Influence of current on field-driven domain wall motion in permalloy nanowires from time resolved measurements of anisotropic magnetoresistance

Observation of topological Hall torque exerted on a domain wall in the ferromagnetic oxide SrRuO3

In a ferromagnetic Weyl metal SrRuO₃, a large effective magnetic field H_eff exerted on a magnetic domain wall (DW) by current has been reported. We show that the ratio of H_eff to current density exhibits nonmonotonic temperature dependence and surpasses those of conventional spin-transfer torques and spin-orbit torques. This enhancement is described well by topological Hall torque (THT), which is exerted on a DW by Weyl electrons emerging around Weyl points when an electric field is applied across the DW. The ratio of the H_eff arising from the THT to current density is over one order of magnitude higher than that originating from spin-transfer torques and spin-orbit torques reported in metallic systems, showing that the THT may provide a better way for energy-efficient manipulation of magnetization in spintronics devices.

Quantification of Competing Magnetic States and Switching Pathways in Curved Nanowires by Direct Dynamic Imaging

For viable applications, spintronic devices based, for example, on domain wall motion need to be highly reliable with stable magnetization states and highly reproducible switching pathways transforming one state to another. The existence of multiple stable states and switching pathways in a system is a definitive barrier for device operation, yet rare and stochastic events are difficult to detect and understand. We demonstrate an approach to quantify competing magnetic states and stochastic switching pathways based on time-resolved scanning electron microscopy with polarization analysis, applied to the technologically relevant control of vortex domain wall chirality via field and curvature in curved wires. As a pump-probe technique, our analysis scheme nonetheless allows for the disentanglement of different occurring dynamic pathways, and we can even identify the rare events leading to changes from one magnetization switching pathway to another pathway via temperature- and geometry-dependent measurements. The experimental imaging is supported by micromagnetic simulations to reveal the mechanisms responsible for the change of the pathway. Together the results allow us to explain the origin and details of the domain wall chirality control and to quantify the frequency and the associated energy barriers of thermally activated changes of the states and switching pathways.

Nonvolatile Multistates Memories for High-Density Data Storage

In the current information age, the realization of memory devices with energy efficient design, high storage density, nonvolatility, fast access, and low cost is still a great challenge. As a promising technology to meet these stringent requirements, nonvolatile multistates memory (NMSM) has attracted lots of attention over the past years. Owing to the capability to store data in more than a single bit (0 or 1), the storage density is dramatically enhanced without scaling down the memory cell, making memory devices more efficient and less expensive. Multistates in a single cell also provide an unconventional in-memory computing platform beyond the Von Neumann architecture and enable neuromorphic computing with low power consumption. In this review, an in-depth perspective is presented on the recent progress and challenges on the device architectures, material innovation, working mechanisms of various types of NMSMs, including flash, magnetic random-access memory (MRAM), resistive random-access memory (RRAM), ferroelectric random-access memory (FeRAM), and phase-change memory (PCM). The intriguing properties and performance of these NMSMs, which are the key to realizing highly integrated memory hierarchy, are discussed and compared.

Thermal gradient driven domain wall dynamics

The issue of whether a thermal gradient acts like a magnetic field or an electric current in the domain wall (DW) dynamics is investigated. Broadly speaking, magnetization control knobs can be classified as energy-driving or angular-momentum driving forces. DW propagation driven by a static magnetic field is the best known example of the former in which the DW speed is proportional to the energy dissipation rate, and the current-driven DW motion is an example of the latter. Here we show that DW propagation speed driven by a thermal gradient can be fully explained as the angular momentum transfer between thermally generated spin current and DW. We found DW-plane rotation speed increases as DW width decreases. Both DW propagation speed along the wire and DW-plane rotation speed around the wire decrease with the Gilbert damping. These facts are consistent with the angular momentum transfer mechanism, but are distinct from the energy dissipation mechanism. We further show that magnonic spin-transfer torque (STT) generated by a thermal gradient has both damping-like and field-like components. By analyzing DW propagation speed and DW-plane rotational speed, the coefficient ([Formula: see text]) of the field-like STT arising from the non-adiabatic process, is obtained. It is found that [Formula: see text] does not depend on the thermal gradient; increases with uniaxial anisotropy [Formula: see text] (thinner DW); and decreases with the damping, in agreement with the physical picture that a larger damping or a thicker DW leads to a better alignment between the spin-current polarization and the local magnetization, or a better adiabaticity.

Engineering Planar Transverse Domain Walls in Biaxial Magnetic Nanostrips by Tailoring Transverse Magnetic Fields with Uniform Orientation

Designing and realizing various magnetization textures in magnetic nanostructures are essential for developing novel magnetic nanodevices in the modern information industry. Among all these textures, planar transverse domain walls (pTDWs) are the simplest and the most basic, which make them popular in device physics. In this work, we report the engineering of pTDWs with arbitrary tilting attitude in biaxial magnetic nanostrips by transverse magnetic field profiles with uniform orientation but tuneable strength distribution. Both statics and axial-field-driven dynamics of these pTDWs are analytically investigated. It turns out that, for statics, these pTDWs are robust against disturbances which are not too abrupt, while for dynamics, it can be tailored to acquire higher velocity than Walker's ansatz predicts. These results should provide inspiration for designing magnetic nanodevices with novel one-dimensional magnetization textures, such as 360 ∘ walls, or even two-dimensional ones, such as vortices and skyrmions.

Spin-wave duplexer studied by finite-element micromagnetic simulation

We conceptually designed a robust nano-scale waveguide structure suitable for potential use as a spin-wave duplexer that allows signal propagation only of selected narrow-band frequencies and duplex transmission in a three-port device comprising a receiver, a transmitter, and their common antenna. The waveguide structure combines three different arms and a circular ring, both made of nanostrip waveguides and a single magnetic material for reliably controllable propagations of spin waves. We attribute the observed duplex transmission of spin waves of narrow pass bands to scattering of spin waves by edge solitons placed at contact areas between the arms and the circular ring. This work proposes the first concept of nano-scale magnonic duplexers operating beyond GHz-frequency ranges.

Efficient and controlled domain wall nucleation for magnetic shift registers

Ultrathin ferromagnetic strips with high perpendicular anisotropy have been proposed for the development of memory devices where the information is coded in tiny domains separated by domain walls. The design of practical devices requires creating, manipulating and detecting domain walls in ferromagnetic strips. Recent observations have shown highly efficient current-driven domain wall dynamics in multilayers lacking structural symmetry, where the walls adopt a chiral structure and can be driven at high velocities. However, putting such a device into practice requires the continuous and synchronous injection of domain walls as the first step. Here, we propose and demonstrate an efficient and simple scheme for nucleating domain walls using the symmetry of the spin orbit torques. Trains of short sub-nanosecond current pulses are injected in a double bit line to generate a localized longitudinal Oersted field in the ferromagnetic strip. Simultaneously, other current pulses are injected through the heavy metal under the ferromagnetic strip. Notably, the Slonczewski-like spin orbit torque assisted by the Oersted field allows the controlled injection of a series of domain walls, giving rise to a controlled manner for writing binary information and, consequently, to the design of a simple and efficient domain wall shift register.

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.

Geometrical control of pure spin current induced domain wall depinning

We investigate the pure spin-current assisted depinning of magnetic domain walls in half ring based Py/Al lateral spin valve structures. Our optimized geometry incorporating a patterned notch in the detector electrode, directly below the Al spin conduit, provides a tailored pinning potential for a transverse domain wall and allows for a precise control over the magnetization configuration and as a result the domain wall pinning. Due to the patterned notch, we are able to study the depinning field as a function of the applied external field for certain applied current densities and observe a clear asymmetry for the two opposite field directions. Micromagnetic simulations show that this can be explained by the asymmetry of the pinning potential. By direct comparison of the calculated efficiencies for different external field and spin current directions, we are able to disentangle the different contributions from the spin transfer torque, Joule heating and the Oersted field. The observed high efficiency of the pure spin current induced spin transfer torque allows for a complete depinning of the domain wall at zero external field for a charge current density of [Formula: see text] A m^-2, which is attributed to the optimal control of the position of the domain wall.

General planar transverse domain walls realized by optimized transverse magnetic field pulses in magnetic biaxial nanowires

The statics and field-driven dynamics of transverse domain walls (TDWs) in magnetic nanowires (NWs) have attracted continuous interests because of their theoretical significance and application potential in future magnetic logic and memory devices. Recent results demonstrate that uniform transverse magnetic fields (TMFs) can greatly enhance the wall velocity, meantime leave a twisting in the TDW azimuthal distribution. For application in high-density NW devices, it is preferable to erase the twisting so as to minimize magnetization frustrations. Here we report the realization of a completely planar TDW with arbitrary tilting attitude in a magnetic biaxial NW under a TMF pulse with fixed strength and well-designed orientation profile. We smooth any twisting in the TDW azimuthal plane thus completely decouple the polar and azimuthal degrees of freedom. The analytical differential equation describing the polar angle distribution is derived and the resulting solution is not the Walker-ansatz form. With this TMF pulse comoving, the field-driven dynamics of the planar TDW is investigated with the help of the asymptotic expansion method. It turns out the comoving TMF pulse increases the wall velocity under the same axial driving field. These results will help to design a series of modern magnetic devices based on planar TDWs.

Highly Efficient Domain Walls Injection in Perpendicular Magnetic Anisotropy Nanowire

Electrical injection of magnetic domain walls in perpendicular magnetic anisotropy nanowire is crucial for data bit writing in domain wall-based magnetic memory and logic devices. Conventionally, the current pulse required to nucleate a domain wall is approximately ~10¹² A/m². Here, we demonstrate an energy efficient structure to inject domain walls. Under an applied electric potential, our proposed Π-shaped stripline generates a highly concentrated current distribution. This creates a highly localized magnetic field that quickly initiates the nucleation of a magnetic domain. The formation and motion of the resulting domain walls can then be electrically detected by means of Ta Hall bars across the nanowire. Our measurements show that the Π-shaped stripline can deterministically write a magnetic data bit in 15 ns even with a relatively low current density of 5.34 × 10¹¹ A/m². Micromagnetic simulations reveal the evolution of the domain nucleation – first, by the formation of a pair of magnetic bubbles, then followed by their rapid expansion into a single domain. Finally, we also demonstrate experimentally that our injection geometry can perform bit writing using only about 30% of the electrical energy as compared to a conventional injection line.

Field-driven domain wall motion under a bias current in the creep and flow regimes in Pt/[CoSiB/Pt]N nanowires

The dynamics of magnetic domain wall (DW) in perpendicular magnetic anisotropy Pt/[CoSiB/Pt]N nanowires was studied by measuring the DW velocity under a magnetic field (H) and an electric current (J) in two extreme regimes of DW creep and flow. Two important findings are addressed. One is that the field-driven DW velocity increases with increasing N in the flow regime, whereas the trend is inverted in the creep regime. The other is that the sign of spin current-induced effective field is gradually reversed with increasing N in both DW creep and flow regimes. To reveal the underlying mechanism of new findings, we performed further experiment and micromagnetic simulation, from which we found that the observed phenomena can be explained by the combined effect of the DW anisotropy, Dzyaloshinskii-Moriya interaction, spin-Hall effect, and spin-transfer torques. Our results shed light on the mechanism of DW dynamics in novel amorphous PMA nanowires, so that this work may open a path to utilize the amorphous PMA in emerging DW-based spintronic devices.

Indirect localization of a magnetic domain wall mediated by quasi walls

The manipulation of magnetic domain walls in thin films and nanostructures opens new opportunities for fundamental and applied research. But controlling reliably the position of a moving domain wall still remains challenging. So far, most of the studies aimed at understanding the physics of pinning and depinning processes in the magnetic layer in which the wall moves (active layer). In these studies, the role of other magnetic layers in the stack has been often ignored. Here, we report an indirect localization process of 180° domain walls that occurs in magnetic tunnel junctions, commonly used in spintronics. Combining Scanning Transmission X-Ray Microscopy and micromagnetic simulations, magnetic configurations in both layers are resolved. When nucleating a 180° domain wall in the active layer, a quasi wall is created in the reference layer, atop the wall. The wall and its quasi wall must then be moved or positioned together, as a unique object. As a mutual effect, a localized change of the magnetic properties in the reference layer induces a localized quasi wall in the active layer. The two types of quasi walls are shown to be responsible for an indirect localization process of the 180° domain wall in the active layer.

Highly efficient in-line magnetic domain wall injector

We demonstrate a highly efficient and simple scheme for injecting domain walls into magnetic nanowires. The spin transfer torque from nanosecond long, unipolar, current pulses that cross a 90° magnetization boundary together with the fringing magnetic fields inherently prevalent at the boundary, allow for the injection of single or a continual stream of domain walls. Remarkably, the currents needed for this "in-line" domain wall injection scheme are at least one hundred times smaller than conventional methods.

Synchronous precessional motion of multiple domain walls in a ferromagnetic nanowire by perpendicular field pulses

Magnetic storage and logic devices based on magnetic domain wall motion rely on the precise and synchronous displacement of multiple domain walls. The conventional approach using magnetic fields does not allow for the synchronous motion of multiple domains. As an alternative method, synchronous current-induced domain wall motion was studied, but the required high-current densities prevent widespread use in devices. Here we demonstrate a radically different approach: we use out-of-plane magnetic field pulses to move in-plane domains, thus combining field-induced magnetization dynamics with the ability to move neighbouring domain walls in the same direction. Micromagnetic simulations suggest that synchronous permanent displacement of multiple magnetic walls can be achieved by using transverse domain walls with identical chirality combined with regular pinning sites and an asymmetric pulse. By performing scanning transmission X-ray microscopy, we are able to experimentally demonstrate in-plane magnetized domain wall motion due to out-of-plane magnetic field pulses.

Magnetic domain walls could form the basis for information technology with high storage density, but require comparatively high current densities to be moved by spin torque. Here, the authors demonstrate a radically different approach with perpendicular magnetic field pulses moving domain walls synchronously.

Ferroelectric domain wall injection

Ferroelectric domain wall injection has been demonstrated by engineering of the local electric field, using focused ion beam milled defects in thin single crystal lamellae of KTiOPO4 (KTP). The electric field distribution (top) displays localized field hot-spots, which correlate with nucleation events (bottom). Designed local field variations can also dictate subsequent domain wall mobility, demonstrating a new paradigm in ferroelectric domain wall control.

Discontinuous properties of current-induced magnetic domain wall depinning

The current-induced motion of magnetic domain walls (DWs) confined to nanostructures is of great interest for fundamental studies as well as for technological applications in spintronic devices. Here, we present magnetic images showing the depinning properties of pulse-current-driven domain walls in well-shaped Permalloy nanowires obtained using photoemission electron microscopy combined with x-ray magnetic circular dichroism. In the vicinity of the threshold current density (J_th = 4.2 × 10¹¹ A.m⁻²) for the DW motion, discontinuous DW depinning and motion have been observed as a sequence of “Barkhausen jumps”. A one-dimensional analytical model with a piecewise parabolic pinning potential has been introduced to reproduce the DW hopping between two nearest neighbour sites, which reveals the dynamical nature of the current-driven DW motion in the depinning regime.

High domain wall velocities via spin transfer torque using vertical current injection

Domain walls, nanoscale transition regions separating oppositely oriented ferromagnetic domains, have significant promise for use in spintronic devices for data storage and memristive applications. The state of these devices is related to the wall position and thus rapid operation will require a controllable onset of domain wall motion and high speed wall displacement. These processes are traditionally driven by spin transfer torque due to lateral injection of spin polarized current through a ferromagnetic nanostrip. However, this geometry is often hampered by low maximum wall velocities and/or a need for prohibitively high current densities. Here, using time-resolved magnetotransport measurements, we show that vertical injection of spin currents through a magnetic tunnel junction can drive domain walls over hundreds of nanometers at ~500 m/s using current densities on the order of 6 MA/cm(2). Moreover, these measurements provide information about the stochastic and deterministic aspects of current driven domain wall mediated switching.

Factors affecting the shape of MBE-grown laterally aligned Fe nanowires

Various microstructural and chemical analysis techniques were applied to study two types (type-A and B) of self-assembled laterally aligned Fe nanowires (NWs) fabricated by molecular beam epitaxy on a ZnS buffer layer. The formation of the three-dimensional shapes of these NWs was found to be driven by the principle of surface energy minimization. We have provided phenomenological models to address the factors affecting the observed topological shape of these NWs, including the role of the lattice relationship between the Fe NWs and the underlying buffer layer, growth temperature, Fe nominal coverage and substrate orientation. Magnetic hysteresis measurements were performed at different temperature, demonstrating the Fe NWs possess a coercivity about 30 times larger than that of a Fe thin film. The observed gradual magnetization reversal indicates the magnetization process is accomplished by the rotation of magnetic moments within a single domain.

Current-induced magnetic domain wall motion below intrinsic threshold triggered by Walker breakdown

Controlling the position of a magnetic domain wall with electric current may allow for new types of non-volatile memory and logic devices. To be practical, however, the threshold current density necessary for domain wall motion must be reduced below present values. Intrinsic pinning due to magnetic anisotropy, as recently observed in perpendicularly magnetized Co/Ni nanowires, has been shown to give rise to an intrinsic current threshold J(th)(0). Here, we show that domain wall motion can be induced at current densities 40% below J(th)(0) when an external magnetic field of the order of the domain wall pinning field is applied. We observe that the velocity of the domain wall motion is the vector sum of current- and field-induced velocities, and that the domain wall can be driven against the direction of a magnetic field as large as 2,000 Oe, even at currents below J(th)(0). We show that this counterintuitive phenomenon is triggered by Walker breakdown, and that the additive velocities provide a unique way of simultaneously determining the spin polarization of current and the Gilbert damping constant.

Unified drift-diffusion theory for transverse spin currents in spin valves, domain walls, and other textured magnets

Spins transverse to the magnetization of a ferromagnet only survive over a short distance. We develop a drift-diffusion approach that captures the main features of transverse spin effects in systems with arbitrary spin textures (e.g., vortices and domain walls) and generalizes the Valet-Fert theory. In addition to the standard characteristic lengths (mean free path for majority and minority electrons, and spin diffusion length), the theory introduces two length scales, the transverse spin coherence length ℓ(⊥) and the (Larmor) spin precession length ℓ(L). We show how ℓ(L) and ℓ(⊥) can be extracted from ab initio calculations or measured with giant magnetoresistance experiments. In long (adiabatic) domain walls, we provide an analytic formula that expresses the so-called "nonadiabatic" (or fieldlike) torque in terms of these length scales. However, this nonadiabatic torque is no longer a simple material parameter but depends on the actual spin texture: in thin (<10  nm) domain walls, we observe very significant deviations from the adiabatic limit.

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.

Current-induced torques in magnetic materials

The magnetization of a magnetic material can be reversed by using electric currents that transport spin angular momentum. In the reciprocal process a changing magnetization orientation produces currents that transport spin angular momentum. Understanding how these processes occur reveals the intricate connection between magnetization and spin transport, and can transform technologies that generate, store or process information via the magnetization direction. Here we explain how currents can generate torques that affect the magnetic orientation and the reciprocal effect in a wide variety of magnetic materials and structures. We also discuss recent state-of-the-art demonstrations of current-induced torque devices that show great promise for enhancing the functionality of semiconductor devices.

Studies of nanomagnetism using synchrotron-based x-ray photoemission electron microscopy (X-PEEM)

As interest in magnetic devices has increased over the last 20 years, research into nanomagnetism has experienced a corresponding growth. Device applications from magnetic storage to magnetic logic have compelled interest in the influence of geometry and finite size on magnetism and magnetic excitations, in particular where the smallest dimensions reach the important magnetic interaction length scales. The dynamical behavior of nanoscale magnets is an especially important subset of research, as these phenomena are both critical for device physics and profoundly influenced by finite size. At the same time, nanoscale systems offer unique geometries to promote and study model systems, such as magnetic vortices, leading to new fundamental insights into magnetization dynamics. A wide array of experimental and computational techniques have been applied to these problems. Among these, imaging techniques that provide real-space information on the magnetic order are particularly useful. X-ray microscopy offers several advantages over scanning probe or optical techniques, such as high spatial resolution, element specificity and the possibility for high time resolution. Here, we review recent contributions using static and time-resolved x-ray photoemission electron microscopy to nanomagnetism research.

The interaction of transverse domain walls

The interaction between transverse domain walls is calculated analytically using a multipole expansion up to third order. Starting from an analytical expression for the magnetization in the wall, the monopole, dipole, and quadrupole moments are derived and their impact on the interaction is investigated using the surface and volume charges. The surface charges are important for the dipole moment while the volume charges constitute the monopole and quadrupole moments. For domain walls that are situated in different wires it is found that there is a strong deviation from the interaction of two monopoles. This deviation is caused by the interaction of the monopole of the wall in the first wire with the dipole of the wall in the second wire and vice versa. The dipole-dipole and the quadrupole-monopole interactions are found to be also of considerable size and non-negligible. A comparison with micromagnetic simulations shows a good agreement.

Transverse and vortex domain wall structure in magnetic nanowires with uniaxial in-plane anisotropy

Micromagnetic and analytical models are used to investigate how in-plane uniaxial anisotropy affects transverse and vortex domain walls in nanowires where shape anisotropy dominates. The effect of the uniaxial anisotropy can be interpreted as a modification of the effective wire dimensions. When the anisotropy axis is aligned with the wire axis (θ(a) = 0), the wall width is narrower than when no anisotropy is present. Conversely, the wall width increases when the anisotropy axis is perpendicular to the wire axis (θ(a) = π/2). The anisotropy also affects the nanowire dimensions at which transverse walls become unstable. This phase boundary shifts to larger widths or thicknesses when θ(a) = 0, but smaller widths or thicknesses when θ(a) = π/2.

Temperature estimation in a ferromagnetic Fe-Ni nanowire involving a current-driven domain wall motion

We observed a magnetic domain wall (DW) motion induced by the spin-polarized pulsed current in a nanoscale Fe(19)Ni(81) wire using a magnetic force microscope. High current density, which is of the order of 10(11) A m(-2), was required for the DW motion. A simple method to estimate the temperature of the wire was developed by comparing the wire resistance measured during the DW motion with the temperature dependence of the wire resistance. Using this method, we found the temperature of the wire was proportional to the square of the current density and became just beneath at the threshold Curie temperature. Our experimental data qualitatively support this analytical model that the temperature is proportional to the resistivity, thickness, width of the wire and the square of the current density, and also inversely proportional to the thermal conductivity.

Time-domain measurement of current-induced spin wave dynamics

The performance of spintronic devices critically depends on three material parameters, namely, the spin polarization in the current (P), the intrinsic Gilbert damping (α), and the coefficient of the nonadiabatic spin transfer torque (β). However, there has been no method to determine these crucial material parameters in a self-contained manner. Here we show that P, α, and β can be simultaneously determined by performing a single series of time-domain measurements of current-induced spin wave dynamics in a ferromagnetic film.

Suppression of the intrinsic stochastic pinning of domain walls in magnetic nanostripes

Nanofabrication has allowed the development of new concepts such as magnetic logic and race-track memory, both of which are based on the displacement of magnetic domain walls on magnetic nanostripes. One of the issues that has to be solved before devices can meet the market demands is the stochastic behaviour of the domain wall movement in magnetic nanostripes. Here we show that the stochastic nature of the domain wall motion in permalloy nanostripes can be suppressed at very low fields (0.6–2.7 Oe). We also find different field regimes for this stochastic motion that match well with the domain wall propagation modes. The highest pinning probability is found around the precessional mode and, interestingly, it does not depend on the external field in this regime. These results constitute an experimental evidence of the intrinsic nature of the stochastic pinning of domain walls in soft magnetic nanostripes.

The propagation of magnetic domain walls in nanowires offers promise as the basis of future memory storage technologies. Muñoz and Prieto show that the random pinning of domain walls to structural defects in the nanowires can be suppressed at low fields, thus improving the reliability of the transmission of the domain walls substantially.

All-magnonic spin-transfer torque and domain wall propagation

The spin-wave transportation through a transverse magnetic domain wall (DW) in a magnetic nanowire is studied. It is found that the spin wave passes through a DW without reflection. A magnon, the quantum of the spin wave, carries opposite spins on the two sides of the DW. As a result, there is a spin angular momentum transfer from the propagating magnons to the DW. This magnonic spin-transfer torque can efficiently drive a DW to propagate in the opposite direction to that of the spin wave.

Magneto-optical Kerr effect susceptometer for the analysis of magnetic domain wall dynamics

Domain wall dynamics in thin magnetic films with perpendicular and in-plane anisotropy is studied using a novel magneto-optical Kerr effect susceptometery method. The method allows for measurements of domain wall motion under ac field excitation and the analysis of dynamic modes as a function of driving frequency and magnetic field amplitude. Domain wall dynamics in the perpendicular anisotropy system, a Co/Pt multilayer, is characterized by thermally activated creep motion. For this dynamic mode, a polydispersivity exponent of β = 0.50 ± 0.03 is derived at small excitation energy, which is in excellent agreement with theoretical models. The dynamics of the other system, a Co wire with transverse uniaxial anisotropy, is dominated by viscous slide motion in a regular magnetic stripe pattern. Analytical expressions are derived for this magnetic configuration and by using these expressions, accurate values for the depinning field and the domain wall mobility are extracted from the susceptibility measurements.

Current-induced spin-orbit torques

The ability to reverse the magnetization of nanomagnets by current injection has attracted increased attention ever since the spin-transfer torque mechanism was predicted in 1996. In this paper, we review the basic theoretical and experimental arguments supporting a novel current-induced spin torque mechanism taking place in ferromagnetic (FM) materials. This effect, hereafter named spin-orbit (SO) torque, is produced by the flow of an electric current in a crystalline structure lacking inversion symmetry, which transfers orbital angular momentum from the lattice to the spin system owing to the combined action of SO and exchange coupling. SO torques are found to be prominent in both FM metal and semiconducting systems, allowing for great flexibility in adjusting their orientation and magnitude by proper material engineering. Further directions of research in this field are briefly outlined.

Externally driven transmission and collisions of domain walls in ferromagnetic wires

Analytical multidomain solutions to the dynamical (Landau-Lifshitz-Gilbert) equation of a one-dimensional ferromagnet including an external magnetic field and spin-polarized electric current are found using the Hirota bilinearization method. A standard approach to solve the Landau-Lifshitz equation (without the Gilbert term) is modified in order to treat the dissipative dynamics. I establish the relations between the spin interaction parameters (the constants of exchange, anisotropy, dissipation, external-field intensity, and electric-current intensity) and the domain-wall parameters (width and velocity) and compare them to the results of the Walker approximation and micromagnetic simulations. The domain-wall motion driven by a longitudinal external field is analyzed with especial relevance to the field-induced collision of two domain walls. I determine the result of such a collision (which is found to be an elastic one) on the domain-wall parameters below and above the Walker breakdown (in weak- and strong-field regimes). Single-domain-wall dynamics in the presence of an external transverse field is studied with relevance to the challenge of increasing the domain-wall velocity below the breakdown.

Observation of the intrinsic pinning of a magnetic domain wall in a ferromagnetic nanowire

The spin transfer torque is essential for electrical magnetization switching. When a magnetic domain wall is driven by an electric current through an adiabatic spin torque, the theory predicts a threshold current even for a perfect wire without any extrinsic pinning. The experimental confirmation of this 'intrinsic pinning', however, has long been missing. Here, we give evidence that this intrinsic pinning determines the threshold, and thus that the adiabatic spin torque dominates the domain wall motion in a perpendicularly magnetized Co/Ni nanowire. The intrinsic nature manifests itself both in the field-independent threshold current and in the presence of its minimum on tuning the wire width. The demonstrated domain wall motion purely due to the adiabatic spin torque will serve to achieve robust operation and low energy consumption in spintronic devices.

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.

Fast domain wall motion in magnetic comb structures

Modern fabrication technology has enabled the study of submicron ferromagnetic strips with a particularly simple domain structure, allowing single, well-defined domain walls to be isolated and characterized. However, these domain walls have complex field-driven dynamics. The wall velocity initially increases with field, but above a certain threshold the domain wall abruptly slows down, accompanied by periodic transformations of the domain wall structure. This behaviour is potentially detrimental to the speed and proper functioning of proposed domain-wall-based devices, and although methods for suppression of the breakdown have been demonstrated in simulations, a convincing experimental demonstration is lacking. Here, we show experimentally that a series of cross-shaped traps acts to prevent transformations of the domain wall structure and increase the domain wall velocity by a factor of four compared to the maximum velocity on a plain strip. Our results suggest a route to faster and more reliable domain wall devices for memory, logic and sensing.

Magnetic antivortex-core reversal by circular-rotational spin currents

Topological singularities occur as antivortices in ferromagnetic thin-film microstructures. Antivortices behave as two-dimensional oscillators with a gyrotropic eigenmode which can be excited resonantly by spin currents and magnetic fields. We show that the two excitation types couple in an opposing sense of rotation in the case of resonant antivortex excitation with circular-rotational currents. If the sense of rotation of the current coincides with the intrinsic sense of gyration of the antivortex, the coupling to the Oersted fields is suppressed and only the spin-torque contribution locks into the gyrotropic eigenmode. We report on the experimental observation of purely spin-torque induced antivortex-core reversal. The dynamic response of an isolated antivortex is imaged by time-resolved scanning transmission x-ray microscopy on its genuine time and length scale.

Enhanced stochasticity of domain wall motion in magnetic racetracks due to dynamic pinning

Understanding the details of domain wall (DW) motion along magnetic racetracks has drawn considerable interest in the past few years for their applications in non-volatile memory devices. The propagation of the DW is dictated by the interplay between its driving force, either field or current, and the complex energy landscape of the racetrack. In this study, we use spin-valve nanowires to study field-driven DW motion in real time. By varying the strength of the driving magnetic field, the propagation mode of the DW can be changed from a simple translational mode to a more complex precessional mode. Interestingly, the DW motion becomes much more stochastic at the onset of this propagation mode. We show that this unexpected result is a consequence of an unsustainable gain in Zeeman energy of the DW, as it is driven faster by the magnetic field. As a result, the DW periodically releases energy and thereby becomes more susceptible to pinning by local imperfections in the racetrack.

Effects of disorder and internal dynamics on vortex wall propagation

Experimental measurements of domain wall propagation are typically interpreted by comparison to reduced models that ignore both the effects of disorder and the internal dynamics of the domain wall structure. Using micromagnetic simulations, we study vortex wall propagation in magnetic nanowires induced by fields or currents in the presence of disorder. We show that the disorder leads to increases and decreases in the domain wall velocity depending on the conditions. These results can be understood in terms of an effective damping that increases as disorder increases. As a domain wall moves through disorder, internal degrees of freedom get excited, increasing the energy dissipation rate.

Magnetic domain wall pumping by spin transfer torque

We show that spin transfer torque from a direct spin-polarized current applied parallel to a magnetic domain wall (DW) induces DW motion in a direction independent of the current polarity. This unidirectional response of the DW to spin torque enables DW pumping--long-range DW displacement driven by an alternating current. Our numerical simulations reveal that DW pumping can be resonantly amplified through excitation of internal degrees of freedom of the DW by the current.

Proposal of a robust measurement scheme for the nonadiabatic spin torque using the displacement of magnetic vortices

A spin-polarized current traversing a ferromagnet with continuously varying magnetization exerts a torque on the magnetization. The nonadiabatic contribution to this spin-transfer torque is currently under strong debate, as its value differs by orders of magnitude in theoretical predictions and in measurements. Here, a measurement scheme is presented that allows us to determine the strength of the nonadiabatic spin torque accurately and directly. Analytical and numerical calculations show that the scheme is robust against the uncertainties of the exact current direction and Oersted fields.

Fast domain wall propagation under an optimal field pulse in magnetic nanowires

We investigate field-driven domain wall (DW) propagation in magnetic nanowires in the framework of the Landau-Lifshitz-Gilbert equation. We propose a new strategy to speed up the DW motion in a uniaxial magnetic nanowire by using an optimal space-dependent field pulse synchronized with the DW propagation. Depending on the damping parameter, the DW velocity can be increased by about 2 orders of magnitude compared to the standard case of a static uniform field. Moreover, under the optimal field pulse, the change in total magnetic energy in the nanowire is proportional to the DW velocity, implying that rapid energy release is essential for fast DW propagation.

Dependence of magnetic domain-wall motion on a fast changing current

A dependence of current-induced domain-wall motion in nanowires on the temporal shape of current pulses is observed. The results show that the motion of the wall is amplified for alterations of the current on a time scale smaller than the intrinsic time scale of the domain wall which is a few nanoseconds in permalloy. This effect arises from an additional force on the wall by the spin-transfer torque due to a fast changing current and improves the efficiency of domain-wall motion. The observations provide an understanding for the efficient domain-wall motion with nanosecond current pulses.

Current-induced control of spin-wave attenuation

The current-induced modification of the attenuation of a propagating spin wave in a magnetic nanowire is studied theoretically and numerically. The attenuation length of spin wave can increase when the spin waves and electrons move in the same direction. It is directly affected by the nonadiabaticity of the spin-transfer torque and thus can be used to estimate the nonadiabaticity. When the nonadiabatic spin torque is sufficiently large, the attenuation length becomes negative, resulting in the amplification of spin waves.

Dependence of domain-wall depinning threshold current on pinning profile

We have investigated the threshold current density required for depinning a domain wall from constrictions in NiFe nanowires, which give rise to pinning potentials of fixed amplitude but variable profile. We observed it to vary linearly with the angle of the triangular constriction. These results are reproduced using micromagnetic simulations including the adiabatic and nonadiabatic spin-torque terms. By curve-fitting the calculated variations to the experimental results, we obtain the nonadiabaticity parameter beta=0.04(+/-0.005) and current spin polarization P=0.51(+/-0.02).

Universal electromotive force induced by domain wall motion

The electromotive force induced by a moving magnetic domain wall in a nanostrip has been calculated theoretically and detected experimentally. It is found that the emf depends only on the domain wall transformation frequency through a universal Josephson type relation, which is closely related to the topological nature of the domain wall. Our experimental measurements confirm the theoretical prediction.

Probing the spin polarization of current by soft x-ray imaging of current-induced magnetic vortex dynamics

Time-resolved soft x-ray transmission microscopy is applied to image the current-induced resonant dynamics of the magnetic vortex core realized in a micron sized Permalloy disk. The high spatial resolution better than 25 nm enables us to observe the resonant motion of the vortex core. The result also provides the spin polarization of the current to be 0.67+/-0.16 for Permalloy by fitting the experimental results with an analytical model in the framework of the spin-transfer torque.

Dynamical pinning of a domain wall in a magnetic nanowire induced by Walker breakdown

Transmission probability of a domain wall through a magnetic nanowire is investigated as a function of the external magnetic field. A very intriguing phenomenon is found that the transmission probability shows a significant drop after exceeding the threshold driving field, which contradicts our intuition that a domain wall is more mobile in the higher magnetic field. The micromagnetics simulation reveals that the domain wall motion in the wire with finite roughness causes the dynamical pinning due to the Walker breakdown, which semiquantitatively explains our experimental results.

Current-induced torques due to compensated antiferromagnets

We analyze the influence of current-induced torques on the magnetization configuration of a ferromagnet in a circuit containing a compensated antiferromagnet. We argue that these torques are generically nonzero and determine their form by considering spin-dependent scattering at a compensated antiferromagnetic interface. Because of symmetry dictated differences in the form of the current-induced torque, the phase diagram which expresses the dependence of the ferromagnetic configuration on the current and external magnetic field differs qualitatively from its ferromagnet-only counterpart.