Domain Walls In Nanowires Research Articles

Dynamic Bloch Chirality and Enhanced Velocities from Spin-Orbit Torque Driven Domain Wall Motion in Thick Magnetic Films

Spin-orbit torque (SOT) driven domain wall motion has attracted significant attention as the basis for a variety of spintronic devices due to its potential use as a high speed, low power means to manipulate the magnetic state of an object. While most previous attention has focused on ultrathin films wherein the material thickness is significantly less than the magnetic exchange length, recent reports have suggested unique dynamics may be achieved in intermediate and high thickness films. We used micromagnetic modelling to explore the role of the vertically non-uniform spin textures associated with the domain wall in nanowires of varying thickness on SOT driven domain wall motion. We found large velocity asymmetries between Bloch chiralities near the current density required for reversal of the Bloch component of the magnetization and linked these asymmetries to a gradual reorientation of the domain wall structure which drives a non-negligible, chiral Néel component of the domain wall. We further explored the influence of saturation magnetization, film thickness, the Dzyaloshinskii-Moriya interaction, and in-plane fields on domain wall dynamics. These results provide a framework for the development of SOT based devices based on domain wall motion in nanowires beyond the ultrathin film limit.

Analytical description of the topological interaction between magnetic domain walls in nanowires

Magnetic domain walls in nanowires behave as particles interacting through the exchange field. As topological objects, their interaction is determined by their chirality or topological charge. We investigate analytically the topological repulsion between magnetic domain walls with the same topological charge in nanostripes (with easy-plane magnetization) and show that it decays algebraically as ${r}^{\ensuremath{-}2}$, being part of a larger class of interactions that produce topological long-range order in two dimensions. We compare the topological repulsion between the walls with other types of fundamental interactions with exponential spatial decay, such as the Yukawa-Reid potential, and with micromagnetic simulations. We determine that trains of such walls can be well described analytically and can be displaced regularly in nanowires leading to practical applications.

Magnetic characterization of cobalt nanowires and square nanorings fabricated by focused electron beam induced deposition.

The magnetic properties of nanowires (NWs) and square nanorings, which were deposited by focused electron beam induced deposition (FEBID) of a Co carbonyl precursor, are studied using off-axis electron holography (EH), Lorentz transmission electron microscopy (L-TEM) and magnetic force microscopy (MFM). EH shows that NWs deposited using beam energies of 5 and 15 keV have the characteristics of magnetic dipoles, with larger magnetic moments observed for NWs deposited at lower energy. L-TEM is used to image magnetic domain walls in NWs and nanorings and their motion as a function of applied magnetic field. The NWs are found to have almost square hysteresis loops, with coercivities of ca. 10 mT. The nanorings show two different magnetization states: for low values of the applied in-plane field (0.02 T) a horseshoe state is observed using L-TEM, while for higher values of the applied in-plane field (0.3 T) an onion state is observed at remanence using L-TEM and MFM. Our results confirm the suitability of FEBID for nanofabrication of magnetic structures and demonstrate the versatility of TEM techniques for the study and manipulation of magnetic domain walls in nanostructures.

Chaotic dynamics of magnetic domain walls in nanowires

The nonlinear dynamics of a transverse domain wall (TDW) in Permalloy and Nickel nanostrips with two artificially patterned pinning centers is studied numerically up to rf frequencies. The phase diagram frequency - driving amplitude shows a rich variety of dynamical behaviors depending on the material parameters and the type and shape of pinning centers. We find that T-shaped traps (antinotches) create a classical double well Duffing potential that leads to a small chaotic region in the case of Nickel and a large one for Py. In contrast, the rectangular constrictions (notches) create an exponential potential that leads to larger chaotic regions interspersed with periodic windows for both Py and Ni. The influence of temperature manifests itself by enlarging the chaotic region and activating thermal jumps between the pinning sites while reducing the depinning field at low frequency in the notched strips.

Selection and Control of Individual Domain Walls in Nanowire Arrays via Asymmetric Depinning Fields

Artificially inscribed notches are often used to pin domain walls (DWs) in ferromagnetic nanowires. The process of selecting and moving the trapped DW in nanowire arrays is an important step for potential applications. The chirality of a DW leads to a pair of pinning positions at the inscribed notches, which can be modeled by a symmetric double well. The depinning field depends on the side of the well, the DW is trapped with respect to the applied field direction, and the DWs can also be transitioned between the two wells without depinning. We demonstrate how manipulating the double well improves the DW selectivity and control in wire arrays containing multiple DWs.

Analytic theory for the switch from Bloch to Néel domain wall in nanowires with perpendicular anisotropy

Rectangular nanowires may have domain walls nucleated and moved through them to realize many devices. It has been shown that at a particular width and thickness of a nanowire with perpendicular anisotropy, there is a switch from the domain wall being of Bloch-type to it being of N\'eel-type. This critical shape can be found through micromagnetics simulations, but here we present an analytic calculation for the energies of both wall types involving two iterations for the demagnetizing energy density. The expressions developed are long, but have the advantage that by simply inputting material parameters for the magnetic material, the critical shape can be found using a calculator in a matter of seconds. We compare our results to those found using micromagnetics and those found experimentally and the agreement is good.

Domain walls within domain walls in wide ferromagnetic strips

We carry out large-scale micromagnetic simulations which demonstrate that due to topological constraints, internal domain walls (Bloch lines) within extended domain walls are more robust than domain walls in nanowires. Thus, the possibility of spintronics applications based on their motion channeled along domain walls emerges. Internal domain walls are nucleated within domain walls in perpendicularly magnetized media concurrent with a Walker breakdown-like abrupt reduction of the domain wall velocity above a threshold driving force, and may also be generated within pinned, localized domain walls. We observe fast field and current driven internal domain wall dynamics without a Walker breakdown along pinned domain walls, originating from topological protection of the internal domain wall structure due to the surrounding out-of-plane domains.

Speed of field-driven domain walls in nanowires with large transverse magnetic anisotropy

Recent analytical and numerical work on field-driven domain wall propagation in nanowires and thin films has shown that for large transverse anisotropy and sufficiently large applied fields the Walker profile becomes unstable before the breakdown field, giving way to a domain wall whose speed increases at a slower rate with the applied field. We perform an asymptotic expansion of the Landau-Lifshitz-Gilbert equation for large transverse magnetic anisotropy and show that the asymptotic dynamics reproduces this behavior. The appearance of a different regime in the asymptotic dynamics is due to a transition from a pushed to a pulled front of a reaction diffusion equation in which the speed of the domain wall increases with the square root of the applied field

Thermal stability of a magnetic domain wall in nanowires

Thermal stability of a magnetic domain wall in nanowires

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.

X-Ray Imaging of Magnetic Structures

The characterization of nanoscale magnetic structures, their static properties, and fast spin dynamics with polarized soft X-rays has become an indispensable analytical tool due to the unique features of those probes. The spectroscopic magnetic response serves as a fingerprint of the specimen and can give quantitative information on element-specific spin and orbital magnetic moments. Images of magnetic domain structures at a spatial resolution down to nearly 10 nm, ultimately in all three dimensions, can be obtained with various X-ray microscopy techniques and can further be combined with stroboscopic pump-probe schemes to image the spin dynamics of spin structures, such as the motion of domain walls in nanowires or the vortex core dynamics in micropatterned magnetic elements. Next generation sources of polarized soft X-rays such as X-ray free electron lasers or high-harmonic generation laser sources hold the promise to provide nanometer spatial and femtosecond time resolution, enabling to address thus fundamental magnetic length and time scales in magnetism. This paper reviews the various X-ray imaging techniques using polarized soft X-rays by summarizing their characteristic features, recent achievements, and current limitations as well as future opportunities. A brief overview on other magnetic imaging techniques are given to set magnetic X-ray imaging techniques into context.

Analytical Modelling of Magnetic DW Motion

The main analytical model for describing the motion of magnetic domain walls is the 1-D model formulated based on the profile of a Bloch wall. This model qualitatively describes the motion of magnetic domain wall in nanowires, while it may fail to match experimental and numerical results quantitatively. In recent years, the 1-D model has been further generalized by the introduction of terms such as spin transfer torques and spin orbit torques. It has also been used to describe the motion of different domain walls, including vortex walls. It seems that in many such attempts, formalisms are not followed accurately and the main assumptions of the model (such as the Bloch wall profile used in developing the model) are underestimated. In this paper, we first derive an analytical model to describe the motion of a tilting Bloch wall in perpendicularly magnetized materials using four collective coordinates. We then compare the energy landscape predicted by this model to that of micromagnetic simulations, highlighting the possibility of using such comparisons to develop corrections for the 1-D model.

On the simulation of the Brownian motion of a domain wall in nanowires

A method has been proposed for computer simulation of thermal fluctuation motion of domain walls in polycrystalline ferromagnetic nanowires with allowance for their interaction with a field of magnetic inhomogeneities. The algorithm includes the stochastic Langevin function and takes into account the term describing the random force relief of the pinning of a domain wall at magnetic inhomogeneities. The proposed algorithm has been used to obtain different statistical characteristics of the process of displacement of the domain walls: distributions of magnetization jumps, activation energies, depinning waiting times, and jump times. It has been shown that the Einstein-Smoluchowski relation is not applicable to the description of thermal fluctuation motion of a particle in a random force relief.

Suppression of stochastic pinning in magnetic nanowire devices using “virtual” domain walls

We have investigated the pinning and depinning of “virtual” domain walls in planar magnetic nanowires. Such virtual walls are created when a conventional domain wall becomes annihilated at a narrow gap between two segments of a discontinuous nanowire. By using focused magneto-optical Kerr effect magnetometry to study the repeatability of their depinning, we show that virtual walls exhibit single-mode depinning distributions, characterized by remarkably low, sub-Oersted standard deviations. This is in stark contrast to the depinning of domain walls from conventional notch-shaped defects, which typically exhibit multi-mode depinning field distributions spanning tens to hundreds of Oersteds. High-resolution magnetic soft x-ray microscopy measurements are used to reveal that this high level of repeatability is the result of a simple mediated-nucleation process, which decouples the depinning mechanism from structure of the initially injected DWs. Our work serves as an example of how the complex and dynamical stochastic behaviors exhibited by domain walls in nanowires can be controlled.

Depinning probability of a magnetic domain wall in nanowires by spin-polarized currents

Current-induced magnetic domain wall motion is attractive for manipulating magnetization direction in spintronics devices, which open a new era of electronics. Up to now, in spite of a crucial significance to applications, investigation on a current-induced domain wall depinning probability, especially in sub-nano to a-few-nanosecond range has been lacking. Here we report on the probability of the depinning in perpendicularly magnetized Co/Ni nanowires in this timescale. A high depinning probability was obtained even for 2-ns pulses with a current density of less than 10¹² A m⁻². A one-dimensional Landau-Lifshitz-Gilbert calculation taking into account thermal fluctuations reproduces well the experimental results. We also calculate the depinning probability as functions of various parameters and found that parameters other than the coercive field do not affect the transition width of the probability. These findings will allow one to design high-speed and reliable magnetic devices based on the domain wall motion.

On the theory of the thermofluctuation motion of domain walls in nanowires

Using the Arrhenius law, the thermofluctuation motion of a domain wall in a nanowire in the field of energy barriers formed by magnetic nonuniformities is investigated. The expression for the density of the distribution of the activation energy in the case of the domain wall pinning at magnetic nonuniformities has been obtained. The velocity of the thermally activated motion of the domain wall for certain particular cases of the probabilistic distribution of the activation energy has been estimated.

Generation and annihilation of domain walls in nanowires by localized fields

We study the creation and annihilation of domain walls in a permalloy nanowire by local Oersted fields of current pulses passing through a perpendicularly aligned stripline. The occurrence of both processes is investigated for current pulses of different polarities and for various external magnetic fields. Reliable creation and annihilation are achieved for small and zero external fields, while higher externally applied fields lead to the suppression of both processes as well as to the creation of multiple domain walls in the wire.

Effects of notch shape on the magnetic domain wall motion in nanowires with in-plane or perpendicular magnetic anisotropy

Magnetic domain walls (DWs) in nanowires have been extensively investigated for potential applications in spintronic devices. For the precise storage of magnetic data, the control of DW pinning and depinning is critical. Here, we report upon the micromagnetic modeling results of the DW motion behaviors in notched or anti-notched nanowires possessing in-plane magnetic anisotropy (IMA) or perpendicular-to-the-plane magnetic anisotropy (PMA). In the nanowires with IMA, the energy of the DW in nanowires with anti-notches was lower compared to that of the nanowires with normal notches. Easier DW depinning motions were observed in the anti-notched nanowires. Unlike in the IMA case, the DW energy in the nanowires with PMA was lower with normal notches. Thus, the DW was able to move faster and easier through the normal notches compared to the anti-notches in the nanowire with the PMA at the same current density.

Effect of Non-polar Longitudinal Optical Phonons on Domain Wall Resistance in Diluted Magnetic Semiconductor Nanowires

In the present paper, the effect of non-polar longitudinal optical phonons on domain wall resistance has been studied using the semiclassical approach. The analysis has been based on the Boltzmann transport equation, within the relaxation time approximation. We have determined the magnetoresistance of domain wall in nanowires based on diluted magnetic semiconductors. The modulation of the exchange and the impurity interactions by lattice vibrations, and the hole–phonon interaction are considered. The results indicate that the scattering role of phonons becomes significant by increasing temperature, which leads to the resistivity enhancement. It is also found that the magnetic impurities play an impressive role in enhancing the contribution of the domain wall in the resistance. In providing room temperature spintronics devices, understanding the effects of phonons and magnetic impurities on the domain wall resistance is crucial.

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.