Domain Wall Structure Research Articles

Chiral magnetic domain wall in ferrimagnetic GdFeCo wires

Field-driven magnetic domain wall (DW) motion was investigated in ferrimagnetic GdFeCo wires with perpendicular magnetic anisotropy. The DW velocity as a function of the out-of-plane magnetic field exhibited the Walker breakdown phenomenon. The DW velocity was found to be significantly affected by the in-plane bias field: a minimum DW velocity was observed at a finite in-plane magnetic field (Hm), and the sign of Hm was found to reverse when the DW structure was changed from up-down- to down-up. These results imply that chiral DWs are formed in ferrimagnetic GdFeCo wires, despite their bulk and amorphous phase.

1D Modulation: Atomic Level 1D Structural Modulations at the Negatively Charged Domain Walls in BiFeO3 Films (Adv. Mater. Interfaces 9/2015)

Atomic structures of tail-to-tail negatively charged domain walls in BiFeO3 thin films are revealed via aberration-corrected transmission electron microscopy, as described in article 1500024 by Y.-L. Zhu, X. L. Ma, and co-workers. On (100) type charged domain walls, one-dimensional structural modulations are demonstrated, with lattice spacing and lattice rotation varying in a periodic way along the domain wall. The structural variations show a remarkable contrast to uncharged domain walls and imply delicate interactions between bound charges and structural compensations of the domain wall. These findings may help to provide new information on domain wall structures and to improve understanding of domain wall properties in ferroelectrics.

Structure of Magnetic Domain Wall in Cylindrical Microwire

The magnetization in the domain walls (DWs) formed inside the inner core of the amorphous ferromagnetic microwire is studied within a simple analytical model proposed. The influence of the ordering in the internal-stress created outer shell of the wire is included via an effective Dzyaloshinskii-Moriya-like anisotropy and resulting DW textures have been classified. The model is applicable to periodically constricted nanowires (whose core-shell magnetic structure follows from the magnetostatics) as well, which has enabled the verification of the predictions on DW structure with the micromagnetic simulations.

Atomic Level 1D Structural Modulations at the Negatively Charged Domain Walls in BiFeO3 Films

Charged domain walls (CDWs) show great potentials to mediate the properties of ferroelectrics. Direct mapping of these domain walls at an atomic scale is of critical importance for understanding the domain wall dominated properties. Here, based on aberration‐corrected scanning transmission electron microscopy, tail‐to‐tail CDWs at 71°, 109°, and 180° domains in BiFeO3 thin films have been identified. 2D mappings demonstrate 1D structural modulations with alternate lattice expansions and clockwise/counterclockwise lattice rotations at these CDWs. Such behaviors of CDWs reveal a remarkable contrast to the uncharged domain walls and imply delicate interactions between bound charges and structural compensations of domain wall. These results are expected to provide new information on domain wall structures and shed some light on the understanding of domain wall properties in ferroelectrics.

Magnetic domain wall motion in notch patterned permalloy nanowire devices

We report a study of magnetization reversal process of notch-patterned permalloy (Py) nanowires (NWs) by using an in-situ magnetic force microscopy (MFM). Three neighboring straight NWs and an individual straight NW with discs connected to the wires ends are fabricated by standard electron beam lithography through a lift-off technique. MFM images are taken in the presence of an in-plane magnetic field applied along the wires length. As a result, the nucleation, pinning and depinning of domain walls (DWs) along the NW are observed. The artificial constraints (notch) in such symmetrical geometry of NWs indeed serve as pinning sites to pin the DWs. The nature of magnetization reversal, pinning field and depinning field for the DWs that are observed in these permalloy NWs, indicate the key roles of notch depth, the terminal connection structure of NW end and the inter-wire interaction among the NWs. The in-situ MFM measurements are examined with the micromagnetic simulations. Consequently, good agreements are obtained for the DW structures and the effect of DWs pining/depinning, however a dissimilarity in experimental and simulation observations for the direction of propagation of DWs in NWs needs further investigation.

Domain-wall velocities of up to 750 m s(-1) driven by exchange-coupling torque in synthetic antiferromagnets.

The operation of racetrack memories is based on the motion of domain walls in atomically thin, perpendicularly magnetized nanowires, which are interfaced with adjacent metal layers with high spin-orbit coupling. Such domain walls have a chiral Néel structure and can be moved efficiently by electrical currents. High-capacity racetrack memory requires closely packed domain walls, but their density is limited by dipolar coupling from their fringing magnetic fields. These fields can be eliminated using a synthetic antiferromagnetic structure composed of two magnetic sub-layers, exchange-coupled via an ultrathin antiferromagnetic-coupling spacer layer. Here, we show that nanosecond-long current pulses can move domain walls in synthetic antiferromagnetic racetracks that have almost zero net magnetization. The domain walls can be moved even more efficiently and at much higher speeds (up to ∼750 m s(-1)) compared with similar racetracks in which the sub-layers are coupled ferromagnetically. This is due to a stabilization of the Néel domain wall structure, and an exchange coupling torque that is directly proportional to the strength of the antiferromagnetic exchange coupling between the two sub-layers. Moreover, the dependence of the wall velocity on the magnetic field applied along the nanowire is distinct from that of the single-layer racetrack due to the exchange coupling torque. The high domain wall velocities in racetracks that have no net magnetization allow for densely packed yet highly efficient domain-wall-based spintronics.

Head-to-head domain wall structures in wide permalloy strips

We analyze the equilibrium micromagnetic domain wall structures encountered in Permalloy strips of a wide range of thicknesses and widths, with strip widths up to several micrometers. By performing an extensive set of micromagnetic simulations, we show that the equilibrium phase diagram of the domain wall structures exhibits in addition to the previously found structures (symmetric and asymmetric transverse walls, vortex wall) also double vortex and triple vortex domain walls for large enough strip widths and thicknesses. Also several metastable domain wall structures are found for wide and/or thick strips. We discuss the details of the relaxation process from random magnetization initial states towards the stable domain wall structure, and show that our results are robust with respect to changes of e.g. the magnitude of the Gilbert damping constant and details of the initial conditions.

Halogen Phases on Pd(110): Compression Structures, Domain Walls, and Corrosion

Halogens are used as modifiers in catalytic processes, notably including photocatalytic watersplitting; as redox-active species in dye-sensitized solar cells; and as etchants in device fabrication. Atomically resolved studies of the adsorption and reactivity of halogens on Pt and Pd surfaces are scarce in view of the prominent role these metals play in the mentioned applications. The present study reports phases of halogens on Pd(110) in the submonolayer coverage range as monitored by temperature-programmed desorption, low-energy electron diffraction, scanning tunneling microscopy, and density functional calculations. Domain wall and compression structures are observed, as is typical for halogens (except fluorine) on transition and noble metals, but not on Pt, where the bonding is much more site-specific and a different succession of phases is found. The reactivity of Br toward Pd(110) is greater than that of Cl, as judged by the corrosive attack and by the bond strength derived from the thermal desorption temperature. The results confirm that an ionic-bonding picture based on a large metal-to-halogen charge transfer is not valid for Pd and Pt. Rather, the bonding is predominantly covalent, and the reactivity does not obey simple intuitive rules.

In situ electron microscopy of ferroelectric domains

Abstract

Defect formation and coarsening in hexagonal 2D curved crystals.

In this work we study the processes of defect formation and coarsening of two-dimensional (2D) curved crystal structures. These processes are found to strongly deviate from their counterparts in flat systems. In curved backgrounds the process of defect formation is deeply affected by the curvature, and at the onset of a phase transition the early density of defects becomes highly inhomogeneous. We observe that even a single growing crystal can produce varying densities of defects depending on its initial position and local orientation with regard to the substrate. This process is completely different from flat space, where grain boundaries are formed due to the impingement of different propagating crystals. Quenching the liquid into the crystal phase leads to the formation of a curved polycrystalline structure, characterized by complex arrays of defects. During annealing, mechanisms of geodesic curvature-driven grain boundary motion and defect annihilation lead to increasing crystalline order. Linear arrays of defects diffuse to regions of high curvature, where they are absorbed by disclinations. At the early stage of coarsening the density of dislocations is insensitive to the geometry while the population of isolated disclinations is deeply affected by curvature. The regions with high curvature act as traps for the diffusion of different structures of defects, including disclinations and domain walls.

Programmable Logic Operation via Domain Wall Profile Manipulation

In this paper, we propose a prototype domain wall (DW) programmable magnetic logic device that is able to perform the AND and OR logic functions. The device operates by manipulating the information encoded in the internal spin structure of a transverse domain wall (TDW). The input and output bits in this scheme are the transverse profiles of the domain wall. By exploiting the inherent pinning and depinning mechanisms of the TDW within the device structure, the output DW profile can be deterministically controlled. The logical operation can be programmed at run time by the application of a local Oersted field.

Topologically protected dynamics of spin textures

We study current-induced dynamics of spin textures in thin magnetic nanowires. We derive effective equations of motion describing the dynamics of the domain-wall soft modes associated with topological defects. Because the magnetic domain walls are topological objects, these equations are universal and depend only on a few parameters. We obtain spin spiral domain-wall structure in ferromagnetic wires with Dzyaloshinskii–Moriya interaction and critical current dependence on this interaction. We also find the most efficient way to move the domain walls by resonant current pulses and propose a procedure to determine their dynamics by measuring the voltage induced by a moving domain wall. Based on translationally non-invariant nanowires, we show how to make prospective magnetic memory nanodevices much more energy efficient.

Current inversion at the edges of a chiralp-wave superconductor

Motivated by Sr$_2$RuO$_4$, edge quasiparticle states are analyzed based on the self-consistent solution of the Bogolyubov-de Gennes equations for a topological chiral $p$-wave superconductor. Using a tight-binding model of a square lattice for the dominant $\gamma$-band we explore the non-trivial geometry and band structure dependence of the edge states and currents. As a peculiar finding we show that for high band fillings currents flow in reversed direction comparing straight and zigzag edges. We give a simple explanation in terms of the positions of the zero-energy bound states using a quasi-classical picture. We also show that a Ginzburg-Landau approach can reproduce these results. Moreover, the band filling dependence of the most stable domain wall structure is discussed.

Origin of the Bloch-type polarization components at the 180° domain walls in ferroelectric PbTiO3

Determination of atomic and electronic structures of ferroelectric domain walls is crucial to understand and explore their unusual properties. Using first-principles calculations based on the density functional theory, we explored the atomic and electronic structures of 180° domain walls in PbTiO3, in order to understand the origin of Bloch-type polarization components. It is found that Bloch-type polarization components originate from the large displacements of Pb atoms and the Pb-O hybridization at the domain walls. The development of Bloch-type polarization components significantly reduce the domain wall energies and change the Peierls barriers of domain wall motion in different orientations.

The mechanism of domain-wall structure formation in Ar-Kr submonolayer films on graphite

Using Monte Carlo simulation method in the canonical ensemble, we have studied the commensurate-incommensurate transition in two-dimensional finite mixed clusters of Ar and Kr adsorbed on graphite basal plane at low temperatures. It has been demonstrated that the transition occurs when the argon concentration exceeds the value needed to cover the peripheries of the cluster. The incommensurate phase exhibits a similar domain-wall structure as observed in pure krypton films at the densities exceeding the density of a perfect $(\sqrt{3}\times\sqrt{3})R30^\circ$ commensurate phase, but the size of commensurate domains does not change much with the cluster size. When the argon concentration increases, the composition of domain walls changes while the commensurate domains are made of pure krypton. We have constructed a simple one-dimensional Frenkel-Kontorova-like model that yields the results being in a good qualitative agreement with the Monte Carlo results obtained for two-dimensional systems.

Analytic form of transverse head-to-head domain walls in thin cylindrical wires

Abstract The static problem of a one-dimensional, transverse head-to-head domain wall structure in a thin soft-magnetic nanowire with circular cross-section is treated within the framework of micromagnetic theory. An analytic form of the domain wall profile is derived, which yields that the domain wall profile depends on the wire radius. The analysis is performed by decomposing the magnetostatic energy into a monopolar and a dipolar term. We present a model in which the dipolar term of the magnetostatic energy resulting from the transverse magnetization in the center of the domain wall is calculated with Osborn's formulas for homogeneously magnetized ellipsoids [Phys. Rev. 67 (1945) 351] [22] . The analytic results agree almost perfectly with simulation data as long as the wire diameter is sufficiently small to prevent inhomogeneities of the magnetization along the cross-section. Owing to the recently demonstrated negligible Doring mass of these walls, our results should also apply to the dynamic case, where domain walls are driven by spin-transfer toque effects and/or an axial magnetic field.

Spin Hall torque magnetometry of Dzyaloshinskii domain walls

Current-induced domain wall motion in the presence of the Dzyaloshinskii-Moriya interaction (DMI) is experimentally and theoretically investigated in heavy-metal/ferromagnet bilayers. The angular dependence of the current-induced torque and the magnetization structure of Dzyaloshinskii domain walls are described and quantified simultaneously in the presence of in-plane fields. We show that the DMI strength depends strongly on the heavy metal, varying by a factor of 20 between Ta and Pa, and that strong DMI leads to wall distortions not seen in conventional materials. These findings provide essential insights for understanding and exploiting chiral magnetism for emerging spintronics applications.

Piezoelectric enhancement of(PbTiO3)m/(BaTiO3)nferroelectric superlattices through domain engineering

The phase diagram of ${(\mathrm{PbTiO}}_{3}{)}_{m}/{(\mathrm{BaTiO}}_{3}{)}_{n}$ ferroelectric superlattices was computed using the phase-field approach as a function of layer volume fraction and biaxial strain to tune ferroelectric properties through domain engineering. Two interesting domain structures are found: one with mixed Bloch-N\'eel-Ising domain wall structures and the other with stabilized monoclinic ${\mathrm{M}}_{\mathrm{c}}$ phases. The polarization of the monoclinic ${\mathrm{M}}_{\mathrm{c}}$ phase is able to rotate from out-of-plane to in-plane or vice versa under an electric field, and thus facilitates the domain reversal of rhombohedral domains. This contributes significantly to both reduced coercive fields and enhanced piezoelectric responses.

Hard domain walls in superfluidHe3−B

We study theoretically planar interfaces between two domains of superfluid $^{3}\mathrm{He}$-B. The structure of the B-B walls is determined on the scale of the superfluid condensation energy, and thus the domain walls have thickness on the order of the Ginzburg-Landau coherence length ${\ensuremath{\xi}}_{\mathrm{GL}}$. We study the stability and decay schemes of five inequivalent structures of such domain walls using a one-dimensional Ginzburg-Landau simulation. We find that only one of the structures is stable against small perturbations. We also argue that B-B interfaces could result from the adiabatic $A\ensuremath{\rightarrow}B$ transition and study textures at B-B interfaces. The B-B interface has a strong orienting effect on the spin-orbit rotation axis $\stackrel{\ifmmode \hat{}\else \^{}\fi{}}{\mathbit{n}}$ producing textures similar to those caused by external walls. We study the B-B interface in a parallel-plate geometry and find that the conservation of spin current sets an essential condition on the structure. The stable B-B interface gives rise to half-quantum circulation. The energies of bound quasiparticle excitations are studied in a simple model.

Nonlinear rearrangement of the structure of domain walls in a thin magnetic film with a uniaxial in-plane anisotropy

The structures of domain walls have been investigated by the method of three-dimensional computer simulation in films with uniaxial in-plane anisotropy at different film thicknesses. For the calculations, the parameters characteristic of permalloy films have been taken. It has been established that, depending on the film thickness, the walls that prove to be stable are one-dimensional Neel walls, cross-tie walls, and C- and S-shaped walls. Film thicknesses at which the transition between the different types of walls occurs have been determined. The structure of Bloch lines and Bloch points in C- and S-shaped walls has been investigated. The values of topological charges for different micromagnetic structures have been calculated.