Domain Walls In Magnetic Nanowires Research Articles

Application of the Point-Like Contact Model: Resistance Oscillations of the Domain Wall in Magnetic Nanowires and Junctions Due to Mean Free Path Effects

This work is focused on determining the electrical resistance, which is induced by single domain wall (DW) in magnetic nanowire (NW) with a negligible defect. The provided model covers a wide range of NW diameters. The obtained result demonstrates a few-order rapid reduction of the DW resistance accompanied by its possible deviations versus the diameter growth ranging from 1.2[Formula: see text]nm to 15.2[Formula: see text]nm. The origin of these deviations, which are also identified as oscillations, is referred to the nonuniform electron scattering on the DW due to the intermixing electron scattering conditions: ballistic for one spin channel and quasi-ballistic for other one with opposite spin direction. It may happen when the DW width by value is approximately in between two lengths: a mean free path (MFP) with the spin down and spin up. The indirect evidence of this finding also comes from the fact that homogeneous NWs show the most valuable DW resistance oscillations by magnitude rather than segmented magnetic NWs. In addition to the approach, where DW width is constant, the other reasonable model is used when the DW can be constrained for some conditions. The same results are valid for magnetic junctions with DW. Finally, resistance simulation in the diffusive range, when a diameter of the NW (or point-like junction) is larger than any of spin-resolved MFP of electrons, successfully follows experimental data for the single and double DW resistances available in literature.

Neuromorphic computation with a single magnetic domain wall

Machine learning techniques are commonly used to model complex relationships but implementations on digital hardware are relatively inefficient due to poor matching between conventional computer architectures and the structures of the algorithms they are required to simulate. Neuromorphic devices, and in particular reservoir computing architectures, utilize the inherent properties of physical systems to implement machine learning algorithms and so have the potential to be much more efficient. In this work, we demonstrate that the dynamics of individual domain walls in magnetic nanowires are suitable for implementing the reservoir computing paradigm in hardware. We modelled the dynamics of a domain wall placed between two anti-notches in a nickel nanowire using both a 1D collective coordinates model and micromagnetic simulations. When driven by an oscillating magnetic field, the domain exhibits non-linear dynamics within the potential well created by the anti-notches that are analogous to those of the Duffing oscillator. We exploit the domain wall dynamics for reservoir computing by modulating the amplitude of the applied magnetic field to inject time-multiplexed input signals into the reservoir, and show how this allows us to perform machine learning tasks including: the classification of (1) sine and square waves; (2) spoken digits; and (3) non-temporal 2D toy data and hand written digits. Our work lays the foundation for the creation of nanoscale neuromorphic devices in which individual magnetic domain walls are used to perform complex data analysis tasks.

Voltage control of domain walls in magnetic nanowires for energy-efficient neuromorphic devices

An energy-efficient voltage-controlled domain wall (DW) device for implementing an artificial neuron and synapse is analyzed using micromagnetic modeling in the presence of room temperature thermal noise. By controlling the DW motion utilizing spin transfer or spin–orbit torques in association with voltage generated strain control of perpendicular magnetic anisotropy in the presence of Dzyaloshinskii–Moriya interaction, different positions of the DW are realized in the free layer of a magnetic tunnel junction to program different synaptic weights. The feasibility of scaling of such devices is assessed in the presence of thermal perturbations that compromise controllability. Additionally, an artificial neuron can be realized by combining this DW device with a CMOS buffer. This provides a possible pathway to realize energy-efficient voltage-controlled nanomagnetic deep neural networks that can learn in real time.

Energetics of domain wall in magnetic nanowire

Micromagnetic modeling is used to study the energetics of magnetic switching of single-layer permalloy nanowire. The energy landscape of the system is studied using Nudged Elastic Band method. It has been shown that presence of rectangular shape defects on long side and inside nanowire leads to the appearance of local maxima and minima on the energy profile. Thus artificially created imperfections can be used for effective DW pinning.

Dynamic nucleation of domain-chains in magnetic nanotracks**Project supported by the National Natural Science Foundation of China (Grant No. 11704191), the Jiangsu Specially-Appointed Professor, the Natural Science Foundation of Jiangsu Province of China (Grant No. BK20171026), and the Six-Talent Peaks Project in Jiangsu Province, China (Grant No. XYDXX-038).

Most of the reported observations are about the dynamic properties of individual domain-walls in magnetic nanowires, but the properties of multiple stripe-domains have rarely been investigated. Here, we demonstrate a simple but efficient scenario for multiple domains injection in magnetic nanowires. The domain-chains (DCs), a cluster of multiple domains, can be dynamically generated with tunable static properties. It is found that the number of domains in a single DC can be dynamically adjusted by varying the frequency of microwave field (MF) and the period of spin-polarized current (SPC) intensity. The static properties of the DCs, i.e., its length, spacing, and period between neighboring DCs, can be dynamically controlled by regulating the frequency of MF and the intensity of SPC. We have also discussed the possibility of using domain-chains as information carries, which provides a meaningful approach for flexible multi-bit information storage applications.

Thermal gradients for the stabilization of a single domain wall in magnetic nanowires

By means of Monte Carlo simulations we studied field driven nucleation and propagation of transverse domain walls (DWs) in magnetic nanowires subjected to temperature gradients. Simulations identified the existence of critical thermal gradients that allow the existence of reversal processes driven by a single DW. Critical thermal gradients depend on external parameters such as temperature, magnetic field and wire length, and can be experimentally obtained through the measurement of the mean velocity of the magnetization reversal as a function of the temperature gradient. Our results show that temperature gradients provide a high degree of control over DW propagation, which is of great importance for technological applications.

The Spatial Resolution Limit for an Individual Domain Wall in Magnetic Nanowires.

Magnetic nanowires are the foundation of several promising nonvolatile computing devices, most notably magnetic racetrack memory and domain wall logic. Here, we determine the analog information capacity in these technologies, analyzing a magnetic nanowire containing a single domain wall. Although wires can be deliberately patterned with notches to define discrete positions for domain walls, the line edge roughness of the wire can also trap domain walls at dimensions below the resolution of the fabrication process, determining the fundamental resolution limit for the placement of a domain wall. Using a fractal model for the edge roughness, we show theoretically and experimentally that the analog information capacity for wires is limited by the self-affine statistics of the wire edge roughness, a relevant result for domain wall devices scaled to regimes where edge roughness dominates the energy landscape in which the walls move.

Controlling the stability of both the structure and velocity of domain walls in magnetic nanowires

For magnetic nanowire devices, the precise control of both domain wall (DW) motion and pinning behaviour is essential for reliable functional performance. The domain wall velocity and wall structure are typically sensitive to the driving field or spin-polarized current, and the pinning behaviour depends on the walls' structure and chirality, leading to variability in behaviour. Here, a systematic study combining experimental measurements and micromagnetic simulations of planar nanowires with small fixed-angle structural modulations on both edges was undertaken to study the domain wall reversal regime. A phase diagram for the reversal field as a function of modulation amplitude was obtained that shows that three DW reversal regime. A range of field and modulation amplitudes were identified in which stable DW reversal occurs, where the wall velocity is constant as a function of field and the wall structure is stable, which is well suited to applications.

Electric-field-driven dynamics of magnetic domain walls in magnetic nanowires patterned on ferroelectric domains

Strong coupling of magnetic domain walls onto straight ferroelastic boundaries of a ferroelectric layer enables full and reversible electric-field control of magnetic domain wall motion. In this paper, the dynamics of this new driving mechanism is analyzed using micromagnetic simulations. We show that transverse domain walls with a near-180° spin structure are stabilized in magnetic nanowires and that electric fields can move these walls with high velocities. Above a critical velocity, which depends on material parameters, nanowire geometry and the direction of domain wall motion, the magnetic domain walls depin abruptly from the ferroelastic boundaries. Depinning evolves either smoothly or via the emission and annihilation of a vortex or antivortex core (Walker breakdown). In both cases, the magnetic domain wall slows down after depinning in an oscillatory fashion and eventually comes to a halt. The simulations provide design rules for hybrid ferromagnetic–ferroelectric domain-wall-based devices and indicate that material disorder and structural imperfections only influence Walker-breakdown-like depinning at high domain wall velocities.

Tunable short-wavelength spin wave excitation from pinned magnetic domain walls.

Miniaturization of magnonic devices for wave-like computing requires emission of short-wavelength spin waves, a key feature that cannot be achieved with microwave antennas. In this paper, we propose a tunable source of short-wavelength spin waves based on highly localized and strongly pinned magnetic domain walls in ferroelectric-ferromagnetic bilayers. When driven into oscillation by a microwave spin-polarized current, the magnetic domain walls emit spin waves with the same frequency as the excitation current. The amplitude of the emitted spin waves and the range of attainable excitation frequencies depend on the availability of domain wall resonance modes. In this respect, pinned domain walls in magnetic nanowires are particularly attractive. In this geometry, spin wave confinement perpendicular to the nanowire axis produces a multitude of domain wall resonances enabling efficient spin wave emission at frequencies up to 100 GHz and wavelengths down to 20 nm. At high frequency, the emission of spin waves in magnetic nanowires becomes monochromatic. Moreover, pinning of magnetic domain wall oscillators onto the same ferroelectric domain boundary in parallel nanowires guarantees good coherency between spin wave sources, which opens perspectives towards the realization of Mach-Zehnder type logic devices and sensors.

Fast current-induced motion of a transverse domain wall induced by interfacial Dzyaloshinskii–Moriya interaction

Based on a theoretical study, we show that the interfacial Dzyaloshinskii–Moriya interaction results in very efficient current-induced manipulation of a transverse domain wall in magnetic nanowires. The efficient domain wall motion is caused by combined effects of the domain wall distortion induced by the interfacial Dzyaloshinskii–Moriya interaction and the damping-like spin–orbit spin transfer torque. We find that with reasonable parameters, the domain wall velocity reaches a few hundreds m/s at the current density of 107 A/cm2, which has never been achieved before. Our result will be beneficial for low-power operation of domain wall devices.

Detection of current-driven magnetic domains in [Co/Pd] nanowire by tunneling magnetoresistive sensor

Current-driven magnetic domain walls in magnetic nanowires have attracted a great deal of interest in terms of both physical studies and engineering applications. The anomalous Hall effect measurement is widely used for detecting the magnetization direction of current-driven magnetic domains in a magnetic nanowire. However, the problem with this measurement is that the detection point for current-driven domain wall motion is fixed at only the installed sensing wire across the specimen nanowire. A potential solution is the magnetic domain scope method, whereby the distribution of the magnetic flux leaking from the specimen can be analyzed directly by contact-scanning a tunneling magnetoresistive field sensor on a sample. In this study, we fabricated specimen nanowires consisting of [Co (0.3)/Pd (1.2)]21/Ta(3) films (units in nm) with perpendicular magnetic anisotropy on Si substrates. A tunneling magnetoresistive sensor was placed on the nanowire surface and a predetermined current pulse was applied. Real-time detection of the current-driven magnetic domain motion was successful in that the resistance of the tunneling magnetoresistive sensor was changed with the magnetization direction beneath the sensor. This demonstrates that magnetic domain detection using a tunneling magnetoresistive sensor is effective for the direct analysis of micro magnetic domain motion.

Analysis of Three-Dimensional Magnetic Domain Wall Racetrack Memory

An overview of magnetic racetrack operation and components necessary to successfully realize this memory technology is presented. Fundamental physical concepts of adiabatic and non-adiabatic spin-torque transfer is presented and used to explain how bits of information are read, written, and pushed through ferromagnetic racetracks. Recent developments in the controlled movement of domain walls in magnetic nanowires by short pulses of spinpolarized current give promise of a nonvolatile memory device with the high performance and reliability of conventional solid-state memory but at the low cost of conventional magnetic disk drive storage. Resonant amplification of spin-torque transfer via pulsed current operation has been proposed to overcome issues with current density. The racetrack memory comprises an array of magnetic nanowires arranged horizontally or vertically on a silicon chip. Individual spintronics reading and writing nanodevices are used to modify or read a train of ~10 to 100 domain walls, which store a series of data bits in each nanowire. This racetrack memory is an example of the move toward innately three-dimensional microelectronic devices.

Chargeless spin current for switching and coupling of domain walls in magnetic nanowires

The demonstration of the generation and control of a pure spin current (without net charge flow) by electric fields and/or temperature gradient has been an essential leap in the quest for low-power consumption electronics. The key issue of whether and how such a current can be utilized to drive and control information stored in magnetic domain walls (DWs) is still outstanding and is addressed here. We demonstrate that pure spin current acts on DWs in a magnetic stripe with an effective spin-transfer torque resulting in a mutual DWs separation dynamics and picosecond magnetization reversal. In addition, long-range ($\sim$ mm) antiferromagnetic DWs coupling emerges. If one DW is pinned by geometric constriction, the spin current induces a dynamical spin orbital interaction that triggers an internal electric field determined by $\vec{E} \sim \hat{e}_{x} \cdot (\vec{n}_{1} \times \vec{n}_{2})$ where $\vec{n}_{1/2}$ are the effective DWs orientations and $\hat{e}_{x} $ is their spatial separation vector. This leads to charge accumulation or persistent electric current in the wire. As DWs are routinely realizable and tuneable, the predicted effects bear genuine potential for power-saving spintronics devices.

A numerical approach to incorporate intrinsic material defects in micromagnetic simulations

Spintronics devices like racetrack memory rely on the controlled movement of domain walls in magnetic nanowires. The effects of distributed disorder on this movement have not yet been studied extensively. Defects give rise to a pinning potential that can be characterized in terms of a depth and an interaction range. We investigate how the effects of defects can be realistically introduced in micromagnetic simulations by comparing the properties of the pinning potential to experimental results in the literature. We show that the full 3-dimensional simulations can be replaced by equivalent 2-dimensional ones and propose two approaches to include defects.

Fast Moving Multiple Magnetic Bits in Permalloy Cylindrical Nanowires

Controlling the movement of domain walls in magnetic nanowires is important due to the impact on the viability of data storage devices. A series of micromagnetic simulations of multiple current-induced domain walls motion (CIDWM) have been performed. Multiple CIDWM in the cylindrical permalloy nanowires display outstanding dynamic properties. In cases of different domain bits, we observed the motion of transverse domain walls (TDWs) did not show oscillatory behavior. The domain walls only changed their positions in the same direction as they propagated and kept the distance between the walls almost the same, with their internal magnetic structure unchanged. Furthermore, we have found that the TDW velocity in cylindrical thin wires was closely related to the wire thickness and showed a strong dependence on the Gilbert damping factor.

Instability of Walker Propagating Domain Wall in Magnetic Nanowires

The stability of the well-known Walker propagating domain wall (DW) solution of the Landau-Lifshitz-Gilbert equation is analytically investigated. Surprisingly, a propagating DW is always dressed with spin waves so that the Walker rigid-body propagating DW mode does not occur in reality. In the low field region only stern spin waves are emitted while both stern and bow waves are generated under high fields. In a high enough field, but below the Walker breakdown field, the Walker solution could be convective or absolute unstable if the transverse magnetic anisotropy is larger than a critical value, corresponding to a significant modification of the DW profile and DW propagating speed.

Three dimensional magnetic nanowires grown by focused electron-beam induced deposition

Control of the motion of domain walls in magnetic nanowires is at the heart of various recently proposed three-dimensional (3D) memory devices. However, fabricating 3D nanostructures is extremely complicated using standard lithography techniques. Here we show that highly pure 3D magnetic nanowires with aspect-ratios of ~100 can be grown using focused electron-beam-induced-deposition. By combining micromanipulation, Kerr magnetometry and magnetic force microscopy, we determine that the magnetisation reversal of the wires occurs via the nucleation and propagation of domain walls. In addition, we demonstrate that the magnetic switching of individual 3D nanostructures can be directly probed by magneto-optical Kerr effect.

Topological repulsion between domain walls in magnetic nanowires leading to the formation of bound states

Head-to-head and tail-to-tail magnetic domain walls in nanowires behave as free magnetic monopoles carrying a single magnetic charge. Since adjacent walls always carry opposite charges, they attract one another. In most cases this long-range attractive interaction leads to annihilation of the two domain walls. Here, we show that, in some cases, a short-range repulsive interaction suppresses annihilation of the walls, even though the lowest energy state is without any domain walls. This repulsive interaction is a consequence of topological edge defects that have the same winding number. We show that the competition between the attractive and repulsive interactions leads to the formation of metastable bound states made up of two or more domain walls. We have created bound states formed from up to eight domain walls, corresponding to the magnetization winding up over four complete 360° rotations.

Tunable Remote Pinning of Domain Walls in Magnetic Nanowires

Domain wall (DW) pinning in ferromagnetic nanowires is in general a complex process. Distortions of the DW shape make quantitative agreement between modeling and experiment difficult. Here we demonstrate pinning using nanometer scale localized stray fields. This type of interaction gives well-characterized, tailorable potential landscapes that do not appreciably distort the DW. Our experimental results are in excellent quantitative agreement with an Arrhenius-Néel model of depinning--a result only possible when the modeled potential profile agrees fully with that experienced by the DW.