Dynamics of magnetic domain walls under their own inertia

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.

Ferroelectric domain-wall logic units

The electronic conductivities of ferroelectric domain walls have been extensively explored over the past decade for potential nanoelectronic applications. However, the realization of logic devices based on ferroelectric domain walls requires reliable and flexible control of the domain-wall configuration and conduction path. Here, we demonstrate electric-field-controlled stable and repeatable on-and-off switching of conductive domain walls within topologically confined vertex domains naturally formed in self-assembled ferroelectric nano-islands. Using a combination of piezoresponse force microscopy, conductive atomic force microscopy, and phase-field simulations, we show that on-off switching is accomplished through reversible transformations between charged and neutral domain walls via electric-field-controlled domain-wall reconfiguration. By analogy to logic processing, we propose programmable logic gates (such as NOT, OR, AND and their derivatives) and logic circuits (such as fan-out) based on reconfigurable conductive domain walls. Our work might provide a potentially viable platform for programmable all-electric logic based on a ferroelectric domain-wall network with low energy consumption.

Ferroelectric domain walls have been extensively explored for nanoelectronics, but the logic devices are still challenging. Here, the authors propose programmable logic gates and circuits based on electric-field controllable conductive domain walls.

Effect of Annealing Process on Microstructure and Magnetic Properties of FeSiBPCNbCu Nanocrystalline Soft Magnetic Powder Cores

In this work, the effect of the annealing process (heating rate (HR) and holding time (HT)) on microstructure and magnetic properties of FeSiBPCNbCu nanocrystalline soft magnetic powder cores (NPCs) are systematically studied. NPCs annealed under the HR of 100 K/min and HT of 30 min exhibit a finely uniform nanocrystalline structure with a concentrated grain size distribution and a small average grain size of 18.71 nm and show a modified magnetic domain structure where the domain walls move easily with the changes in the external magnetic field. The optimized microstructure leads to outstanding soft magnetic properties, including the low coercivity of 10.5 A/m (50 mT, 500 kHz), low core loss of 751 mW/cm3 (50 mT, 500 kHz), and highly effective permeability of 64.7 (100 kHz). We believe that the annealing process regulation can contribute to the industrial production of high-performance NPCs, which can meet the performance requirements of high-end electronic components such as molding chokes used in power supplies, mobile phones, and other terminal equipment.

The origin of spin wave pulse-induced domain wall inertia

The fundamental problem of domain wall (DW) inertia-the property that gives to inertial behaviors remains unclear in the physics of magnetic solitons. To understand its nature as well as to achieve accurate DW positioning and efficient manipulation of domain wall motion (DWM), spin wave (SW) pulse-induced DW transient effect is studied both numerically and theoretically in a magnetic nanostrip. It is shown for the first time that there occurs inevitable deceleration/automotion after SW pulse, which indicates nonzero DW inertia. The induced DWM is revealed to relate to two factors: energy storing within DW and out-of-plane tilting of DW. To explain the DWM dynamics, a one-dimensional collective model is developed to account for the excitation of spin wave pulse. The model successfully bridges DW energy, DW tilting and DW displacement and provides descriptions in accordance with numerical findings. It is made clear that the DW automotion hence DW inertia originate from the process of DW relaxation toward equilibrium. The DW inertia is expressed in terms of effective mass and turns out to be a time-dependent function with damping constantαas the governing parameter, which opposes the nature of intrinsic mass. For case containing multiple DWs, the total effective mass is shown to concern the reached velocity and stored energy of DWs instead of the number of DWs, which is against common intuition.

Electron Induced Massive Dynamics of Magnetic Domain Walls

We study the dynamics of domain walls (DWs) in a metallic, ferromagnetic nanowire, focusing on inertial effects on the DW due to interaction with a conduction electron bath. We develop a Keldysh collective coordinate technique to describe the effect of conduction electrons on rigid magnetic structures. The effective Lagrangian and Langevin equations of motion for a DW are derived microscopically, including the full response kernel which is nonlocal in time. The DW dynamics is described by two collective degrees of freedom: position and tilt-angle. The coupled Langevin equations therefore involve two correlated noise sources, leading to a generalized fluctuation-dissipation theorem (FDT). The DW response kernel due to electrons contains two parts: one related to dissipation via FDT, and another reactive part. We prove that the latter term leads to a mass for both degrees of freedom, even though the intrinsic bare mass is zero. The electron-induced mass is present even in a clean system without pinning or specifically engineered potentials. The resulting equations of motion contain rich dynamical solutions and point toward a way to control domain wall motion in metals via the electronic system properties. We discuss two observable consequences of the mass, hysteresis in the DW dynamics and resonant response to ac current.

Neuromorphic Spintronics

Neuromorphic computing uses basic principles inspired by the brain to design circuits that perform artificial intelligence tasks with superior energy efficiency. Traditional approaches have been limited by the energy area of artificial neurons and synapses realized with conventional electronic devices. In recent years, multiple groups have demonstrated that spintronic nanodevices, which exploit the magnetic as well as electrical properties of electrons, can increase the energy efficiency and decrease the area of these circuits. Among the variety of spintronic devices that have been used, magnetic tunnel junctions play a prominent role because of their established compatibility with standard integrated circuits and their multifunctionality. Magnetic tunnel junctions can serve as synapses, storing connection weights, functioning as local, nonvolatile digital memory or as continuously varying resistances. As nano-oscillators, they can serve as neurons, emulating the oscillatory behavior of sets of biological neurons. As superparamagnets, they can do so by emulating the random spiking of biological neurons. Magnetic textures like domain walls or skyrmions can be configured to function as neurons through their non-linear dynamics. Several implementations of neuromorphic computing with spintronic devices demonstrate their promise in this context. Used as variable resistance synapses, magnetic tunnel junctions perform pattern recognition in an associative memory. As oscillators, they perform spoken digit recognition in reservoir computing and when coupled together, classification of signals. As superparamagnets, they perform population coding and probabilistic computing. Simulations demonstrate that arrays of nanomagnets and films of skyrmions can operate as components of neuromorphic computers. While these examples show the unique promise of spintronics in this field, there are several challenges to scaling up, including the efficiency of coupling between devices and the relatively low ratio of maximum to minimum resistances in the individual devices.

Domain Wall Motion-Based Dual-Threshold Activation Unit for Low-Power Classification of Non-Linearly Separable Functions

Recently, a great deal of scientific endeavour has been devoted to developing spin-based neuromorphic platforms owing to the ultra-low-power benefits offered by spin devices and the inherent correspondence between spintronic phenomena and the desired neuronal, synaptic behavior. While domain wall motion-based threshold activation unit has previously been demonstrated for neuromorphic circuits, it remains well known that neurons with threshold activation cannot completely learn nonlinearly separable functions. This paper addresses this fundamental limitation by proposing a novel domain wall motion-based dual-threshold activation unit with additional nonlinearity in its function. Furthermore, a new learning algorithm is formulated for a neuron with this activation function. We perform 100 trials of tenfold training and testing of our neural networks on real-world datasets taken from the UCI machine learning repository. On an average, the proposed algorithm achieves [Formula: see text] lower misclassification rate (MCR) than the traditional perceptron learning algorithm. In a circuit-level simulation, the neural networks with the proposed activation unit are observed to outperform the perceptron networks by as much as [Formula: see text] MCR. The energy consumption of a neuron having the proposed domain wall motion-based activation unit averages to [Formula: see text] approximately.

Composite topological structure of domain walls in synthetic antiferromagnets

We experimentally study the structure and dynamics of magnetic domains in synthetic antiferromagnets based on Co/Ru/Co films. Dramatic effects arise from the interaction among the topological defects comprising the dual domain walls in these structures. Under applied magnetic fields, the dual domain walls propagate following the dynamics of bi-meronic (bi-vortex/bi-antivortex) topological defects built in the walls. Application of an external field triggers a rich dynamical response: The propagation depends on mutual orientation and chirality of bi-vortices and bi-antivortices in the domain walls. For certain configurations, we observe sudden jumps of composite domain walls in increasing field, which are associated with the decay of composite skyrmions. These features allow for the enhanced control of domain-wall motion in synthetic antiferromagnets with the potential of employing them as information carriers in future logic and storage devices.

Highly Asymmetric Chiral Domain-Wall Velocities in Y-Shaped Junctions

Recent developments in spin-orbit torques allow for highly efficient current-driven domain wall (DW) motion in nanowires with perpendicular magnetic anisotropy. Here, we show that chiral DWs can be driven into nonequilibrium states that can persist over tens of nanoseconds in Y-shaped magnetic nanowire junctions that have an input and two symmetric outputs. A single DW that is injected into the input splits and travels at very different velocities in the two output branches until it reaches its steady-state velocity. We find that this is due to the disparity between the fast temporal evolution of the spin current derived spin-orbit torque and a much-slower temporal evolution of the DMI-derived torque. Changing the DW polarity inverts the velocity asymmetry in the two output branches, a property that we use to demonstrate the sorting of domains.

Direct observation of the topological spin configurations mediated by the substitution of rare-earth element Y in MnNiGa alloy

The evolution of topological magnetic domains microscopically correlates the dynamic behavior of memory units in spintronic application. Nanometric bubbles with variation of spin configurations have been directly observed in a centrosymmetric hexagonal magnet (Mn_0.5Ni_0.5)₆₅(Ga_1-yY_y)₃₅ (y = 0.01) using Lorentz transmission electron microscopy. Magnetic bubbles instead of biskyrmions are generated due to the enhancement of quality factor Q caused by the substitution of rare-earth element Y. Furthermore, the bubble density and diversified spin configurations are systematically manipulated via combining the electric current with perpendicular magnetic fields. The magnetic bubble lattice at zero field is achieved after the optimized manipulation.

Current-induced instability of domain walls in cylindrical nanowires

We study the current-driven domain wall (DW) motion in cylindrical nanowires using micromagnetic simulations by implementing the Landau-Lifshitz-Gilbert equation with nonlocal spin-transfer torque in a finite difference micromagnetic package. We find that in the presence of DW, Gaussian wave packets (spin waves) will be generated when the charge current is suddenly applied to the system. This effect is excluded when using the local spin-transfer torque. The existence of spin waves emission indicates that transverse domain walls can not move arbitrarily fast in cylindrical nanowires although they are free from the Walker limit. We establish an upper velocity limit for DW motion by analyzing the stability of Gaussian wave packets using the local spin-transfer torque. Micromagnetic simulations show that the stable region obtained by using nonlocal spin-transfer torque is smaller than that by using its local counterpart. This limitation is essential for multiple DWs since the instability of Gaussian wave packets will break the structure of multiple DWs.

Inertia-driven resonant excitation of a magnetic skyrmion

Topological spin structures such as magnetic domain walls, vortices, and skyrmions, have been receiving great interest because of their high potential application in various spintronic devices. To utilize them in the future spintronic devices, it is first necessary to understand the dynamics of the topological spin structures. Since inertial effect plays a crucial role in the dynamics of a particle, understanding the inertial effect of topological spin structures is an important task. Here, we report that a strong inertial effect appears steadily when a skyrmion is driven by an oscillating spin-Hall-spin-torque (SHST). We find that the skyrmion exhibits an inertia-driven hypocycloid-type trajectory when it is excited by the oscillating SHST. This motion has not been achieved by an oscillating magnetic field, which only excites the breathing mode without the inertial effect. The distinct inertial effect can be explained in terms of a spin wave excitation in the skyrmion boundary which is induced by the non-uniform SHST. Furthermore, the inertia-driven resonant excitation provides a way of experimentally estimating the inertial mass of the skyrmion. Our results therefore pave the way for the development of skyrmion-based device applications.

Hybrid normal metal/ferromagnetic nanojunctions for domain wall tracking

Hybrid normal metal/ferromagnetic, gold/permalloy (Au/Py), nanojunctions are used to investigate magnetoresistance effects and track magnetization spatial distribution in L-shaped Py nanostructures. Transversal and longitudinal resistances are measured and compared for both straight and 90° corner sections of the Py nanostructure. Our results demonstrate that the absolute change in resistance is larger in the case of longitudinal measurements. However, due to the small background resistance, the relative change in the transversal resistance along the straight section is several orders of magnitude larger than the analogous longitudinal variation. These results prove that hybrid nanojunctions represent a significant improvement with respect to previously studied all-ferromagnetic crosses, as they also reduce the pinning potential at the junction and allow probing the magnetization locally. In addition, unusual metastable states with longitudinal domain walls along Py straight sections are observed. Micromagnetic simulations in combination with a magnetotransport model allow interpretation of the results and identification of the observed transitions.

Competition between Superconductor - Ferromagnetic stray magnetic fields in YBa2Cu3O7-x films pierced with Co nano-rods

Superconductivity and ferromagnetism are two antagonistic phenomena that combined can lead to a rich phenomenology of interactions, resulting in novel physical properties and unique functionalities. Here we propose an original hybrid system formed by a high-temperature superconducting film, patterned with antidots, and with ferromagnetic nano-rods grown inside them. This particular structure exhibits the synergic influence of superconductor (SC) - ferromagnetic (FM) stray fields, in both the superconducting behaviour of the film and the three-dimensional (3D) magnetic structure of nano-rods. We show that FM stray fields directly influence the critical current density of the superconducting film. Additional functionalities appear due to the interaction of SC stray fields, associated to supercurrent loops, with the non-trivial 3D remanent magnetic structure of FM nano-rods. This work unravels the importance of addressing quantitatively the effect of stray magnetic fields from both, the superconductor and the ferromagnet in hybrid magnetic nano-devices based on high temperature superconductors.

Noncentrosymmetric Magnets Hosting Magnetic Skyrmions

The concept of a skyrmion, which was first introduced by Tony Skyrme in the field of particle physics, has become widespread in condensed matter physics to describe various topological orders. Skyrmions in magnetic materials have recently received particular attention; they represent vortex-like spin structures with the character of nanometric particles and produce fascinating physical properties rooted in their topological nature. Here, a series of noncentrosymmetric ferromagnets hosting skyrmions is reviewed: B20 metals, Cu₂ OSeO₃ , Co-Zn-Mn alloys, and GaV₄ S₈ , where Dzyaloshinskii-Moriya interaction plays a key role in the stabilization of skyrmion spin texture. Their topological spin arrangements and consequent emergent electromagnetic fields give rise to striking features in transport and magnetoelectric properties in metals and insulators, such as the topological Hall effect, efficient electric-drive of skyrmions, and multiferroic behavior. Such electric controllability and nanometric particle natures highlight magnetic skyrmions as a potential information carrier for high-density magnetic storage devices with excellent energy efficiency.

Out-of-plane chiral domain wall spin-structures in ultrathin in-plane magnets

Chiral spin textures in ultrathin films, such as skyrmions or chiral domain walls, are believed to offer large performance advantages in the development of novel spintronics technologies. While in-plane magnetized films have been studied extensively as media for current- and field-driven domain wall dynamics with applications in memory or logic devices, the stabilization of chiral spin textures in in-plane magnetized films has remained rare. Here we report a phase of spin structures in an in-plane magnetized ultrathin film system where out-of-plane spin orientations within domain walls are stable. Moreover, while domain walls in in-plane films are generally expected to be non-chiral, we show that right-handed spin rotations are strongly favoured in this system, due to the presence of the interfacial Dzyaloshinskii–Moriya interaction. These results constitute a platform to explore unconventional spin dynamics and topological phenomena that may enable high-performance in-plane spin-orbitronics devices.

Chiral domain walls in magnetic films can be electrically controlled, which makes them attractive for applications, but domain walls in ultrathin films are normally non-chiral. Here, the authors observe chiral domain walls in ultrathin Fe/Ni bilayers that are stabilized by the magnetic anisotropy.

Inertial displacement of a domain wall excited by ultra-short circularly polarized laser pulses

Domain wall motion driven by ultra-short laser pulses is a pre-requisite for envisaged low-power spintronics combining storage of information in magnetoelectronic devices with high speed and long distance transmission of information encoded in circularly polarized light. Here we demonstrate the conversion of the circular polarization of incident femtosecond laser pulses into inertial displacement of a domain wall in a ferromagnetic semiconductor. In our study, we combine electrical measurements and magneto-optical imaging of the domain wall displacement with micromagnetic simulations. The optical spin-transfer torque acts over a picosecond recombination time of the spin-polarized photo-carriers that only leads to a deformation of the initial domain wall structure. We show that subsequent depinning and micrometre-distance displacement without an applied magnetic field or any other external stimuli can only occur due to the inertia of the domain wall.

Domain wall motion driven by ultra-short laser pulses has potential for storage of information in magnetoelectronic devices. Here the authors demonstrate the conversion of a circularly polarized femtosecond laser light into inertial displacement of a domain wall in a ferromagnetic semiconductor.

Emergence of Huge Negative Spin-Transfer Torque in Atomically Thin Co layers

Current-induced domain wall motion has drawn great attention in recent decades as the key operational principle of emerging magnetic memory devices. As the major driving force of the motion, the spin-orbit torque on chiral domain walls has been proposed and is currently extensively studied. However, we demonstrate here that there exists another driving force, which is larger than the spin-orbit torque in atomically thin Co films. Moreover, the direction of the present force is found to be the opposite of the prediction of the standard spin-transfer torque, resulting in the domain wall motion along the current direction. The symmetry of the force and its peculiar dependence on the domain wall structure suggest that the present force is, most likely, attributed to considerable enhancement of a negative nonadiabatic spin-transfer torque in ultranarrow domain walls. Careful measurements of the giant magnetoresistance manifest a negative spin polarization in the atomically thin Co films which might be responsible for the negative spin-transfer torque.

Anomalous spin-orbit torque switching due to field-like torque-assisted domain wall reflection

Spin-orbit torques (SOTs) allow the electrical control of magnetic states. Current-induced SOT switching of the perpendicular magnetization is of particular technological importance. The SOT consists of damping-like and field-like torques, and understanding the combined effects of these two torque components is required for efficient SOT switching. Previous quasi-static measurements have reported an increased switching probability with the width of current pulses, as predicted considering the damping-like torque alone. We report a decreased switching probability at longer pulse widths, based on time-resolved measurements. Micromagnetic analysis reveals that this anomalous SOT switching results from domain wall reflections at sample edges. The domain wall reflection was found to strongly depend on the field-like torque and its relative sign to the damping-like torque. Our result demonstrates a key role of the field-like torque in deterministic SOT switching and the importance of the sign correlation of the two torque components, which may shed light on the SOT switching mechanism.

Tunable inertia of chiral magnetic domain walls

The time it takes to accelerate an object from zero to a given velocity depends on the applied force and the environment. If the force ceases, it takes exactly the same time to completely decelerate. A magnetic domain wall is a topological object that has been observed to follow this behaviour. Here we show that acceleration and deceleration times of chiral Neel walls driven by current are different in a system with low damping and moderate Dzyaloshinskii–Moriya exchange constant. The time needed to accelerate a domain wall with current via the spin Hall torque is much faster than the time it needs to decelerate once the current is turned off. The deceleration time is defined by the Dzyaloshinskii–Moriya exchange constant whereas the acceleration time depends on the spin Hall torque, enabling tunable inertia of chiral domain walls. Such unique feature of chiral domain walls can be utilized to move and position domain walls with lower current, key to the development of storage class memory devices.

The controlled motion of magnetic domain walls in nanowire conduits forms the basis of emerging memory and information processing devices. Here, the authors report a pulse-length dependent quasi-static velocity of current-driven chiral domain walls, showing that their inertia is tunable.

Encoding Magnetic States in Monopole-Like Configurations Using Superconducting Dots

A large manifold of nontrivial spin textures, including the stabilization of monopole-like fields, are generated by using a completely new and versatile approach based on the combination of superconductivity and magnetism. Robust, stable, and easily controllable complex spin structures are encoded, modified, and annihilated in a continuous magnetic thin film by defining a variety of magnetic states in superconducting dots.

Dynamic scaling of ferromagnetic micro-rod clusters under a weak magnetic field

A controlled configurational change of micro-clusters in suspensions is essential for many smart material applications. In this paper, the dynamic process of ferromagnetic microrod clusters (FMRCs) under an external magnetic field was studied as a function of the cluster size N and the applied field B. The FMRCs rearranged from a side-by-side raft-like structure to an end-to-end chain-like structure, originating from coupled motions through the field-driven alignment of both ferromagnetic microrods and FMRCs. A theoretical model based on an extension of a zig-zag chain was developed, and both the cluster length and orientation could be characterized by a retardation time constant τ, with a relationship τ ∼ N²/B, which agrees well with the experimental results, τ ∼ N^2.2±0.2/B^0.8±0.1. Such a model can be used to predict other cluster dynamics or the magneto-elastic behavior of other soft matters consisting of FMRCs.

Ring-shaped Racetrack memory based on spin orbit torque driven chiral domain wall motions

Racetrack memory (RM) has sparked enormous interest thanks to its outstanding potential for low-power, high-density and high-speed data storage. However, since it requires bi-directional domain wall (DW) shifting process for outputting data, the mainstream stripe-shaped concept certainly suffers from the data overflow issue. This geometrical restriction leads to increasing complexity of peripheral circuits or programming as well as undesirable reliability issue. In this work, we propose and study ring-shaped RM, which is based on an alternative mechanism, spin orbit torque (SOT) driven chiral DW motions. Micromagnetic simulations have been carried out to validate its functionality and exhibit its performance advantages. The current flowing through the heavy metal instead of ferromagnetic layer realizes the "end to end" circulation of storage data, which remains all the data in the device even if they are shifted. It blazes a promising path for application of RM in practical memory and logic.

Spintronic Nanodevices for Bioinspired Computing

Bioinspired hardware holds the promise of low-energy, intelligent, and highly adaptable computing systems. Applications span from automatic classification for big data management, through unmanned vehicle control, to control for biomedical prosthesis. However, one of the major challenges of fabricating bioinspired hardware is building ultra-high-density networks out of complex processing units interlinked by tunable connections. Nanometer-scale devices exploiting spin electronics (or spintronics) can be a key technology in this context. In particular, magnetic tunnel junctions (MTJs) are well suited for this purpose because of their multiple tunable functionalities. One such functionality, non-volatile memory, can provide massive embedded memory in unconventional circuits, thus escaping the von-Neumann bottleneck arising when memory and processors are located separately. Other features of spintronic devices that could be beneficial for bioinspired computing include tunable fast nonlinear dynamics, controlled stochasticity, and the ability of single devices to change functions in different operating conditions. Large networks of interacting spintronic nanodevices can have their interactions tuned to induce complex dynamics such as synchronization, chaos, soliton diffusion, phase transitions, criticality, and convergence to multiple metastable states. A number of groups have recently proposed bioinspired architectures that include one or several types of spintronic nanodevices. In this paper, we show how spintronics can be used for bioinspired computing. We review the different approaches that have been proposed, the recent advances in this direction, and the challenges toward fully integrated spintronics complementary metal-oxide-semiconductor (CMOS) bioinspired hardware.

Creep turns linear in narrow ferromagnetic nanostrips

The motion of domain walls in magnetic materials is a typical example of a creep process, usually characterised by a stretched exponential velocity-force relation. By performing large-scale micromagnetic simulations, and analyzing an extended 1D model which takes the effects of finite temperatures and material defects into account, we show that this creep scaling law breaks down in sufficiently narrow ferromagnetic strips. Our analysis of current-driven transverse domain wall motion in disordered Permalloy nanostrips reveals instead a creep regime with a linear dependence of the domain wall velocity on the applied field or current density. This originates from the essentially point-like nature of domain walls moving in narrow, line- like disordered nanostrips. An analogous linear relation is found also by analyzing existing experimental data on field-driven domain wall motion in perpendicularly magnetised media.

Third type of domain wall in soft magnetic nanostrips

Magnetic domain walls (DWs) in nanostructures are low-dimensional objects that separate regions with uniform magnetisation. Since they can have different shapes and widths, DWs are an exciting playground for fundamental research, and became in the past years the subject of intense works, mainly focused on controlling, manipulating, and moving their internal magnetic configuration. In nanostrips with in-plane magnetisation, two DWs have been identified: in thin and narrow strips, transverse walls are energetically favored, while in thicker and wider strips vortex walls have lower energy. The associated phase diagram is now well established and often used to predict the low-energy magnetic configuration in a given magnetic nanostructure. However, besides the transverse and vortex walls, we find numerically that another type of wall exists in permalloy nanostrips. This third type of DW is characterised by a three-dimensional, flux closure micromagnetic structure with an unusual length and three internal degrees of freedom. Magnetic imaging on lithographically-patterned permalloy nanostrips confirms these predictions and shows that these DWs can be moved with an external magnetic field of about 1 mT. An extended phase diagram describing the regions of stability of all known types of DWs in permalloy nanostrips is provided.

A soft/hard magnetic nanostructure based on multisegmented CoNi nanowires

In this paper we have introduced a new soft/hard nanostructure based on multisegmented CoNi nanowire arrays having diameters of around 110 nm and made of five segments with nominal compositions of Co, Co66Ni33, Co50Ni50, Co33Ni66 and Ni, each of which has a length of 800 nm, so that the total length of the multisegmented nanowire is 4 μm. These arrays have been synthesized by means of potentiostatic electrodeposition into the pores of hard-anodic alumina templates. The morphology, chemical composition and microstructure of the multisegmented CoNi nanowires were determined by high-resolution scanning electron microscopy, energy dispersive X-ray microanalysis, and powder X-ray diffraction method, respectively. The room temperature magnetic behavior of the multisegmented nanowire arrays is also studied and compared with CoNi nanowire arrays with homogeneous composition (non-segmented nanowires), synthesized in the same templates and having the same dimensions as the segmented ones. These nanostructures could be used to control the movement of magnetic domain walls. In this way, these nanostructures can be an alternative to store information or even perform logic functions.

Controlling domain wall motion in ferroelectric thin films

Domain walls in ferroic materials have attracted significant interest in recent years, in particular because of the unique properties that can be found in their vicinity. However, to fully harness their potential as nanoscale functional entities, it is essential to achieve reliable and precise control of their nucleation, location, number and velocity. Here, using piezoresponse force microscopy, we show the control and manipulation of domain walls in ferroelectric thin films of Pb(Zr,Ti)O₃ with Pt top electrodes. This high-level control presents an excellent opportunity to demonstrate the versatility and flexibility of ferroelectric domain walls. Their position can be controlled by the tuning of voltage pulses, and multiple domain walls can be nucleated and handled in a reproducible fashion. The system is accurately described by analogy to the classical Stefan problem, which has been used previously to describe many diverse systems and is here applied to electric circuits. This study is a step towards the realization of domain wall nanoelectronics utilizing ferroelectric thin films.

Gilbert damping in noncollinear ferromagnets

The precession and damping of a collinear magnetization displaced from its equilibrium are well described by the Landau-Lifshitz-Gilbert equation. The theoretical and experimental complexity of noncollinear magnetizations is such that it is not known how the damping is modified by the noncollinearity. We use first-principles scattering theory to investigate transverse domain walls (DWs) of the important ferromagnetic alloy Ni80Fe20 and show that the damping depends not only on the magnetization texture but also on the specific dynamic modes of Bloch and Néel DWs in ways that were not theoretically predicted. Even in the highly disordered Ni80Fe20 alloy, the damping is found to be remarkably nonlocal.

Magnetic damping: domain wall dynamics versus local ferromagnetic resonance

Magnetic relaxation is one of the dominating features of magnetization dynamics. Depending on the magnetic structure and the experimental approach, different magnitudes of the damping parameter are reported even for a given material. In this study, we experimentally address this issue by accessing the damping parameter in the same magnetic nanotracks using different approaches: local ferromagnetic resonance (α=0.0072) and field-driven domain wall dynamics (α=0.023). The experimental results cannot fully be accounted for by modeling only roughness in micromagnetic simulations. Consequently, we have included nonlocal texture induced damping to the micromagnetic code. We find excellent agreement with the observed increased damping in the vortex structures for the same input Gilbert alpha when texture-induced nonlocal damping is included.

Correlation between spin structure oscillations and domain wall velocities

Magnetic sensing and logic devices based on the motion of magnetic domain walls rely on the precise and deterministic control of the position and the velocity of individual magnetic domain walls in curved nanowires. Varying domain wall velocities have been predicted to result from intrinsic effects such as oscillating domain wall spin structure transformations and extrinsic pinning due to imperfections. Here we use direct dynamic imaging of the nanoscale spin structure that allows us for the first time to directly check these predictions. We find a new regime of oscillating domain wall motion even below the Walker breakdown correlated with periodic spin structure changes. We show that the extrinsic pinning from imperfections in the nanowire only affects slow domain walls and we identify the magnetostatic energy, which scales with the domain wall velocity, as the energy reservoir for the domain wall to overcome the local pinning potential landscape.

Magnetic properties of cylindrical diameter modulated Ni80Fe20 nanowires: interaction and coercive fields

Magnetic properties of cylindrical Ni80Fe20 nanowires with modulated diameters are investigated theoretically as a function of their geometrical parameters and compared with those produced inside the pores of anodic alumina membranes by pulsed electrodeposition. We observe that the Ni80Fe20 nanowires with modulated diameters reverse their magnetization via the nucleation and propagation of a vortex domain wall. The system begins generating vortex domains in the nanowire ends and in the transition region between the two segments to minimize magnetostatic energy generated by surfaces perpendicular to the initial magnetization of the sample. Besides, we observed an increase of the coercivity for the sample with equal volumes in relation to the sample with equal lengths. Finally, the interaction field is stronger in the case of constant volume segments. These structures could be used to control the motions of magnetic domain walls. In this way, these nanowires with modulated diameters can be an alternative to store information or even perform logic functions.

Spin-orbit-coupling-induced domain-wall resistance in diffusive ferromagnets

We investigate diffusive transport through a number of domain wall (DW) profiles of the important magnetic alloy Permalloy taking into account simultaneously noncollinearity, alloy disorder, and spin-orbit-coupling fully quantum mechanically, from first principles. In addition to observing the known effects of magnetization mistracking and anisotropic magnetoresistance, we discover a not-previously identified contribution to the resistance of a DW that comes from spin-orbit-coupling-mediated spin-flip scattering in a textured diffusive ferromagnet. This adiabatic DW resistance, which should exist in all diffusive DWs, can be observed by varying the DW width in a systematic fashion in suitably designed nanowires.

Macroscopic magnetic frustration

Although geometrical frustration transcends scale, it has primarily been evoked in the micro- and mesoscopic realm to characterize such phases as spin ice, liquids, and glasses and to explain the behavior of such materials as multiferroics, high-temperature superconductors, colloids, and copolymers. Here we introduce a system of macroscopic ferromagnetic rotors arranged in a planar lattice capable of out-of-plane movement that exhibit the characteristic honeycomb spin ice rules studied and seen so far only in its mesoscopic manifestation. We find that a polarized initial state of this system settles into the honeycomb spin ice phase with relaxation on multiple time scales. We explain this relaxation process using a minimal classical mechanical model that includes Coulombic interactions between magnetic charges located at the ends of the magnets and viscous dissipation at the hinges. Our study shows how macroscopic frustration arises in a purely classical setting that is amenable to experiment, easy manipulation, theory, and computation, and shows phenomena that are not visible in their microscopic counterparts.

Influence of the magnetoelastic anisotropy on the domain wall dynamics in bistable amorphous wires

We deal with the influence of the applied stress on the domain wall velocity in glass-coated magnetic microwires. In general, the domain wall velocity decreases with the applied tensile stress. Four regimes of the domain wall dynamics appear: (1) diffusion-damped, (2) a regime with variable domain wall width, (3) a viscous and (4) a vortex regime. Detailed analysis of domain wall parameters shows that the structural relaxation plays an important role even at ambient temperatures if high tensile stress is present. At higher fields (viscous regime), the most important damping arises from magnetic relaxation of magnetic moments. Finally, the domain wall velocity steeply increases (reaching a maximum at 7000 m s(-1)) in the vortex regime and so does the domain wall mobility.

Domain-wall dynamics in translationally nonivariant nanowires: theory and applications

We generalize domain-wall dynamics to the case of translationally noninvariant ferromagnetic nanowires. The obtained equations of motion make the description of the domain-wall propagation more realistic by accounting for the variations along the wire, such as disorder or change in the wire shape. We show that the effective equations of motion are very general and do not depend on the model details. As an example of their use, we consider an hourglass-shaped nanostrip in detail. A transverse domain wall is trapped in the middle and has two stable magnetization directions. We study the switching between the two directions by short current pulses. We obtain the exact time dependence of the current pulses required to switch the magnetization with the minimal Ohmic losses per switching. Furthermore, we find how the Ohmic losses per switching depend on the switching time for the optimal current pulse. As a result, we show that as a magnetic memory device this nanodevice may be 10(5) times more energy efficient than the best modern devices.

Direct observation of massless domain wall dynamics in nanostripes with perpendicular magnetic anisotropy

Domain wall motion induced by nanosecond current pulses in nanostripes with perpendicular magnetic anisotropy (Pt/Co/AlO(x)) is shown to exhibit negligible inertia. Time-resolved magnetic microscopy during current pulses reveals that the domain walls start moving, with a constant speed, as soon as the current reaches a constant amplitude, and no or little motion takes place after the end of the pulse. The very low "mass" of these domain walls is attributed to the combination of their narrow width and high damping parameter α. Such a small inertia should allow accurate control of domain wall motion by tuning the duration and amplitude of the current pulses.

Dynamic oscillations of coupled domain walls

In domain wall (DW) excitation experiments, nonlinearity (NL) intrinsic to the DW dynamics is often hard to distinguish from perturbation due to the confining potential or DW distortion. Here we numerically investigate the dynamic oscillations of magnetostatically coupled DWs: a system well understood in the quasistatic limit. NL is observed, even for a harmonic potential, due to the intrinsic DW motion. This behavior is principally dependent on terms normally associated with the DW canonical momentum and is in contrast with a NL restoring potential. This NL is not observable in quasistatic measurements, relatively insensitive to the confining potential, and may be tuned by the nanowire parameters. The shown NLs are present in any DW restoring potential and must be accounted for when probing DW potential landscapes.

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.

Nanowire spintronics for storage class memories and logic

Patterned magnetic nanowires are extremely well suited for data storage and logic devices. They offer non-volatile storage, fast switching times, efficient operation and a bistable magnetic configuration that are convenient for representing digital information. Key to this is the high level of control that is possible over the position and behaviour of domain walls (DWs) in magnetic nanowires. Magnetic random access memory based on the propagation of DWs in nanowires has been released commercially, while more dynamic shift register memory and logic circuits have been demonstrated. Here, we discuss the present standing of this technology as well as reviewing some of the basic DW effects that have been observed and the underlying physics of DW motion. We also discuss the future direction of magnetic nanowire technology to look at possible developments, hurdles to overcome and what nanowire devices may appear in the future, both in classical information technology and beyond into quantum computation and biology.

Origin and tailoring of the antiferromagnetic domain structure in α-Fe2O3 thin films unraveled by statistical analysis of dichroic spectromicroscopy (x-ray photoemission electron microscopy) images

The magnetic microstructure and domain wall distribution of antiferromagnetic α-Fe2O3 epitaxial layers is determined by statistical image analyses. Using dichroic spectromicroscopy images, we demonstrate that the domain structure is statistically invariant with thickness and that the antiferromagnetic domain structure of the thin films is inherited from the ferrimagnetic precursor layer one, even after complete transformation into antiferromagnetic α-Fe2O3. We show that modifying the magnetic domain structure of the precursor layer is a genuine way to tune the magnetic domain structure and domain walls of the antiferromagnetic layers.

Discrete domain wall positioning due to pinning in current driven motion along nanowires

Racetrack memory is a novel storage-class memory device in which a series of domain walls (DWs), representing zeros and ones, are shifted to and fro by current pulses along magnetic nanowires. Here we show, by precise measurements of the DW's position using spin-valve nanowires, that these positions take up discrete values. This results from DW relaxation after the end of the current pulse into local energy minima, likely derived from imperfections in the nanowire.