Domain Wall Structure Research Articles

Some remarks on splitting of domain wall in extra dimension

We study a simple model for thick branes without gravity. To construct a domain wall structure we utilize a potential of the form V(φ) = aφ 2 − bφ 4 + cφ 6 and for simplicity we assume the scalar field to be real. We also assume the coefficient a to be temperature dependent. We find that the phenomena of domain wall splitting occur below and above a critical temperature T c . We examine the behavior of domain wall in these regions.

Time-resolved resistive switching on manganite surfaces: Creep and1/fαnoise signatures indicate pinning of nanoscale domains

We performed time-resolved nanoscale studies on the resistive switching of perovskite manganite thin films by means of conductive atomic force microscopy. Creep and recovery features have been observed in the evolution of metallic domains via pulse-train experiments and current map sequences. Local $I(t)$ curves show $1/{f}^{\ensuremath{\alpha}}$ noise signatures during the switching process, a phenomenon which occurs in various physical processes consisting of discrete jumps of different sizes, such as the Barkhausen effect. Our results imply that the resistive switching falls into this universal class of effects with dynamics determined by the pinning and depinning of structural domain walls.

Micromagnetism in (001) magnetite by spin-polarized low-energy electron microscopy

Spin-polarized low-energy electron microscopy was used to image a magnetite crystal with (001) surface orientation. Sets of spin-dependent images of magnetic domain patterns observed in this surface were used to map the direction of the magnetization vector with high spatial and angular resolution. We find that domains are magnetized along the surface <110> directions, and domain wall structures include 90° and 180° walls. A type of unusually curved domain walls are interpreted as Néel-capped surface terminations of 180° Bloch walls.

Structural domain walls in polar hexagonal manganites

The domain structure in the multiferroic hexagonal manganites, h-RMnO(3) (R=Sc, Y, Dy-Lu), is currently intensely investigated, motivated by the observation of nanoscale electrical conductivity at the domain walls and intriguing sixfold topological defects at their meeting points, as well as reports of coupling between ferroelectricity, magnetism and structural antiphase domains. The detailed structure of the domain walls, as well as the origin of such couplings, however, was previously unknown. Here we use first-principles electronic structure calculations to elucidate the structure and properties of the structural domain walls in the hexagonal manganites. Our results allow us to explain why ferroelectric domain walls are always simultaneously antiphase walls, propose a mechanism for ferroelectric switching through domain-wall motion, suggest a structure for the observed sixfold topological defects and predict a topological protection of experimentally observed stripe domains in hexagonal manganites.

Structural phase transitions and electronic phenomena at 180-degree domain walls in rhombohedral BaTiO3

Using Landau-Ginzburg-Devonshire theory we describe 180-degree domain wall structure, intrinsic energy and carrier accumulation in rhombohedral phase of BaTiO3 as a function of the wall orientation and flexoelectric coupling strength. Two types of domain wall structures (phases of the wall) exist depending on the wall orientation. The low-energy 'achiral' phase occurs in the vicinity of the {110} wall orientation and has odd polarization profile invariant with respect to inversion about the wall center. The second 'chiral' phase occurs around {211} wall orientations and corresponds to mixed parity domain walls that may be of left-handed or right-handed chirality. The transformation between the phases is abrupt, accompanied with 20-30% change of the domain wall thickness and can happen at fixed wall orientation with temperature change. We suggest that the phase transition may be detected through domain wall thickness change or by c-AFM. The structure of the domain wall is correlated to its conductivity through polarization component normal to the domain wall, which causes free carriers accumulation. Depending on the temperature and flexoelectric coupling strength relative conductivity of the wall becomes at least one order of magnitude higher than in the single-domain region, creating c-AFM contrast enhancement pronounced and detectable.

Structural Phase Transition and Symmetry of Parent Phase in Bi4Ti3O12

Bismuth titanate Bi4Ti3O12 (BTO) is a member of the layered Aurivillius phase perovskite ferroelectrics and has a structural phase transition at Tc of 675 C. Below Tc, BTO shows ferroelectricity with a large spontaneous polarization (30 C/cm) parallel to the layered structure. BTO attracted much attention as candidate material for ferroelectric memories because of the fatigue-free nature of the BTO-based mixed crystal Bi4 xLaxTi3O12 (BLT-x). Although the space group of BTO at room temperature is determined to be B2cb ð1⁄4 Aba2 1⁄4 C2cbÞ (Z 1⁄4 4) only from the X-ray and neutron diffraction patterns, its space group has finally been concluded to be Pc (Z 1⁄4 2) with monoclinic symmetry, taking into account the existence of the small spontaneous polarization (4 C/cm) perpendicular to the layered structure. Here, Z is the number of the chemical formula in the conventional unit cell. Various physical properties of BTO, such as a soft mode behavior and domain wall structures, have been intensively investigated. The Landau theory of phase transition in BTO was presented by assuming the point group 4=mmm in the hightemperature phase, where the phase transition of BTO from the tetragonal (4=mmm) phase to the monoclinic (m) phase was named the triggered phase transition. The splitting of the triggered phase transition, that is the existence of the intermediate orthorhombic phase (B2cb), was observed in the mixed crystal systems in Bi4 xRxTi3O12 (R = La, Nd, Sm, and Gd). It was reported that the prototype structure of BTO shows the space group I4=mmm (Z 1⁄4 4). It is conjectured, however, that neither the orthorhombic (B2cb) nor the monoclinic (Pc) phase can be directly induced from the tetragonal (I4=mmm) phase, on the basis of the group theoretical consideration. Even the primitive unit cell size in I4=mmm and B2cb phases is different. Note that the proper ferroelectric phase transition from I4=mmm to B2cb is impossible, because the latter is not any subgroup of the former at the -point. On the other hand, it was reported, on the basis of experimental results, that the Curie–Weiss behavior of the dielectric constant in the high-temperature phase is observed in BTO, indicating the proper ferroelectric phase transition. This seems to be in contradiction. In order to solve the above contradiction, Rae et al. and Perez-Mato et al. assumed the Fmmm symmetry to be the parent phase, where Fmmm is a subgroup of I4=mmm. If the high-temperature parent phase above 675 C is indeed orthorhombic as they claim, however, the Landau theory so far proposed of the triggered phase transition in BTO, which is based on the assumption that it is tetragonal, may fail. Thus, the symmetry of the high-temperature parent phase seems to be of crucial importance. Under these circumstances, to clarify the structural phase transition at 675 C and the symmetry of the parent phase of BTO, we investigate the domain wall structure in the high-temperature phase and discuss its symmetry on the basis of the group theory. Single crystals of BTO were grown by the flux method from a Bi2O3–TiO2 system. For domain wall observation, some c-plate crystals with an area of about 5mm and thicknesses of about 10–50 m were selected among asgrown crystals as samples. The temperature dependence of the domain wall structure in the c-plate of the BTO crystal was observed using a polarizing microscope with a hightemperature sample stage (Linkam TS-1500), where the possible temperature range of this stage is from room temperature to a maximum of 1500 C. Figures 1(a) and 1(b) show photographs of the c-plate crystal in BTO under crossed-Nicols below and above Tc, respectively, where the sensitive plate was used in Fig. 1(b). In Fig. 1(a), the 90 domain wall structure is observed, while no domain wall structure appears in Fig. 1(b), indicating that the c-plate sample of BTO is optically isotropic. Thus, it was confirmed that the symmetry of the high-temperature phase is tetragonal. In our experiment, the phase front was also observed near Tc, indicating the first-order phase transition. 200 μm A P

Optimized cobalt nanowires for domain wall manipulation imaged by in situ Lorentz microscopy

Direct observation of domain wall (DW) nucleation and propagation in focused electron beam induced deposited Co nanowires as a function of their dimensions was carried out by Lorentz microscopy (LTEM) upon in situ application of magnetic field. Optimal dimensions favoring the unambiguous DW nucleation/propagation required for applications were found in 500-nm-wide and 13-nm-thick Co nanowires, with a maximum nucleation field and the largest gap between nucleation and propagation fields. The internal DW structures were resolved using the transport-of-intensity equation formalism in LTEM images and showed that the optimal nanowire dimensions correspond to the crossover between the nucleation of transverse and vortex walls.

OS1209 第一原理計算による強誘電体ドメインウォールの構造と形成過程に関する研究

OS1209 第一原理計算による強誘電体ドメインウォールの構造と形成過程に関する研究

Domain wall motion in nanopillar spin-valves with perpendicular anisotropy driven by spin-transfer torques

Using transport measurements and micromagnetic simulations we have investigated the domain wall motion driven by spin-transfer torques in all-perpendicular hexagonal nanopillar spin-valves. In particular, we probe domain walls nucleated in the free layer of the spin-valves, which are then pinned in the devices. We have determined both the field-current state diagrams for the domain-wall state and the thermally activated dynamics of the nucleation and depinning processes. We show that the nucleation process is well-described by a modified N\'eel-Brown model taking into account the spin-transfer torque, whereas the depinning process is independent of the current. This is confirmed by an analytical calculation which shows that spin-torques have no effect on the Arrhenius escape rate associated with thermally activated domain wall depinning in this geometry. Furthermore, micromagnetic simulations indicate that spin-transfer only weakly affects the domain wall motion, but instead modifies the inner domain wall structure.

Timing and Spectral Diagrams of Magnetic Video-Pulse Excitation Influence on NMR Spin–Echo in Magnets

NMR methods are successfully used in obtaining the microscopic information on the internal magnetic structure and dynamical processes in magnets. The important application of NMR in magnets is also the investigation of structure and dynamics of domain walls. In this work, it is accomplished by observation of nuclear spin echo signals of nuclei arranged in domain walls of magnets at excitation by an additional magnetic video-pulse field. We present the first systematic study of timing and spectral diagrams of magnetic video-pulse influence on the NMR two-pulse echo in a number of magnets (ferromagnets, ferrites, half metals, intermetals). It is shown that the timing diagrams showing the dependence of two-pulse echo intensity on the temporal location of a magnetic video-pulse in respect to radio-frequency pulses and spectral diagram of this influence are defined mainly by local hyperfine field anisotropy and domain walls mobility. These diagrams could be used for the identification of the nature of NMR spectra in multidomain magnetic materials and to improve the resolution capacity of the NMR method in magnets.

Inverted Hexagonal-Pyramid Growth of InN by Electric-Field Enhanced Metal Organic Chemical Vapor Deposition

We report on a single domain growth of InN on sapphire substrates by electric-field enhanced polarity-controlling metal–organic chemical vapor deposition. When the electric field is applied in the opposite direction to the film growth, InN grows inverted hexagonal-pyramid shapes with In-polarity surfaces. A growth model is presented to explain the rapid growth of the single domain InN with In-polarity under electric field using the knowledge of the domain wall structure and the growth of ferroelectrics in the external field.

Domains, Domain Walls and Defects in Perovskite Ferroelectric Oxides: A Review of Present Understanding and Recent Contributions

Ferroelectric oxides are used in many modern technologies including sensors, actuators, thin-film memories and energy harvesting. Ferroelectrics of similar composition often show wide variations in their characteristic properties. Such variations in properties can be largely attributed to differences in the structural arrangements of domains and distributions of defects within a multidomain/polycrystalline material. Recent developments in characterization techniques and first-principle calculations have significantly advanced our understanding of how ferroelectric domains interact with material defects, and thereby influence the properties of a material. This review provides a broad outlook of the contributions from different experimental and computational studies that have clarified the structure of domains, domain walls and defects in perovskite ferroelectric oxides, and the evolution of these structures under the application of electric fields. It is intended that an integrated viewpoint of these issues, as provided here, will further motivate synergistic activities between the various research groups and industries towards the development and characterization of ferroelectric oxides.

Intrawall configurations of magnetization near Bloch-Néel transitions in magnetically triaxial films

The micromagnetic approach is used to study the structure of domain walls and find their energies depending on values of magnetically anisotropic interactions and thicknesses b of magnetically triaxial films with various orientation of the surface relative to (100) plane. This is performed based on the two-dimensional magnetization distribution with the exact consideration of the principal interactions, including dipoledipole interaction. The calculations are carried out for film thicknesses bN that correspond to the transitions of domain wall structures from Neel to Bloch walls. It is shown that the magnetic anisotropy and orientation of film surfaces become significant at great distances from the point bN. Initially, with increasing b, the transition of the one-dimensional Neel domain wall to the asymmetric vortex-free Neel domain wall occurs; the energy of the latter is lower than that of the asymmetric Bloch wall. As b continues to increase, the vortex-free asymmetric Neel wall transforms to a double-vortex wall and its energy begins to exceed that of the asymmetric Bloch wall.

Dynamics of Dzyaloshinskii domain walls in ultrathin magnetic films

We explore a new type of domain wall structure in ultrathin films with perpendicular anisotropy, that is influenced by the Dzyaloshinskii-Moriya interaction due to the adjacent layers. This study is performed by numerical and analytical micromagnetics. We show that these walls can behave like Néel walls with very high stability, moving in stationary conditions at large velocities under large fields. We discuss the relevance of such walls, that we propose to call Dzyaloshinskii domain walls, for current-driven domain wall motion under the spin Hall effect.

Interaction Between Spin Wave Packets and Domain Wall With Various Propagation Modes and Wall Structures

The interaction between the spin wave (SW) packet and the domain wall (DW) have been numerically studied for various spin wave modes and the DW structures. Micromagnetic simulations reveal that the Neel type DW causes practically similar phase shift Δφ (0.4π ~ 0.6π) for all of the three different SW modes, while the Δφ is considerably enhanced in the case of the interaction with the Bloch type DW. The inductive detection of the DW induced phase shift in the SW, emitted with a pulsed microwave current, is also demonstrated.

Origin of piezoelectric response under a biased scanning probe microscopy tip across a 180∘ferroelectric domain wall

The piezoelectric response of a material under a nanoscale biased tip scanned across a sample in piezoelectric force microscopy (PFM) provides insight into the structure and dynamics of domain walls in ferroelectrics. While the vertical displacements of the tip under piezoelectric deformations of the sample have been reasonably explained, the origin of the lateral twisting of the tip remains unclear. This poses a serious problem when combining vertical and lateral signals to create vector PFM maps of polarization distribution in ferroelectrics. Using a combination of finite element modeling and analytical theory, and by comparison with prior experimental work across a single antiparallel domain wall on the (0001) surface of LiNbO${}_{3}$, we unequivocally show that the lateral signal originates from a shear displacement of the surface. We show that there are two types of lateral signals, one arising from the ${d}_{15}$ shear deformation, and the other from the ${d}_{22}$ lateral deformation. The vertical PFM signal surprisingly shows equal contributions from the ${d}_{33}$ (leading to normal displacements) and ${d}_{15}$ (leading to shear displacement) coefficients. We also show that an averaging of the PFM signal over a finite contact area of the tip, as experimentally observed, is essential to understanding the line shape of the PFM responses across the wall. After clarifying the origin of the nanoscale PFM signals, we conclude that, in general, a vertical signal does not automatically indicate a polarization component out of the surface, while a lateral signal does not automatically indicate an in-plane polarization component. Without a detailed theory or simulation especially in materials with nanoscale domain structures, ferroelectric relaxors, and morphotropic compositions, such assumptions may lead to incorrect domain and wall interpretations. The proposed model and numerical simulation method could be applied to all piezoelectric materials.

Domain Wall Splitting in Extra Dimension

We study the splitting of domain walls in 5-dimensional flat Minkowski spacetime. To construct a domain wall structure we utilize a potential of the form and for simplicity we assume the scalar field to be real. We also assume the coefficient a to be temperature-dependent. We find exact analytical expressions for the energy density of the domain wall and from this expression we find close analytical form for the separation of the divided domain walls. We find that near critical temperature the domain walls split. At the critical temperature, the domain walls rejoin. In the region above this critical temperature, the kink solution is nontopological. We find that the phenomena of splitting of domain walls occurs in this region as well. This effect is especially manifest near the inflection point of the potential.

Publisher’s Note: Bichiral structure of ferroelectric domain walls driven by flexoelectricity [Phys. Rev. B86, 134102 (2012)

Publisher’s Note: Bichiral structure of ferroelectric domain walls driven by flexoelectricity [Phys. Rev. B<b>86</b>, 134102 (2012)

Bichiral structure of ferroelectric domain walls driven by flexoelectricity

The influence of flexoelectric coupling on the internal structure of neutral domain walls in the tetragonal phase of perovskite ferroelectrics is studied. The effect is shown to lower the symmetry of ${180}^{\ensuremath{\circ}}$ walls which are oblique with respect to the cubic crystallographic axes, while ${100}$ and ${110}$ walls stay ``untouched.'' Being of the Ising type in the absence of the flexoelectric interaction, the oblique domain walls acquire a new polarization component with a structure qualitatively different from the classical Bloch-wall structure. In contrast to the Bloch-type walls, where the polarization vector draws a helix on passing from one domain to the other, in the flexoeffect-affected wall, the polarization rotates in opposite directions on the two sides of the wall and passes through zero in its center. Since the resulting polarization profile is invariant upon inversion with respect to the wall center, it does not break the wall symmetry, in contrast to the classical Bloch-type walls. The flexoelectric coupling lowers the domain wall energy and gives rise to its additional anisotropy, which is comparable to that conditioned by elastic anisotropy. The atomic order-of-magnitude estimates shows that the new polarization component ${P}_{2}$ may be comparable with spontaneous polarization ${P}_{s}$, thus suggesting that, in general, it is mandatory to include the flexoelectric coupling in domain wall simulations in ferroelectrics. Calculations performed for barium titanate yield the maximal value of ${P}_{2}$, which is much smaller than that of the spontaneous polarization. This smallness is attributed to an anomalously small value of a component of the ``strain-polarization'' electrostrictive tensor in this material.

DOMAIN BOUNDARIES IN FERROELECTRICS

Present paper is a brief review of the information and existing approaches in the study of domain walls in ferroelectric materials. In the framework of the continuum approach the structure of 180° and 90° domain walls was considered. The results of calculation of width and energy of domain walls were compared with those obtained from ab initio calculations and experimental data. Factors conducive to the broadening of domain boundaries are discussed such as profile temperature fluctuation, capture to nearby defects and surface impact. The structure of charged domain walls was considered under the conditions of screening by free carriers. The structure and characteristics of the moving domain wall are discussed: the local effective mass, the top speed and the mobility. The lateral motion of domain walls in the lattice potential relief in the general case creeping mode is investigated. The factors that control the macroscopic movement of domain walls are studied: an effective quasi-elasticity coefficient and nonlocal effective mass associated with involvement in the movement of the elastic medium surrounding wall. Natural frequency of translational oscillations of domain boundaries and the influence of the size effect were estimated. The interaction of domain walls with different types of defects and their effect on the deformation profile and features of the motion of domain walls are considered.