Stability Of Domain Walls Research Articles

Controlled Nucleation and Stabilization of Ferroelectric Domain Wall Patterns in Epitaxial (110) Bismuth Ferrite Heterostructures

AbstractFerroelectric domain walls, topological entities separating domains of uniform polarization, are promising candidates as active elements for nanoscale memories. In such applications, controlled nucleation and stabilization of domain walls are critical. Here, using in situ transmission electron microscopy and phase‐field simulations, a controlled nucleation of vertically oriented 109° domain walls in (110)‐oriented BiFeO3 (BFO) thin films is reported. In the switching experiment, reversed domains that are nucleated preferentially at the nanoscale edges of the “crest and sag” pattern‐like electrode under external bias subsequently grow into a stable stripe configuration. In addition, when triangular pockets (with an in‐plane polarization component) are present, these domain walls are pinned to form stable flux‐closure domains. Phase field simulations show that i) field enhancement at the edges of the electrode causes site‐specific domain nucleation, and ii) the local electrostatics at the domain walls drives the formation of flux closure domains, thus stabilizing the striped pattern, irrespective of the initial configuration. The results demonstrate how flux closure pinning can be exploited in conjunction with electrode patterning and substrate orientation to achieve a desired topological defect configuration. These insights constitute critical advancements in exploiting domain walls in next generation ferroelectronic devices.

Vortex domain wall dynamics in stepped magnetic nanowire with in-plane magnetic anisotropy

Controlling Vortex Domain wall (VDW) dynamics and stability in a stepped nanowire with in-plane magnetic anisotropy was investigated by using micromagnetic simulation with fixed nanowire dimensions. A stepped area is constricted at the center of the nanowire with proportions of length (d = 50 nm) and width (λ = 50 nm) to pin the magnetic domain wall (DW) with high barrier potential energy to achieve a high information storage capacity. From this study, it was found that the DW with different structures was pinned at the stepped area with high stability. Also, a reduction of VDW behaviors due to its chirality and polarity has been obtained according to saturation magnetization (Ms). By increasing the values of Ms, the VDW attraction to the nanowire edges based on its chirality and polarity becoming less and VDW moves in a straight line towards the stepped area. Therefore, with high values of MS, the VDW is stable in type and moves towards the stepped area with a speed of 500 m/s until pinning there. In addition, the symmetry of the stepped area design helps the VDW to move in a straight line through the stepped area and maintain its magnetization configuration during the depinning. This is important for writing and reading the information in storage memory devices.Furthermore, current density values (J) have affected the stability of the VDW by decreasing the VDW behaviors regarding its chirality and polarity. With low driven current density values, the VDW kept its structure until reaching and got pinning at the stepped area. Further investigations were done to examine the transverse domain wall (TDW) and VDW depinning through the stepped area. The results have shown that TDWs have a high barrier potential than VDWs.

Tunable domain wall dynamics in amorphous ferromagnetic microwires

Abstract In this work, we show the possibility of tuning the domain wall dynamics in amorphous ferromagnetic microwires by means of thermal annealing. We investigate the effect of annealing time and temperature on the field dependence of the domain wall velocity in magnetically bistable Fe- and CoFeNi-based microwires. We demonstrate that the magnitude of the magnetostriction coefficient determines the tendency of the domain wall mobility and velocity change and we relate the magnetostriction coefficient to the stress relaxation upon annealing. Thus, in the case of Fe-based microwires with large positive magnetostriction ∼10−6 the stress relaxation caused by the annealing leads to an increase of the velocity and mobility of the domain wall, while the same parameters of the domain wall dynamics for CoFeNi-based microwires with nearly zero magnetostriction coefficient ∼10−7-10−8 significantly decrease. Growth of the minimum magnetic field for domain wall propagation upon annealing is observed in CoFeNi microwires with vanishing magnetostriction coefficient. This influence of annealing on the domain wall dynamics of CoFeNi microwires is explained by considering domain wall stabilization due to pair ordering. The opposite tendency observed for Fe-based microwires with only one transition metal is associated with the stress relaxation upon annealing.

Tuning Magnetic Chirality by Dipolar Interactions.

The stabilization of chiral magnetic domain walls and skyrmions has been attributed to the actively investigated Dzyaloshinskii-Moriya interaction. Recently, however, predictions were made that suggest dipolar interactions can also stabilize chiral domain walls and skyrmions, but direct experimental evidence has been lacking. Here we show that dipolar interactions can indeed stabilize chiral domain walls by directly imaging the magnetic domain walls using scanning electron microscopy with polarization analysis in archetype Pt/CoB/Ir thin film multilayers. We further demonstrate the competition between the Dzyaloshinskii-Moriya and dipolar interactions by imaging a reversal of the domain wall chirality as a function of the magnetic layer thickness. Finally, we suggest that this competition can be tailored by a Ruderman-Kittel-Kasuya-Yosida interaction. Our work therefore reveals that dipolar interactions play a key role in the stabilization of chiral spin textures. This insight will open up new routes towards balancing interactions for the stabilization of chiral magnetism.

Measurement-induced dynamics and stabilization of spinor-condensate domain walls.

Weakly measuring many-body systems and allowing for feedback in real time can simultaneously create and measure new phenomena in quantum systems. We theoretically study the dynamics of a continuously measured two-component Bose-Einstein condensate (BEC) potentially containing a domain wall and focus on the tradeoff between usable information obtained from measurement and quantum backaction. Each weakly measured system yields a measurement record from which we extract real-time dynamics of the domain wall. We show that quantum backaction due to measurement causes two primary effects: domain-wall diffusion and overall heating. The system dynamics and signal-to-noise ratio depend on the choice of measurement observable. We propose a feedback protocol to dynamically create a stable domain wall in the regime where domain walls are unstable, giving a prototype example of Hamiltonian engineering using measurement and feedback.

Motion and stability of chiral domain walls driven by non-gradient spin torques: Antiferromagnets and ferromagnets compared

Abstract We present a comparative study on the ferromagnetic and antiferromagnetic chiral domain walls under non-gradient spin torques by collective coordinates method. Based on the steady solutions, the stable chiral walls are picked out by linear stability analysis. We find that the spin torques drive the antiferromagnetic wall more quickly and stable than the ferromagnetic one. For the antiferromagnetic wall, the velocity is proportional to the exchange interaction, while Dzyaloshinskii-Moriya interaction for the ferromagnetic wall. Due to the strongness of exchange interaction, the antiferromagnetic wall propagates much faster than the ferromagnetic one. In addition, the antiferromagnetic wall remains the Neel type, while the ferromagnetic wall switches to a Bloch type with the current increasing. Finally, Dzyaloshinskii-Moriya interaction influences the motion direction of antiferromagnetic wall, but has no effect on the magnitude of velocity. For ferromagnetic walls, it determines the magnitude of velocity.

Observation of a topologically protected state in a magnetic domain wall stabilized by a ferromagnetic chemical barrier

The precise control and stabilization of magnetic domain walls is key for the development of the next generation magnetic nano-devices. Among the multitude of magnetic configurations of a magnetic domain wall, topologically protected states are of particular interest due to their intrinsic stability. In this work, using XMCD-PEEM, we have observed a topologically protected magnetic domain wall in a ferromagnetic cylindrical nanowire. Its structure is stabilized by periodic sharp alterations of the chemical composition in the nanowire. The large stability of this topologically protected domain wall contrasts with the mobility of other non-protected and non-chiral states also present in the same nanowire. The micromagnetic simulations show the structure and the conditions required to find the topologically protected state. These results are relevant for the design of future spintronic devices such as domain wall based RF oscillators or magnetic memories.

Orbital Stability of Domain Walls in Coupled Gross--Pitaevskii Systems

Domain walls are minimizers of energy for coupled one-dimensional Gross--Pitaevskii systems with nontrivial boundary conditions at infinity. It has been shown in [S. Alama, L. Bronsard, A. Contreras, and D. E. Pelinovsky, Arch. Ration. Mech. Anal., 215 (2015), pp. 579--610] that these solutions are orbitally stable in the space of complex $\dot{H}^1$ functions with the same limits at infinity. In the present work we adopt a new weighted $H^1$ space to control perturbations of the domain walls and thus to obtain an improved orbital stability result. A major difficulty arises from the degeneracy of linearized operators at the domain walls and the lack of coercivity.

Engineering of domain wall dynamics in amorphous microwires by annealing

Abstract Domain wall (DW) propagation and magnetic properties in as-prepared and annealed Fe- and Fe-Ni-rich microwires are experimentally studied. Observed DW dynamics is discussed considering the effect of magnetoelastic anisotropy, internal stresses relaxation after annealing and domain wall stabilization owing to pair ordering. Additionally, modification of the magnetostriction coefficient related to stress relaxation and formation of nanocrystalline structure after annealing are considered. Annealing allows considerable improvement of DW velocity in Fe-rich and Fe-Ni based (low Ni content) microwires. In Fe-Ni-based microwires the DW velocity increasing is less appreciated. Moreover coercivity increasing after annealing of Fe-Ni based microwires is observed. Consequently, annealing is the effective method for engineering of the DW dynamics in glass-coated microwires.

The Stability of Fake Flat Domain Walls on Kähler Manifold

In this paper, we study the stability of flat fake domain walls solution of fake N = 1 supergravity in d + 1 dimensions with Kahler surface as the sigma model. We start with Lagrangian for N = 1 fake supergravity which is coupling between gravity and complex scalar in d + 1 dimensions with scalar potential turned on. Then, as in supergravity theory, we demand that the scalar fields span the Kahler manifold. The equations of motion for fields can be reduced into first order equations by defining the superpotential and the resulting equations are called the projection equation and the fake BPS equation. Finally, we discuss about the stability of flat fake domain walls by investigating the critical points of the superpotential and the scalar potential.

Thermal stability of ferroelectric domain gratings in Rb-doped KTP

We study the thermal stability of domain walls in periodically poled Rb-doped KTP crystals. Domain-wall motion is observed after annealing the crystals above 550 °C. This motion is highly anisotropic along the a- and b- crystallographic axes. Along the b-axis domain wall motion is in the order of tens of micrometers. In the a-direction, it results in either three orders of magnitude smaller domain wall displacement or in domain merging, depending on the initial domain configuration. We show that the thermal stability of the domain gratings depends on their periodicity, resulting in complete backswitching for sub-micrometer domains annealed at 730 °C.

Processes of structural relaxation in the amorphous alloy Co69Fe3.7Cr3.8Si12.5B11 with a near-zero magnetostriction and their effect on the magnetic properties and the characteristics of magnetic noise caused by Barkhausen jumps

The evolution of hysteretic magnetic properties and the characteristics of magnetic noise caused by Barkhausen jumps have been studied in different ranges of annealing temperature where different processes of structural relaxation develop. It has been shown that the amorphous cobalt-based alloy under study is characterized by a high (in comparison with the iron-based alloys) spatial homogeneity of magnetic noise. The stabilization of domain walls was caused by directional ordering (at annealing temperatures T a < T C) and the processes of clustering (at T a > T C) fixed by the method of small-angle X-ray scattering not only affect the level of hysteretic magnetic properties, but also determine the magnetic-noise characteristics of the alloy. A comparison of the dynamics of magnetic-noise behavior with changes in the saturation magnetostriction λs made it possible to conclude that the magnetic-noise characteristics depend not only on the directional, but also on the isotropic short-range ordering. The ranges of annealing temperature that ensure acceptable values of hysteretic magnetic properties and, simultaneously, a low level of magnetic noise have been established. This situation takes place at a certain optimum concentration of clusters arising in the alloy studied.

Domain walls and bubble droplets in immiscible binary Bose gases

The existence and stability of domain walls (DWs) and bubble-droplet (BD) states in binary mixtures of quasi-one-dimensional ultracold Bose gases with inter- and intra-species repulsive interactions is considered. Previously, DWs were studied by means of coupled systems of Gross-Pitaevskii equations (GPEs) with cubic terms, which model immiscible binary Bose-Einstein condensates (BECs). We address immiscible BECs with two- and three-body repulsive interactions, as well as binary Tonks--Girardeau (TG) gases, using systems of GPEs with cubic and quintic nonlinearities for the binary BEC, and coupled nonlinear Schr\"{o}dinger equations with quintic terms for the TG gases. Exact DW\ solutions are found for the symmetric BEC mixture, with equal intra-species scattering lengths. Stable asymmetric DWs in the BEC mixtures with dissimilar interactions in the two components, as well as of symmetric and asymmetric DWs in the binary TG gas, are found by means of numerical and approximate analytical methods. In the BEC system, DWs can be easily put in motion by phase imprinting. Combining a DW and anti-DW on a ring, we construct BD states for both the BEC and TG models. These consist of a dark soliton in one component (the "bubble"), and a bright soliton (the "droplet") in the other. In the BEC system, these composite states are mobile too.

Domain wall stability in ferroelectrics with space charges

Significant effect of semiconductor properties on domain configurations in ferroelectrics is demonstrated, especially in the case of doped materials. Phase field simulations are performed for ferroelectrics with space charges due to donors and electronic charge carriers. The free charges introduced thereby can act as a source for charge compensation at domain walls with uncompensated polarization bound charges. Results indicate that the equilibrium position of a domain wall with respect to its rotation in a head-to-head or a tail-to-tail domain configuration depends on the charge defect concentration and the Fermi level position.

Domain-wall free energy in Heisenberg ferromagnets

We consider Gaussian fluctuations about domain walls embedded in one- or two-dimensional spin lattices. Analytic expressions for the free energy of one domain wall are obtained. From these, the temperature dependence of experimentally relevant spatial scales---i.e., the correlation length for spin chains and the size of magnetic domains for thin films magnetized out of plane---are deduced. Stability of chiral order inside domain walls against thermal fluctuations is also discussed.

Impact of Strain Effects on the Stability of Ising Walls in Ferroelectrics

The stability of Ising 180-degree domain walls with respect to appearance of chirality is analytically studied in tetragonal perovskite-type ferroelectrics taking into account electro-mechanical coupling. It is shown that the widely used approximation neglecting the elastic effects may lead to qualitatively wrong results. Sufficient condition for the stability of Ising walls is formulated only in terms of elastic and electrostrictive properties, regardless the correlation energy. We demonstrate that elasticity stabilizes Ising walls in tetragonal Pb(Zr1-cTic)O3 and makes chiral walls unfavorable for any composition of the material (factor c), while nonelastic model predicts chirality of 180-degree walls near the morphotropic boundary.

Stability of topological defects in chiral superconductors: London theory

This paper examines thermodynamic stability of chiral domain walls and vortices - topological defects which can exist in chiral superconductors. Using London theory it is demonstrated that at sufficiently small applied and chiral fields the existence of domain walls and vortices in the sample is not favored and the sample's configuration is a single domain. The particular chirality of the single-domain configuration is neither favored nor disfavored by the applied field. Increasing the field leads to an entry of a domain wall loop or a vortex into the sample. Formation of a straight domain wall is never preferred in equilibrium. Values of the entry (critical) fields for both types of defects, as well as the equilibrium size of the domain wall loop, are calculated. We also consider a mesoscopic chiral sample and calculate its zero-field magnetization, susceptibility and a change in the magnetic moment due to a vortex or a domain wall entry. We show that in a case of a soft domain wall whose energetics is dominated by the chiral current (and not by the surface tension) its behavior in mesoscopic samples is substantially different from that in the bulk case and can be used for a controllable transfer of edge excitations. The applicability of these results to Sr2RuO4 - a tentative chiral superconductor - is discussed.

Topology and properties of the 0-degree domain wall in a transverse magnetic field

The conditions of formation, the structure, and the stability of 0-degree domain walls with noncircular trajectories of the magnetization vector in cubic ferromagnets with induced uniaxial anisotropy along the [011] direction have been investigated. It has been found that magnetic inhomogeneities with such topology can appear only in an external magnetic field perpendicular to the domain wall plane. It has been shown that the Euler-Lagrange equations in the low-field limit can be reduced to second-order linear differential equations, whose solutions describe the structure of the above inhomogeneities, while the eigenvalues of the corresponding differential operators specify their stability conditions.

Large thermal stability independent of critical current of domain wall motion in Co/Ni nanowires with step pinning sites

The relation between critical current, critical field, and thermal stability of domain wall (DW) trapped at step pinning sites was studied using Co/Ni nanowires with perpendicular magnetic anisotropy (PMA). A sharp step structure was fabricated, which increased the critical field of DW motion, while the critical current was independent of the critical field. Also, the derived thermal stability (ΔE/kBT) for the step samples was much more than 60. These results indicate that the DW motion in PMA nanowires has potential for memory devices with both a small driving current and large thermal stability.

Dependence of domain wall stability on vortex chirality in asymmetric nanoring

We report on the direct observation of notch-free domain wall (DW) trapping and field history effect on the DW behavior in Ni80Fe20 asymmetric ring. We found that a 360° DW is trapped at the narrow arm while the ring adopts a vortex configuration. The stability of DW is dependent on the chirality of the vortex state and the external field direction. A 360° DW trapped in a clockwise vortex configuration is highly resistant to annihilation upon the application of +x field; the 360° DW trapped in an anticlockwise vortex breaks apart with a small +x field.