Domain Wall Position Research Articles

Exponential dependence between motion acceleration and diameters of skyrmions under the driven of periodical strains

The internal strain in practical materials is usually seen as defects and a large of methods have been proposed to avoid its appearance. However, strains in magnetic materials can be effective in regulating the performance mediated by magnetoelastic coupling effect. Herein, we theoretically demonstrate the motion of skyrmions driven by time-dependent periodical strains which imitate strain fluctuations in real materials. It is found that the motion acceleration of skyrmions is exponential correlation with diameters and skyrmions can be rebounded near the end of magnetic racetrack for larger size of diameters. Such a motion results from the excitation of spin wave modes on the position of circular domain walls in skyrmions. Our results can provide insight for manipulating skyrmions by strain engineering for applications in information storage and processing.

Energy-efficient neural network using an anisotropy field gradient-based self-resetting neuron and meander synapse

Neuromorphic computing (NC) is considered a potential solution for energy-efficient artificial intelligence applications. The development of reliable neural network (NN) hardware with low energy and area footprints plays a crucial role in realizing NC. Even though neurons and synapses have already been investigated using a variety of spintronic devices, the research is still in the primitive stages. Particularly, there is not much experimental research on the self-reset (and leaky) aspect(s) of domain wall (DW) device-based neurons. Here, we have demonstrated an energy-efficient NN using a spintronic DW device-based neuron with self-reset (leaky) and integrate-and-fire functions. An “anisotropy field gradient” provides the self-resetting behavior of auto-leaky, integrate, and fire neurons. The leaky property of the neuron was experimentally demonstrated using a voltage-assisted modification of the anisotropy field. A synapse with a meander wire configuration was used to achieve multiple-resistance states corresponding to the DW position and controlled pinning of the DW. The NN showed an energy efficiency of 0.189 nJ/image/epoch while achieving an accuracy of 92.4%. This study provides a fresh path for developing more energy-efficient DW-based NN systems.

Granular Magnetization Switching in Pt/Co/Ti Structure with HfOx Insertion for In-Memory Computing Applications.

Exploring multiple states based on the domain wall (DW) position has garnered increased attention for in-memory computing applications, particularly focusing on the utilization of spin-orbit torque (SOT) to drive DW motion. However, devices relying on the DW position require efficient DW pinning. Here, we achieve granular magnetization switching by incorporating an HfOx insertion layer between the Co/Ti interface. This corresponds to a transition in the switching model from the DW motion to DW nucleation. Compared to the conventional Pt/Co/Ti structure, incorporation of the HfOx layer results in an enhanced SOT efficiency and a lower switching current density. We also realized stable multistate storage and synaptic plasticity by applying pulse current in the Pt/Co/HfOx/Ti device. The simulation of artificial neural networks (ANN) based on the device can perform digital recognition tasks with an accuracy rate of 91%. These results identify that DW nucleation with a Pt/Co/HfOx/Ti based device has potential applications in multistate storage and ANN.

Weak Pinning and Long-Range Anticorrelated Motion of Phase Boundaries in Driven Diffusive Systems.

We show that domain walls separating coexisting extremal current phases in driven diffusive systems exhibit complex stochastic dynamics with a subdiffusive temporal growth of position fluctuations due to long-range anticorrelated current fluctuations and a weak pinning at long times. This weak pinning manifests itself in a saturated width of the domain wall position fluctuations that increases sublinearly with the system size. As a function of time t and system size L, the width w(t,L) has a scaling behavior w(t,L)=L^{3/4}f(t/L^{9/4}), with f(u) constant for u≫1 and f(u)∼u^{1/3} for u≪1. An Orstein-Uhlenbeck process with long-range anticorrelated noise is shown to capture this scaling behavior. The exponent 9/4 is a new dynamical exponent for relaxation processes in driven diffusive systems.

Abrupt increase of stochastic behavior in domain-wall motion near depinning field

The domain-wall motion in ferromagnetic films exhibits stochastic behavior due to thermal agitation with quenched disorders. The stochasticity is an obstacle in the sense of consistent repeatability of domain-wall position control in magnetic domain-wall devices. In general, the level of stochasticity is expected to decrease as driving force increases. This property suggests that the magnetic domain-wall devices are capable of simultaneously achieving both high operational speed and decrease in the level of stochasticity. However, we report here an observation of stochasticity anomaly, which involves a significant increase in relative speed dispersion near the depinning field. Domain-wall motion measurements were performed in ferromagnetic wires with perpendicular magnetic anisotropy over the same position to measure the relative speed dispersion. The stochasticity in domain-wall motion is intertwined with the number of pinning–depinning events throughout the domain-wall motion. The size of cluster events, which leads to the number of events, reflects the trend in the relative speed dispersion. The observed anomaly is provided by occurrence of large avalanches of cluster events. The anomaly occurs within the tech-relevant speed range of 1–100 m/s, signaling the necessity of material engineering to mitigate its effects.

Non‐Destructive Tomographic Nanoscale Imaging of Ferroelectric Domain Walls

AbstractExtraordinary physical properties arise at polar interfaces in oxide materials, including the emergence of 2D electron gases, sheet‐superconductivity, and multiferroicity. A special type of polar interface is ferroelectric domain walls, where electronic reconstruction phenomena can be driven by bound charges. Great progress has been achieved in the characterization of such domain walls and, over the last decade, their potential for next‐generation nanotechnology has become clear. Established tomography techniques, however, are either destructive or offer insufficient spatial resolution, creating a pressing demand for 3D imaging compatible with future fabrication processes. Here, non‐destructive tomographic imaging of ferroelectric domain walls is demonstrated using secondary electrons. Utilizing conventional scanning electron microscopy (SEM), the position, orientation, and charge state of hidden domain walls are reconstructed at distances up to several hundreds of nanometers away from the surface. A mathematical model is derived that links the SEM intensity variations at the surface to the local domain wall properties, enabling non‐destructive tomography with good noise tolerance on the timescale of seconds. The SEM‐based approach facilitates high‐throughput screening of materials with functional domain walls and domain‐wall‐based devices, which is essential for monitoring during the production of device architectures and quality control in real‐time.

Magnetic-field-controlled positioning of magnetic domain wall in tie-shaped asymmetric nanowire and its application for magnetic field detection.

With topological spin texture, magnetic domain walls have soliton-like dynamic behaviors in magnetic nanowires, which can be used in information transmission and storage technology. Therefore, precisely controlling the dynamic behavior of the magnetic domain wall and its pinning behavior is one of the important technical challenges in realizing domain-wall-based spintronic devices. In this work, a geometrically defect-free scheme for domain wall pinning/depinning is proposed using micromagnetic simulations based on a tie-shaped asymmetric nanowire, which can precisely control the position of the magnetic domain wall in an external magnetic field. The results show that the domain wall in tie-shaped nanowires exhibits excellent linear response and ultrafast time response to external magnetic fields, which endow them with potential applications for high-frequency weak-magnetic-field detection. We further propose a scheme for constructing a magnetic-field sensor using the tie-structured nanowire, and we study its feasibility.

Spacer Thickness and Temperature Dependences of the Interlayer Exchange Coupling in a Co/Pt/Co Three-Layer Structure

Domain wall mobility as a function of nonmagnetic interlayer thickness and temperature was studied in ultrathin exchange-coupled ferromagnetic layers using magneto-optic Kerr microscopy. The system under study is a Pt/Co/Pt/Co/Pt heterostructure having perpendicular magnetic anisotropy and a middle Pt layer with spatially variable thickness. The ferromagnetic interaction between the Co layers is observed when the Pt interlayer thickness varies from 5 to 6 nm in a temperature range of 200–300 K. There is a certain interval of Pt layer thickness where domain walls in both ferromagnetic layers move independently. Nonlinear dependence of the domain wall displacement on the applied field was measured. It is shown that an equilibrium position of the relaxed domain wall depends on field, temperature, and the nonmagnetic interlayer thickness. This position is determined by the energy balance: (i) domain wall displacement provided by the applied field, (ii) interlayer exchange interaction in the area swept by the domain wall, and (iii) domain wall coercivity. The mechanism of domain wall stabilization in terms of independent wall motion near critical thickness was considered. It is found that both the coercivity of the Co layer and the critical thickness decrease at higher temperature, while the interlayer exchange constant J is changed weakly.

Position-reconfigurable pinning for magnetic domain wall motion

Precise control of magnetic domain wall (DW) motion is crucial for DW-based spintronic devices. To date, artificially designed DW pinning sites, such as notch structures, have been used to precisely control the DW position. However, the existing DW pinning methods are not reconfigurable because they cannot change the position of pinning site after being fabricated. Herein, a novel method for attaining reconfigurable DW pinning is proposed, which relies on the dipolar interactions between two DWs located in different magnetic layers. Repulsion between DWs in both layers was observed, indicating that one of the DWs acts as a pinning barrier for the other. Because the DW is mobile in the wire, the position of pinning can be modulated, thereby resulting in reconfigurable pinning that was experimentally demonstrated for current-driven DW motion. These findings provide additional controllability of DW motion, which may expand the functionality of DW-based devices to broader spintronic applications.

Ga+ Ion Irradiation-Induced Tuning of Artificial Pinning Sites to Control Domain Wall Motion

Domain-wall-based devices are considered one of the candidates for the next generation of storage memories and nanomagnetic logic devices due to their unique properties, such as nonvolatility, scalability, and low power consumption. Field or current-driven domain walls require a regular and controlled motion along the track in which they are stored in order to maintain the information integrity during operation. However, their dynamics can vary along the track due to film inhomogeneities, roughness of the edges, and thermal fluctuations. Consequently, the final position of the domain walls may be difficult to predict, making difficult the development of memory and logic applications. In this paper, we demonstrate how Ga+ ion irradiation can be used to locally modify the material properties of the Ta/CoFeB/MgO thin film, creating regions in which the domain wall can be trapped, namely motion barriers. The aim is to push the domain wall to overcome thin-film inhomogeneities effects, while stopping its motion at artificially defined positions corresponding to the irradiated regions. Increasing the driving force strength, the domain wall can escape, allowing the shifting between consecutive irradiated regions. In this way, the correct positioning of the domain walls after the motion is ensured. The study shows that the driving force strength, namely current density or magnetic field amplitude, needed to overcome the irradiated regions depends on the ion dose. These results show a reliable approach for domain wall manipulation, enabling a precise control of the domain wall position along a track with synchronous motion.

In-plane charged domain walls with memristive behaviour in a ferroelectric film.

Domain-wall nanoelectronics is considered to be a new paradigm for non-volatile memory and logic technologies in which domain walls, rather than domains, serve as an active element. Especially interesting are charged domain walls in ferroelectric structures, which have subnanometre thicknesses and exhibit non-trivial electronic and transport properties that are useful for various nanoelectronics applications1-3. The ability to deterministically create and manipulate charged domain walls is essential to realize their functional properties in electronic devices. Here we report a strategy for the controllable creation and manipulation of in-plane charged domain walls in BiFeO3 ferroelectric films a few nanometres thick. By using an in situ biasing technique within a scanning transmission electron microscope, an unconventional layer-by-layer switching mechanism is detected in which ferroelectric domain growth occurs in the direction parallel to an applied electric field. Based on atomically resolved electron energy-loss spectroscopy, in situ charge mapping by in-line electron holography and theoretical calculations, we show that oxygen vacancies accumulating at the charged domain walls are responsible for the domain-wall stability and motion. Voltage control of the in-plane domain-wall position within a BiFeO3 film gives rise to multiple non-volatile resistance states, thus demonstrating the key functional property of being a memristor a few unit cells thick. These results promote a better understanding of ferroelectric switching behaviour and provide a new strategy for creating unit-cell-scale devices.

Shape‐Dependent Multi‐Weight Magnetic Artificial Synapses for Neuromorphic Computing (Adv. Electron. Mater. 12/2022)

Neuromorphic Computing This frontispiece imagines the use of the studied devices in a neural network crossbar array for brain-inspired computing. The devices function as artificial synapses at each crosspoint and as artificial neurons at the input and output. The glowing lines show the magnetic domain wall positions, compared to the orange magnetic tunnel junctions. More details can be found in article number 2200563 by Christopher H. Bennett, Jean Anne C. Incorvia, and co-workers.

Dynamics of Single Domain Wall Propagating in Bistable Microwire in Rapidly Changing Magnetic Field

The presented experimental method enables the study of the dynamics of a domain wall (DW) moving in bistable microwire in a region of rapidly changing magnetic field. DW velocity versus DW position dependence is obtained in this experiment. Measurements were carried out on Fe77.5Si15B7.5 microwire with strong unidirectional effect in DW propagation. The propagating DW is forced to change its parameters in a very short time, which results in the velocity increasing above its equilibrium value after the DW passes the region of rapid increase in magnetic field. In order to interpret the observed experimental behavior, a simple theoretical model was proposed. Comparison of experimental and model dependences produced a high value of DW inertial mass, indicating that the DW area was much larger than the cross-sectional area of the microwire. Another interesting conclusion was that a DW with stronger damping (shorter wall) does not have a lower value of inertial mass.

Area law for magnetic domain walls in bent cylindrical nanowires

The dynamics of several systems in nature occurs under some constraints and symmetries that ensure the appearance of constants of motion. In this work, we discuss the dynamics of the magnetic domain wall (DW) under the Walker regime (i.e., when its position oscillates as a function of time) in bent cylindrical magnetic nanowires (NWs) with constant curvatures. It is shown that the DW position sweeps, in relation to the curvature center, the same area for different NW curvatures. This phenomenon appears due to an exchange-driven curvature-induced interaction. The translational DW motion is accompanied by its rotation around the NW axis, leading to a periodic curvature-independent angular momentum, from which one obtains an area's law for the DW motion.

Compact Model of Domain Wall MTJ Driven by Spin Orbit Torque and Dzyaloshinskii–Moriya Interaction

Current-induced domain wall motion (CIDWM) shows promising prospects with low power, high density, high speed, and so on. Recent studies have demonstrated that magnetic tunnel junction (MTJ) based on CIDWM has great potential in mimicking a non-volatile artificial neuron and synapse. By combining the effect of the interfacial Dzyaloshinskii–Moriya interaction (DMI) to stabilize the Néel-type domain wall (DW) and the high-speed low-power advantages of spin orbit torque (SOT), the novel MTJ device is experimentally demonstrated with low threshold current and high propagation speed, which shows potential applications in the field of the artificial neuron and synapse. In this article, a compact model for CIDWM-MTJ based on SOT and DMI is presented. The model integrates the SOT mechanism for magnetization reversal and DW nucleation, CIDWM behaviors, and tunnel resistance theory of MTJ nanopillar. The micromagnetic simulation and the temporal evolution of the DW position are implemented by solving the Landau–Lifshitz–Gilbert (LLG) equation and the 1-D model. Based on the developed model, a hybrid CIDWM-MTJ/CMOS circuit is simulated for verification. The presented model combines the CIDWM dynamics and the MTJ magnetic dynamics, showing potential application for the simulation of all-spin artificial neural network (ANN).

Empirical relation between the Hall voltage and domain wall position in a Hall bar geometry

The anomalous Hall effect has been used as a versatile tool for the measurement of various transport phenomena in magnetic systems, particularly those with perpendicular magnetic anisotropy. The anomalous Hall voltage responds not only to the magnetization state but also to the position of magnetic domain walls when the magnetic domain passes through the Hall bar structure. In this study, an empirical relation was developed between the Hall voltage and domain wall position in the Hall bar geometry. This relation was first developed by numerical simulations and then, confirmed by analytical formulae. The validity of the empirical relation was finally verified by experimental results. The present empirical relation provides an experimental method for the electric detection of the position of magnetic domain walls.

Kinetics of Domain Structure in Co/Pt/Co Ultrathin Films with Ferromagnetic Interlayer Exchange Interaction: Dependence on Interlayer Thickness

We studied the in-field evolution of the domain structure in ultrathin Co(0.6 nm)/Pt(t)/Co(0.6) nm trilayers with perpendicular magnetic anisotropy for 5 nm < t < 6 nm using polar Kerr microscopy. The critical interlayer thickness tcr = 5.3 nm was found to separate two principal patterns of domain behavior including interlayer correlations and motility of the domain walls. It is shown that magnetization in both Co layers is coupled with strong ferromagnetic interaction for small Pt thickness (t < tcr), while this coupling is weak for thicker (t > tcr) Pt layers. Nonlinear dependence of the wall displacement on the field value is observed. The established final position of domain walls after relaxation depends on the Pt layer thickness. It is determined by balance of the interlayer exchange and energy gain due to the field. The mechanism of wall stabilization is considered in the case of independent wall motion. In the region with weak coupling, dependence of the interlayer interaction energy on Pt thickness was measured.

Domain wall pinning through nanoscale interfacial Dzyaloshinskii–Moriya interaction

Neuromorphic computing (NC) has been gaining attention as a potential candidate for artificial intelligence. The building blocks for NC are neurons and synapses. Research studies have indicated that domain wall (DW) devices are one of the most energy-efficient contenders for realizing NC. Moreover, synaptic functions can be achieved by obtaining multi-resistance states in DW devices. However, in DW devices with no artificial pinning, it is difficult to control the DW position, and hence achieving multilevel resistance is difficult. Here, we have proposed the concept of nanoscale interfacial Dzyaloshinskii–Moriya interaction (iDMI) for controllably stopping the DWs at specific positions, and hence, realizing multi-resistance states. We show that the nanoscale iDMI forms an energy barrier (well), which can controllably pin the DWs at the pinning sites. Moreover, a tunable depinning current density was achieved by changing the width and iDMI constant of the confinement region. We have also studied pinning in a device with five successive pinning sites. This feature is a proof-of-concept for realizing multi-resistance states in the proposed concept. Based on these observations, a magnetic tunnel junction—where the free layer is made up of the proposed concept—can be fabricated to achieve synapses for NC applications.

Numerical simulation of domain wall motion in a surface discharge over a ferroelectric

The article presents a simplified numerical simulation of a vacuum ferroelectric cathode operating in a low-current mode (without surface plasma formation). The field emission from the cathode was simulated for the range of applied electric field magnitudes. The polarization domain growth process during the charging of ferroelectric surface was simulated using Landau-Ginzburg-Devonshire model. Interaction of the electrons with a depolarization field of a domain wall led to an attraction of the electrons to the polarization domain boundaries. A close to the linear dependence of the equilibrium domain wall position from the applied electric field was found with the total emitted charge proportional to the domain size.

Domain wall AdS/QCD

We construct a new holographic description of QCD using domain wall fermions. The construction consists of probe D7 branes in a D5 brane geometry describing quarks on a 4+1d defect in a 5+1d gauge theory. We then compactify one dimension of the D5 to introduce confinement in the gauge degrees of freedom. In addition we allow a spatial dependent mass term for the D7 brane quarks to isolate chiral fermions on 3+1d domain walls. The D7 world volume fields, when restricted to the domain wall position, provide an AdS/QCD description. We compute the spectrum and compare to data. We include higher dimension operators to systematically improve the description.