Domain Wall Width Research Articles

Exploring deep learning models for 4D-STEM-DPC data processing

For the study of magnetic materials at the nanoscale, differential phase contrast (DPC) imaging is a potent tool. With the advancements in direct detector technology, and consequent popularity gain for four-dimensional scanning transmission electron microscopy (4D-STEM), there has been an ongoing development of new and enhanced ways for STEM-DPC big data processing. Conventional algorithms are experimentally tailored, and so in this article we explore how supervised learning with convolutional neural networks (CNN) can be utilized for automated and consistent processing of STEM-DPC data. Two different approaches are investigated, one with direct tracking of the beam with regression analysis, and one where a modified U-net is used for direct beam segmentation as a pre-processing step. The CNNs are trained on experimentally obtained 4D-STEM data, enabling them to effectively handle data collected under similar instrument acquisition parameters. The model outputs are compared to conventional algorithms, particularly in how they process data in the presence of strong diffraction contrast, and how they affect domain wall profiles and width measurement.

Energy and Structure of the Terbium Domain Wall

The domain wall energy is calculated by the balance between exchange, magnetocrystalline anisotropy and magnetoelastic energy contributions. The described method is theoretical and is based on experimental measurements of neutron inelastic scattering. The domain wall energy is determined by both finding the minimum of energy and deriving the energy and setting it to zero. The determination was undertaken for the discrete case, and this means that the calculation was performed for each plane or atomic layer. This is in contrast with the Bloch wall, which assumes continuum mean. The energy of the Lilley domain wall was discussed. Most of the energy of the Bloch wall was comprised inside the Lilley distance (above 99.9% of the energy). Antiferromagnetic interactions strongly decreased the domain wall energy. The negative terms due to antiferromagnetism must be considered in the Hamiltonian describing the exchange energy terms. The domain wall energy and width of terbium were reassessed. The values varied between 83.7 and 95.2 Kelvin (10.3 to 11.2 ergs/cm2). The domain width was estimated to be 57 Angstroms. It was found that a significant part of the total domain wall energy was concentrated on the planes at the center of the domain wall.

Interlayer coupled domain wall dynamics induced by external magnetic field in synthetic antiferromagnets

The response of a magnetic domain wall to an external magnetic field in a perpendicularly magnetized synthetic antiferromagnet is studied using both micromagnetic simulations and a reduced model. It is found that the external field induces a sizable displacement between the position of the domain wall in each layer, which can be larger than the domain wall width for a sufficiently strong field. We also study the dynamic evolution of the system when this field is applied or removed. In both cases we find a complex response with two distinct phases that involve both internal domain wall rotation and coupled interlayer domain wall oscillations. As a result of this dynamics spin waves are radiated. The emitted radiation is characterized by a broadband spectrum and can be detected far away from the domain wall.

Influence of Stress on the Chiral Polarization and Elastrocaloric Effect in BaTiO3 with 180° Domain Structure

The polarization and elastrocaloric effect of chiral barium titanate (BaTiO3) with an Ising–Bloch-type domain wall under stress was investigated using the Landau–Ginzburg–Devonshire (LGD) theory. It has been shown that tensile stresses increase the magnitude of the Ising polarization component in barium titanate, together with a decrease in the domain wall width. Compressive stresses cause a reduction in the Ising polarization component and an increase in the domain width. Under compressive stress, barium titanate exhibits a negative elastrocaloric effect and temperature changes with increasing stress, while BaTiO3 exhibits a positive elastrocaloric effect under tensile stress. Bloch polarization shows angle-dependent polarization under external force, but the temperature change from the elastrocaloric effect is smaller than that of Ising polarization under stress. This work contributes to the understanding of polarization evolution under tension in ferroelectrics with chiral structure.

Optimizing preparation conditions and characterizing for CoxPt1-x alloy cylindrical nanowires fabricated by electrodeposition on nanoporous polycarbonate membranes

This study investigated the influence of the preparation conditions on the Co composition, crystal structure, and magnetic and electric conduction properties of cylindrical CoxPt1-x alloy nanowires having 0.08 ≤ x ≤ 0.90, which were electrodeposited on nanoporous templates. When prepared with an optimal concentration ratio of Co and Pt aqueous solutions and electrodeposition potentials, highly oriented crystal structures of fcc Co-Pt (111) was obtained in CoxPt1-x nanowires (0.58 ≤ x ≤ 0.80). Nanowires with (111)-oriented fcc Co-Pt crystals exhibited average lengths and diameters of 5.8–10.8 μm and 130 nm, respectively, and showed an easy axis of magnetocrystalline anisotropy in the longitudinal direction of the nanowire. These results indicate a direct correlation between the crystal structure and magnetic properties. The concentration ratio of Co and Pt in the electrolytes and the electrodeposition potentials for fabricating CoxPt1-x alloy nanowires using the diluted Co composition (0.08 ≤ x ≤ 0.25) were determined. These nanowires were polycrystalline and had a small saturation magnetization. Furthermore, the anisotropic magnetoresistance (AMR) for a single CoxPt1-x nanowire was measured to estimate the domain wall (DW) width in the single CoxPt1-x nanowire. The value of the magnetoresistance (MR) ratio for the single nanowire (0.58 ≤ x ≤ 0.80) with highly (111)-oriented fcc Co-Pt crystal was 0.082–0.23 %, and the estimated value of DW width was 17–25 nm. These findings provide valuable information for constructing three-dimensional magnetic memory devices.

Microstructure and magnetic properties of Nanomet compacted by spark plasma sintering

Nanocrystalline soft magnetic materials with high saturation polarization and low losses have a high potential in motor applications. Thus, toroidal cores were compacted by spark plasma sintering of flakes of the melt-spun Nanomet alloy Fe-Si-B-P-Cu. The thermal properties of the ribbons were analyzed by DSC to determine the crystallization temperatures. The influence of the initial powder and of the compacting parameters such as maximum temperature and dwell time on the density and the magnetic properties in DC and AC were investigated. An optimum temperature range of approximately 50 K was determined for good soft magnetic properties. An effect of the dwell time was not recognized in the observed range. By compacting flakes of different sizes, the maximum permeability can be adjusted in the range of up to 7000. The microstructure was observed by means of XRD and TEM in order to confirm the amorphous and nanocrystalline state, respectively. Using the Lorenz mode of the TEM, it was possible to calculate the magnetic domain wall width for the samples and compare the resulting calculated magnetic properties with the experiments.

Magnetocaloric effect at the reorientation of the magnetization in ferromagnetic multilayers with perpendicular anisotropy

We investigate the magnetocaloric effect obtained by the rotation of a magnetic field applied to an exchange-coupled multilayer system composed of two different ferromagnetic (FM) materials. We specifically consider a system in which the two FMs have perpendicular uniaxial anisotropy axes and utilize conditions which yield a reorientation of the total magnetization when compensation between the anisotropies of the two layers occurs. We calculate the consequent entropy change associated with the “artificial” reorientation. By using known parameters from MnBi and Co we predict an entropy change of Δs=0.34 J kg−1 K−1 for perfect coupling. Lastly, we study the behavior of the multilayer under a rotating magnetic field via a micromagnetic model. When the layer thicknesses are of the order of the local domain wall width, the magnetic field-induced entropy change can be obtained with magnetic fields one order of magnitude lower than in the uncoupled case.

Quantification of Hybrid Topological Spin Textures and Their Nanoscale Fluctuations in Ferrimagnets.

Noncolinear spin textures, including chiral stripes and skyrmions, have shown great potential in spintronics. Basic configurations of spin textures are either Bloch or Néel types, and the intermediate hybrid type has rarely been reported. A major challenge in identifying hybrid spin textures is to quantitatively determine the hybrid angle, especially in ferrimagnets with weak net magnetization. Here, we develop an approach to quantify magnetic parameters, including chirality, saturation magnetization, domain wall width, and hybrid angle with sub-5 nm spatial resolution, based on Lorentz four-dimensional scanning transmission electron microscopy (Lorentz 4D-STEM). We find strong nanometer-scale variations in the hybrid angle and domain wall width within structurally and chemically homogeneous FeGd ferrimagnetic films. These variations fluctuate during different magnetization circles, revealing intrinsic local magnetization inhomogeneities. Furthermore, hybrid skyrmions can also be nucleated in FeGd films. These analyses demonstrate that the Lorentz 4D-STEM is a quantitative tool for exploring complex spin textures.

Magnetization spiral structure and high domain wall velocity induced by inertial effect

In ultrafast magnetism, i.e., the short time scales such as picosecond and femtosecond, we report that the spiral structure of magnetization can be formed by the inertial effect. Comparing with the case of fast magnetism in nanosecond time scale, we can obtain a higher velocity of domain wall in ultrafast magnetism due to the driving of inertial moment. There is a critical value τc of angular momentum relaxation time τ for the inertial breakdown in uniaxial ferromagnet. Under the action of the inertial effect the domain wall width shows the characteristics of increases firstly as τ<τc, and then decreasing as τ>τc. It directly leads to the positive or negative mobility for the domain wall velocity as the inertia is less than or exceeds the critical value, respectively. In the high frequency mode (i.e., high field mode), we obtain the limit domain wall velocity, i.e., V→1/ατ. The smaller the inertia or damping, the faster the domain wall moves. For the case of biaxial anisotropic ferromagnets, the domain wall width and velocity decreases with the increasing inertia term, respectively. In the presence of inertia effect, there is an another critical magnetic field hc. The domain wall width decreases with the increase of the magnetic field as h<hc, while increases as h>hc. However, the domain wall velocity shows a nearly linear increase with the magnetic field. These results indicate that the ultrafast magnetism has more advantages than fast magnetism. It also provides a good control technique for rapid information processing in the future.

Domain wall creep motion dynamics in CoFeB nanowire strips of different thicknesses using micromagnetic simulation approach

Field-induced domain wall motion on thin magnetic films with perpendicular anisotropy has long been attributed with the universal creep theory, in which the domain wall (DW) is able to experience a slow-moving motion with driving fields below the depinning threshold. Despite the numerous research that has been conducted in regards to this phenomenon, creep motion thus far has yet to be observed on a typical single-layered magnetic film. The effects of the film’s thickness towards the creep motion are also scarcely explored. In this study, we conduct micromagnetic simulations of CoFeB nanowire strips with perpendicular anisotropy and varying thicknesses to investigate the dynamics of the creep motion being exhibited. We then analyze the obtained DW velocities and its’ agreement with the universal creep law equation. The velocities obtained with low driving fields is found to be in an agreement with the creep law equation. The varying thicknesses also seem to affect the overall DW velocity and DW width.

Inzhektsiya spina dvizhushcheysya domennoy stenkoy na granitse razdela antiferromagnitnogo izolyatora s dvumernym metallom

A domain wall (DW) which moves parallel to a magnetically compensated interface between an antiferromagnetic insulator (AFMI) and a two-dimensional (2D) metal can pump spin polarization into the metal. It is assumed that localized spins of a collinear AFMI interact with itinerant electrons through their exchange interaction on the interface. We employed the Keldysh formalism of Green’s functions for electrons which experience potential and spin-orbit scattering on random impurities. This formalism allows a unified analysis of spin pumping, spin diffusion and spin relaxation effects on a 2D electron gas. It is shown that the pumping of a nonstaggered magnetization into the metal film takes place in the second order with respect to the interface exchange interaction. At sufficiently weak spin relaxation this pumping effect can be much stronger than the first-order effect of the Pauli magnetism which is produced by the small nonstaggered exchange field of the DW. It is shown that the pumped polarization is sensitive to the geometry of the electron’s Fermi surface and increases when the wave vector of the staggered magnetization approaches the nesting vector of the Fermi surface. In a disordered diffusive electron gas the induced spin polarization follows the motion of the domain wall. It is distributed asymmetrically around the DW over a distance which can be much larger than the DW width.

Geometry effects on the domain wall width in bent nanowires

Spintronic devices using domain walls (DWs) as information carriers require stable high speeds and a clear understanding of their dynamics. The latter strongly depends on the geometry of the magnetic element hosting the DW. This work aims to determine the effects of the geometry on the width of a transverse DW nucleated in a bent magnetic nanowire with a rectangular cross-section. Our results show that a geometry-induced effective anisotropy is responsible for shrinking or stretching the DW width, depending on the direction along which the DW center points (DW phase).

Ultrafast switching dynamics of the ferroelectric order in stacking-engineered ferroelectrics

Recent research has highlighted the potential of ferroelectricity in van der Waals bilayers in providing an unconventional route for improving device performance. Understanding the static and dynamic properties of domain wall (DW) is critical unlocking this potential, as key parameters such as switching field and speed heavily rely on them. In this article, we conduct a theoretical exploration of the fundamental properties of textures in stacking-engineered ferroelectrics using a machine-learning potential model. Our results demonstrate that competition between the switching barrier of stable ferroelectric states and in-plane lattice distortion leads to a DW width of ten nanometers. We also demonstrate that DW motion can drastically reduce the critical ferroelectric switching field of a monodomain by two orders of magnitude and enable domain switching on a picosecond timescale, suggesting the potential for ultrafast and energy-saving non-volatile memory devices. Moreover, twisting the bilayer into a stacking Moiré structure results in a super-paraelectric state, because the ferroelectric order is reversibly broken by DW motion already at ultralow electric fields. These findings offer valuable insights into the behavior and properties of stacking-engineered ferroelectrics, with significant implications for the development of next-generation electronic devices.

Theoretical studies of magnetic domain phase diagrams from micromagnetic simulation

A skyrmion is a kind of quasiparticle observed on the surface of a magnetic material, and the topologically protected vortex structure is known to be produced via spintronics. The special properties allow skyrmions to exist in the interface of devices with an ultralow accumulation rate and a high transportation rate. Magnetic domain walls such as the multiple wormhole domain show up from the ground state with different dendritic densities and shapes when the material is stimulated. The Dzyaloshinskii–Moriya interaction (Ms), anisotropy constant (K), and stiffness coefficient (A) are key parameters that affect the magnetic field relative to the representation of the skyrmion. By tuning these parameters, we can adjust the fragmentation of the magnetic domain, the stability, and the radius of the skyrmion. These parameters also modulate characteristics such as the skyrmion number and helicity, which describe the behavior of the spintronic vortex and strongness. This research shows the relation between the parameters and characteristics with the phase diagram and indicates the range of stable skyrmion existence and its size. The higher saturation magnetization Ms and the lower stiffness coefficient A cause the domain wall width to become thicker. Besides, the skyrmion number N decreases with an increase in the skyrmion size until it transforms into a deformed domain.

Analytic theory for Néel skyrmion size, accounting for finite film thickness

The energy of a Néel skyrmion in a magnetic film with interfacial DMI is developed analytically, with the finite thickness of the film taken into account. Many theories for the energy of magnetic skyrmions use models that are only accurate in the limit that the film thickness vanishes. One theory [Büttner et al. Sci. Rep. 8, 4464 (2018)] provides exceptionally accurate expressions for the skyrmion energy for finite thickness films, but does not yield an analytic solution for the skyrmion size, plus it contains contributions which are found using fitting methods. Here, we approximate the demagnetizing energy of a skyrmion by examining the form of magnetostatic Green’s function expressions for the demagnetizing fields. Then, analytic expressions for the skyrmion radius and the skyrmion domain wall width are derived in the limit of zero applied field. Our methods are rigorously compared to other calculation methods and compare well to numerical calculations and experimental results, both with and without an applied magnetic field. The approximations that allow for an analytic result lead to a loss of accuracy for the skyrmion radius of up to 20% but this loss in accuracy may be offset by the simplicity of the developed physical expressions. Finite thickness is important to consider for skyrmions existing in multilayer stacks with total thickness of a few nanometers.

Direct observation of rotation of polarization at 90-degree domain walls in BaTiO3

The rotation of polarization at 90-degree domain walls in tetragonal BaTiO3 was directly observed by the STEM-CBED method, which combines scanning transmission electron microscopy and convergent-beam electron diffraction (CBED). The CBED patterns in the domain wall region exhibit continuous changes in intensity distribution within disks and specific features corresponding to the direction of the rotation of polarization. Simulations were performed using hypothetical superstructures created by continuously connecting Ti displacement with a 90-degree rotation and showed good qualitative agreement with the experimental patterns. The quantitative evaluation of the mirror symmetries existing in the tetragonal structure in bulk form revealed the width of the domain wall is approximately 9 nm. While distorted regions with slightly broken symmetry in CBED disks were found to extend further on both sides of the domain wall region in 6–7 nm. This finding can explain the discrepancy in the domain wall widths reported in previous studies.

Identifying the domain-wall spin structure in antiferromagnetic NiO/Pt

The understanding of antiferromagnetic domain walls, which are the interface between domains with different N\'eel order orientations, is a crucial aspect to enable the use of antiferromagnetic materials as active elements in future spintronic devices. In this work, we demonstrate that in antiferromagnetic NiO/Pt bilayers circular domain structures can be generated by switching driven by electrical current pulses. The generated domains are T-domains, separated from each other by a domain wall whose spins are pointing toward the average direction of the two T-domains rather than the common axis of the two planes. Interestingly, this direction is the same for the whole circular domain indicating the absence of strong Lifshitz invariants. The domain wall can be micromagnetically modeled by strain distributions in the NiO thin film induced by the MgO substrate, deviating from the bulk anisotropy. From our measurements we determine the domain wall width to have a full width at half maximum of $\Delta = 98 \pm 10$ nm, demonstrating strong confinement.

Strength, plasticity and coercivity tradeoff in soft magnetic high-entropy alloys by multiple coherent interfaces

Traditional strengthening of alloys involves dislocation, second phase and grain boundary, which could deteriorate plasticity and coercivity (Hc). In this work, multiple coherent interfaces are introduced in Fe26Co25Ni20Cu15Al13.1Ga0.9 (denoted HEA2) soft magnetic high-entropy alloy, by which tradeoff among strength, plasticity and coercivity has been achieved. The strength is elevated to 414.6 MPa by the synergistic enhancement of FCC/BCC dual-phase interface, L12 nanoprecipitates in FCC phase and B2 nanoprecipitates in BCC phase. The fully coherent multiple interfaces (FCC/BCC, FCC/L12 and BCC/B2) bestow the HEA2 alloy with excellent plasticity exceeding 200%. More importantly, the smaller size of L12 and B2 nanoprecipitates than domain wall width and the multiple coherent interfaces wouldn't hinder domain wall movement, leading to a low coercivity of 334 A/m. Whereas, heterogeneous ordered B2 precipitates with size exceeding the critical width (δw = 132 nm) impose obvious pinning effect on the domain wall movement. This study provides guidance for developing novel alloys with balanced mechanical and magnetic properties for advanced electrical application.

Control of the interaction between pinning disorder and domain walls in Pt/Co/AlOx ultrathin films by He+ ion irradiation

We have studied the effect of He+ irradiation on the dynamics of chiral domain walls in Pt/Co/AlOx trilayers in the creep regime. Irradiation leads to a strong decrease in the depinning field and a non-monotonous change of the effective pinning barriers. The variations of domain wall dynamics result essentially from the strong decrease in the effective anisotropy constant, which increases the domain wall width. The latter is found to present a perfect scaling with the length-scale of the interaction between domain wall and disorder, ξ. On the other hand, the strength of the domain wall–disorder interaction, fpin, is weakly impacted by the irradiation, suggesting that the length-scales of the disorder fluctuation remain smaller than the domain wall width.

Flexo-Ferroelectricity and a Work Cycle of a Two-Dimensional-Monolayer Actuator.

Well recognized mechanical flexibility of two-dimensional (2D) materials is shown to bring about unexpected behaviors to the recently discovered monolayer ferroelectrics, especially those displaying normal, off-plane polarization. A "ferro-flexo" coupling term is introduced into the energy expression, to account for the connection of ferroelectricity and bending (strain gradient) of the layer, to predict and quantify its spontaneous curvature and how it affects the phase transitions. With InP as a chemically specific representative example, the first-principles calculations indeed reveal strong coupling ∼P·ϰ between the ferroelectric polarization (P) and the curvature of the layer (ϰ ≡ 1/r), having profound consequences for both mechanics and ferroelectricity of the material. Due to flexural relaxation, the spontaneous polarization and the transition barrier rise significantly, leading to large changes in the Curie temperature, coercive field, and domain wall width and energy, based on Monte Carlo simulations. On the other hand, the polarization switching, characteristic to ferroelectrics, does induce an overall layer bending, enabling a conversion of electrical signal to movement as an actuator; its possible work-cycles and maximum work-efficiency are briefly discussed.