and scaling exponents. In particular, excitations in random dimer problems on nonbipartite lattices have the same statistical properties of domain walls in spin glass. Excitations produced in bipartite lattices, instead, are compatible with a loop-erased self-avoiding random walk process. In both cases, we find evidence of conformal invariance of the excitations that is compatible with SLE_{κ} with parameter κ depending on the bipartiteness of the underlying lattice only.

Magnetic Domain Walls Moving in Curved Permalloy Nanowires under Continuous and Pulsed Fields

Magnetic domain walls created and propagated in curved permally nanowires under continuous and pulsed fields in a Lorentz microscope. Using such nanowires aims to create a single or multiple magnetic domain walls in typical areas of those structures, an external magnetic field then applies along the long axis of these nanowires. Following that the created domain walls are propagated from one end to the other end of each wire by increasing the continuous/pulsed field strength. At each increased field value, a Fresnel image is recorded. The obtained results show that the characteristics of those created and propagated domain walls are dependent on various parameters, i.e. connecting structures, wall types and chiralities. Corners between the straight and linking sections of those curved nanowires also play a crucial role along witth the local defects created in these wire-edges and surfaces where a point-defect is considered as a potential well that could pin/distort those created/propagated domain walls. By the aid of this observations, the dynamic properties of domain walls with the creating and propagating processes in those curved nanowires are exposed. These outcomes are vital to design novel domain wall trap structures supporting reproducible domain wall motions. That are of interest in providing a better understanding of multiple bits moving in the furure 3D racetrack memory, logic gates, shift register and other spintronic/computing devices.

Shedding light on non-Ising polar domain walls: Insight from second harmonic generation microscopy and polarimetry analysis

Polar domain walls are currently at the focus of intensive research owing to their unusual and highly localized functional properties, which bear great potential for technological applications. They can present unusual topological features, like swirling polar structures or defect lines. The prediction of possible non-Ising and chiral internal structures of polar domain walls has been a particularly important development in this topic over the past years. This Tutorial highlights the capabilities of non-linear optics to probe these newly discovered aspects in polar non-Ising type domain walls through the second-harmonic generation (SHG) process. Fundamental symmetry properties of domain walls are presented in the context of recent advances on chiral and abnormal polar structures. We introduce the basics of the SHG and its ability to probe the symmetry down to the nanoscale, and we explain how to obtain insight into the non-Ising character of polar domain walls by combining the SHG polarimetry analysis with modeling.

Confinement on \u211d3 \xd7 \U0001d54a1 and double-string collapse

We study confining strings in mathcal{N} = 1 supersymmetric SU(Nc) Yang-Mills theory in the semiclassical regime on ℝ1,2× \U0001d54a1. Static quarks are expected to be confined by double strings composed of two domain walls — which are lines in ℝ2 — rather than by a single flux tube. Each domain wall carries part of the quarks’ chromoelectric flux. We numerically study this mechanism and find that double-string confinement holds for strings of all N-alities, except for those between fundamental quarks. We show that, for Nc≥ 5, the two domain walls confining unit N-ality quarks attract and form non-BPS bound states, collapsing to a single flux line. We determine the N-ality dependence of the string tensions for 2 ≤ Nc≤ 10. Compared to known scaling laws, we find a weaker, almost flat N-ality dependence, which is qualitatively explained by the properties of BPS domain walls. We also quantitatively study the behavior of confining strings upon increasing the \U0001d54a1 size by including the effect of virtual “W-bosons” and show that the qualitative features of double-string confinement persist.

Giant thermoelectric power factor in charged ferroelectric domain walls of GeTe with Van Hove singularities

Increasing the Seebeck coefficient S in thermoelectric materials usually drastically decreases the electrical conductivity σ, making significant enhancement of the thermoelectric power factor σS2 extremelly challenging. Here we predict, using first-principles calculations, that the extraordinary properties of charged ferroelectric domain walls (DWs) in GeTe enable a five-fold increase of σS2 in the DW plane compared to bulk. The key reasons for this enhancement are the confinement of free charge carriers at the DWs and Van Hove singularities in the DW electronic band structure near the Fermi level. These effects lead to an increased energy dependence of the DW electronic transport properties, resulting in more than a two-fold increase of S with respect to bulk, without considerably degrading the in-plane σ. We propose a design of a nano-thermoelectric device that utilizes the exceptional thermoelectric properties of charged ferroelectric DWs. Our findings should inspire further investigation of ferroelectric DWs as efficient thermoelectric materials.

Polarization of domain boundaries in SrTiO3 studied by layer group and order-parameter symmetry

Based on a recently developed combination of layer group analysis with order-parameter symmetry, we study the polarity of antiphase domain boundaries (APBs) and ferroelastic twin boundaries (TBs) in $\mathrm{Sr}\mathrm{Ti}{\mathrm{O}}_{3}$. In addition to the celebrated layer group analysis of domain twins, the present method allows us to investigate tensor properties of domain walls also for the case where order-parameter variables other than the spontaneous ones are active. We find that antiphase boundaries in $\mathrm{Sr}\mathrm{Ti}{\mathrm{O}}_{3}$ can carry a polarization if in addition to the spontaneous order parameter $(0,0,{\ensuremath{\phi}}_{s})$ a second component, i.e., $({\ensuremath{\phi}}_{1},0,{\ensuremath{\phi}}_{s})$, develops within the domain wall. This result, which is solely based on symmetry arguments, strongly suggests that polarization in APBs is possible if a phase transition from an Ising-type wall to a N\'eel- or Bloch-like wall occurs. This is in very good agreement with previous calculations based on Landau-Ginzburg free energy expansions including biquadratic ($\ensuremath{\propto}{P}_{i}{P}_{j}{\ensuremath{\phi}}_{k}{\ensuremath{\phi}}_{l}$) [A. K. Tagantsev et al. Phys. Rev. B 64, 224107 (2001)] and flexoelectric ($\ensuremath{\propto}{P}_{k}\frac{\ensuremath{\partial}{u}_{ij}}{\ensuremath{\partial}\ensuremath{\xi}}$) coupling terms [A. N. Morozovska et al. Phys. Rev. B. 85, 094107 (2012)]. The present results also unveil a close connection between the recently discovered macroscopic polarization in antiferrodistortive cycloids of ferroelastic domain walls of $\mathrm{Sr}\mathrm{Ti}{\mathrm{O}}_{3}$ and a mechanism for explaining polarization of APBs.

First-principles study of topologically protected vortices and ferroelectric domain walls in hexagonal YGaO3

Ferroelectric behavior on the meso- and macroscopic scale depends on the formation and dynamics of domains and controlling the domain patterns is imperative to device performance. While density functional theory (DFT) calculations have successfully described the basic properties of ferroelectric domain walls, the necessarily small cell sizes used for the calculations hampers DFT studies of complex domain patterns. Here, we simulate large-scale complex ferroelectric domain patterns in ferroelectric ${\mathrm{YGaO}}_{3}$ using multisite local orbitals as implemented in the DFT code conquest. The multisite local orbital basis set gives similar bulk structural and electronic properties, and atomic domain wall structures and energetics as those obtained with conventional plane-wave DFT. With this basis set model, 3600-atom cells are used to simulate topologically protected vortices. The local atomic structure at the vortex cores is subtly different from the domain walls, with a lower electronic band gap suggesting enhanced local conductance at these cores.

Current vortices and magnetic fields driven by moving polar twin boundaries in ferroelastic materials

Ferroelastic twin boundaries often have properties that do not exist in bulk, such as superconductivity, polarity etc. Designing and optimizing domain walls can hence functionalize ferroelastic materials. Using atomistic simulations, we report that moving domain walls have magnetic properties even when there is no magnetic element in the material. The origin of a robust magnetic signal lies in polar vortex structures induced by moving domain walls, e.g., near the tips of needle domains and near domain wall kinks. These vortices generate displacement currents, which are the origin of magnetic moments perpendicular to the vortex plane. This phenomenon is universal for ionic crystals and holds for all ferroelastic domain boundaries containing dipolar moments. The magnetic moment depends on the speed of the domain boundary, which can reach the speed of sound under strong mechanical forcing. We estimate that the magnetic moment can reach several tens of Bohr magnetons for a collective thin film of 1000 lattice planes and movements of the vortex by the speed of sound. The predicted magnetic fields in thin slabs are much larger than those observed experimentally in SrTiO3/LaAlO3 heterostructures, which may be due to weak (accidental) forcing and slow changes of the domain patterns during their experiments. The dynamical multiferroic properties of ferroelastic domain walls may have the potential to be used to construct localized magnetic memory devices in future.

Relation between microscopic interactions and macroscopic properties in ferroics.

The driving force in materials to spontaneously form states with magnetic or electric order is of fundamental importance for basic research and device technology. The macroscopic properties and functionalities of these ferroics depend on the size, distribution and morphology of domains; that is, of regions across which such uniform order is maintained1. Typically, extrinsic factors such as strain profiles, grain size or annealing procedures control the size and shape of the domains2-5, whereas intrinsic parameters are often difficult to extract due to the complexity of a processed material. Here, we achieve this separation by building artificial crystals of planar nanomagnets that are coupled by well-defined, tuneable and competing magnetic interactions6-9. Aside from analysing the domain configurations, we uncover fundamental intrinsic correlations between the microscopic interactions establishing magnetically compensated order and the macroscopic manifestations of these interactions in basic physical properties. Experiment and simulations reveal how competing interactions can be exploited to control ferroic hallmark properties such as the size and morphology of domains, topological properties of domain walls or their thermal mobility.

Calibration of material parameters based on 180^circ and 90^circ ferroelectric domain wall properties in Ginzburg\u2013Landau\u2013Devonshire phase field models

Ferroelectric phase field models based on the Ginzburg–Landau–Devonshire theory are characterized by a large number of material parameters with problematic physical interpretation. In this study, we systematically address the relationship between these parameters and the main properties of ferroelectric domain walls. A variational approach is used to derive closed form solutions for the polarization fields at the phase transition regions as well as for the propagation velocities of the domain walls. Introducing a modified set of material parameters, which appropriately scales different contributions to the free energy, we are able to accurately calibrate these parameters based on domain wall thickness and energy of both 180^circ and 90^circ domain walls. Moreover, the mobility parameter appearing in the Ginzburg–Landau evolution equation can be accurately calibrated based on the propagation velocity of the domain walls.

Chirality-dependent properties of domain walls in a U-shaped Permalloy nanostrip

Transverse domain walls (DWs) in a U-shaped ferromagnetic nanostrip possess many dynamic properties different from those in flat nanostrip. By breaking the top–bottom symmetry, the U-shaped strip endows DWs with chirality-dependent structures, mobilities and Walker breakdown fields. More interestingly, Walker breakdown in U-shaped nanostrip is hierarchy, with two different modes. Micromagnetic simulations predicted that DWs with different chiralities have different robustness and (anti)vortex dynamics in Walker breakdown. Our results provide a method for manipulating DW chirality.

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.

Magnetic field threshold for nucleation and depinning of domain walls in the neodymium permanent magnet Nd2Fe14B

The Nd magnet ${\mathrm{Nd}}_{2}{\mathrm{Fe}}_{14}\mathrm{B}$ is an indispensable permanent magnet for high-technology commercial products. We study magnetization reversal in hard-soft-hard magnet systems of the atomistic model of the Nd magnet at zero and room temperatures. We present the nucleation and pinning fields as a function of the strength of the anisotropy energy of the soft magnet, estimated by using the stochastic Landau-Lifshitz-Gilbert equation. In the Nd magnet, reflecting the lattice structure, the properties of domain walls (DWs) depend on their moving directions. Bloch and N\'eel DWs move along the $a$ (or $b$) and $c$ axes, respectively. We investigate the difference in the nucleation and pinning fields between the Bloch and N\'eel DWs. We also analyze the dependence of the threshold fields on the thickness of the soft magnet. We find that the thermal fluctuation effect affects the threshold fields in the Nd magnet model more significantly than those in the simple anisotropic Heisenberg model [Mohakud et al., Phys. Rev. B 94, 054430 (2016)]. We also find that the strength of the anisotropy energies of the soft magnet phase is not so important for the pinning field, while it is essential for the nucleation field, etc. We discuss the detailed features of the dependencies and their microscopic mechanisms.

Domain Dynamics under Ultrafast Electric-Field Pulses.

Exploring the dynamic responses of a material is of importance to both understanding its fundamental physics at high frequencies and potential device applications. Here we develop a phase-field model for predicting the dynamics of ferroelectric materials and study the dynamic responses of ferroelectric domains and domain walls subjected to an ultrafast electric-field pulse. We discover a transition of domain evolution mechanisms from pure domain growth at a relatively low field to combined nucleation and growth of domains at a high field. We derive analytical models for the two regimes which allow us to extract the effective mass and damping coefficient of ferroelectric domain walls. The exhibition of two regimes for the ferroelectric domain dynamics at low and high electric fields is expected to be a general phenomenon that would appear for ferroic domains under other ultrafast stimuli. The present Letter also offers a general framework for studying domain dynamics and obtaining fundamental properties of domain walls and thus for manipulating the dynamic functionalities of ferroelectric materials.

Extreme narrow magnetic domain walls in U ferromagnets: The UCoGa case

Surface magnetic domains of a UCoGa single crystal during magnetization/demagnetization processes in increasing/decreasing magnetic fields were investigated by means of magnetic-force-microscopy (MFM) images at low temperatures. The observed domain structure is typical for a ferromagnet with strong uniaxial anisotropy. The evolution of magnetic domains during cooling of the crystal below TC has also been manifested by MFM images. Analysis of the available data reveals that the high uniaxial magnetocrystalline energy in combination with the relatively small ferromagnetic exchange interaction in UCoGa gives rise to the formation of very narrow domain walls formed by the pairs of the nearest U neighbor ions with antiparallel magnetic moments within the basal plane. Since the very high anisotropy energy is a common feature of the majority of the uniaxial U ferromagnets, analogous domain-wall properties are expected for all these materials.

(2 + 1)-dimensional Boiti–Leon–Pempinelli equation – Domain walls, invariance properties and conservation laws

We analyze domain wall type solutions, symmetry/invariance properties and conservation laws of the (2+1)-dimensional Boiti–Leon–Pempinelli system which describes the evolution of the horizontal velocity component of water waves propagating in two directions. It turns out that the equation is extensive in these properties. Some domain wall properties are also investigated.

Domain walls and deconfinement: a semiclassical picture of discrete anomaly inflow

We study the physics of quark deconfinement on domain walls in four-di- mensional supersymmetric SU(N) Yang-Mills theory, compactified on a small circle with supersymmetric boundary conditions. We numerically examine the properties of BPS domain walls connecting vacua k units apart. We also determine their electric fluxes and use the results to show that Wilson loops of any nonzero N -ality exhibit perimeter law on all k-walls. Our results confirm and extend, to all N and k, the validity of the semiclassical picture of deconfinement of Anber, Sulejmanpasic and one of us (EP), arXiv:1501.06773, providing a microscopic explanation of mixed 0-form/1-form anomaly inflow.