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 applied to the system suddenly. And 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 the 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 domain walls since the instability of Gaussian wave packets will break the structure of multiple domain walls.
Magnetic cylindrical nanowires are very fascinating objects where the curved geometry allows many novel magnetic effects and a variety of non-trivial magnetic structures. Micromagnetic modelling plays an important role in revealing the magnetization distribution in magnetic nanowires, often not accessible by imaging methods with sufficient details. Here we review the magnetic properties of the shape anisotropy-dominated nanowires and the nanowires with competing shape and magnetocrystalline anisotropies, as revealed by micromagnetic modelling. We discuss the variety of magnetic walls and magne…
Understanding the domain wall dynamics is an important issue in modern magnetism. Here we present results of domain wall displacement in curved cylindrical nanowires at a constant magnetic field. We show that the average velocity of a transverse domain wall increases with curvature. Contrary to what it is observed in stripes, in a curved wire the transverse domain wall oscillates along and rotates around the nanowire with the same frequency. These results open the possibility of new oscillation-based applications.
Domain wall propagation in modulated-diameter cylindrical nanowires is a key phenomenon to be studied with a view to designing three-dimensional magnetic memory devices. This paper presents a theoretical study of transverse domain wall behavior under the influence of a magnetic field within a cylindrical nanowire with diameter modulations. In particular, domain wall pinning close to the diameter modulation was quantified, both numerically, using finite element micromagnetic simulations, and analytically. Qualitative analytical model for gently sloping modulations resulted in a simple scaling l…
We discuss the robustness of Majorana edge modes in a finite quantum nanowire of cylindrical shape. The nanowire is modeled as a bidimensional cylindrical shell of semiconductor material with proximity-induced superconductivity and an intrinsic Rashba spin-orbit interaction. The latter is characterized by effective electric and magnetic fields in transverse direction of the nanowire. An applied external magnetic field pointing in an arbitrary orientation is also assumed. The numerical diagonalization of the Hamiltonian allows us to study the spectrum of the nanowire for different experimental …
The exciton ground state and excited state energies are calculated for a model system of an infinitely long cylindrical wire. The effective Coulomb potential between the electron and the hole is studied as function of the wire radius. Within the adiabatic approximation, we obtain `exact' numerical results for the effective exciton potential and the lowest exciton energy levels which are fitted to simple analytical expressions. Furthermore, we investigated the influence of a magnetic field parallel to the nanowire on the effective potential and the exciton energy.
The recent advances in nanowire (NW) growth technology have made possible the growth of more complex structures such as core-multi-shell (CMS) NWs. We propose the approach for calculation of electron subbands in cylindrical CMS NWs within the simple effective mass approximation. Numerical results are presented for ${\rm GaAs/Al_{0.3}Ga_{0.7}As}$ radial heterostructure with AlGaAs-core and 4 alternate GaAs and AlGaAs shells. The influence of an effective mass difference in heterolayers is discussed.
We model the exchange bias effect in thin cylindrical nanowires composed of a ferromagnetic core and an antiferromagnetic shell implementing a classical spin Hamiltonian and Monte Carlo simulations. We address systematically the effect of shell polycrystallinity on the characteristic fields of the isothermal hysteresis loop (coercivity, exchange-bias) and their angular dependence upon the direction of the applied / cooling field. We relate the observed trends to modifications of the underlying magnetization reversal mechanism. We fit our simulation results to an extended Stoner-Wohlfarth model…
The spin precession in a cylindrical semiconductor nanowire due to Rashba spin-orbit coupling has been investigated theoretically using an InAs nanowire containing a surface two-dimensional electron gas as a model. The eigenstates, energy-momentum dispersion, and the energy-magnetic field dispersion relation are determined by solving the Schrödinger equation in a cylindrical symmetry The combination of states with the same total angular momentum but opposite spin orientation results in a periodic modulation of the axial spin component along the axis of the wire. Spin-precession about the wires…
We investigate the scattering phenomena produced by a general finite-range nonseparable potential in a multi-channel two-probe cylindrical nanowire heterostructure. The multi-channel current scattering matrix is efficiently computed using the R-matrix formalism extended for cylindrical coordinates. Considering the contribution of the evanescent channels to the scattering matrix, we are able to put in evidence the specific dips in the tunneling coefficient in the case of an attractive potential. The cylindrical symmetry cancels the "selection rules" known for Cartesian coordinates. If the attra…
Cylindrical magnetic nanowires are promising systems for the development of three-dimensional spintronic devices. Here, we simulate the evolution of magnetic states during fabrication of strongly-coupled cylindrical nanowires with varying degrees of overlap. By varying the separation between wires, the relative strength of exchange and magnetostatic coupling can be tuned. Hence leading to the formation of six fundamental states as a function of both inter-wire separation and wire height. In particular, two complex three-dimensional magnetic states, a 3D Landau Pattern and a Helical Domain wall…
Recent studies in three dimensional spintronics propose that the Œrsted field plays a significant role in cylindrical nanowires. However, there is no direct report of its impact on magnetic textures. Here, we use time-resolved scanning transmission X-ray microscopy to image the dynamic response of magnetization in cylindrical Co$_{30}$Ni$_{70}$ nanowires subjected to nanosecond Œrsted field pulses. We observe the tilting of longitudinally magnetized domains towards the azimuthal Œrsted field direction and create a robust model to reproduce the differential magnetic contrasts and extract the an…
Achieving high velocities of magnetic domain walls is a crucial factor for their use as information carriers in modern nanoelectronic applications. In nanomagnetism and spintronics, these velocities are often limited either by internal domain wall instabilities, known as the Walker breakdown phenomenon, or by spin wave emission, known as the magnonic regime. In the rigid domain wall model, the maximum magnon velocity acts as an effective "speed of light", providing a relativistic analogy for the domain wall speed limitation. Cylindrical magnetic nanowires are an example of systems with the abs…
This brief proposes an analytical approach to model the dc electrical behavior of extremely narrow cylindrical junctionless nanowire field-effect transistor (JLNW-FET). The model includes explicit expressions, taking into account the first-order perturbation theory for calculating eigenstates and corresponding wave functions obtained by the Schrodinger equation in the cylindrical coordinate. Assessment of the proposed model with technology computer-aided design (TCAD) simulations and measurement results confirms its validity for all regions of operation. This represents an essential step towar…
A stability analysis of metal nanowires shows that a Jahn-Teller deformation breaking cylindrical symmetry can be energetically favorable, leading to stable nanowires with elliptic cross sections. The sequence of stable cylindrical and elliptical nanowires allows for a consistent interpretation of experimental conductance histograms for alkali metals, including both the shell and supershell structures. It is predicted that for gold, elliptical nanowires are even more likely to form since their eccentricity is smaller than for alkali metals. The existence of certain metastable ``superdeformed''…
Magnetic nanowires (NW) are promising candidates for heat generation under AC-field application due to their large shape anisotropy. They may be used for catalysis, hyperthermia or water purification treatments. In the present work we theoretically evaluate the heat dissipated by a single magnetic nanowire, originated from the domain wall dynamics under the action of an AC-field. We compare the Permalloy NWs (which demagnetize via the transverse wall propagation) with the Co fcc NWs whose reversal mode is via a vortex domain wall. The average hysteresis loop areas -which are proportional to th…
We analyze the micromagnetics of short longitudinal modulations of a high-magnetization material in cylindrical nanowires made of a soft-magnetic material of lower magnetization such as permalloy, combining magnetic microscopy, analytical modeling, and micromagnetic simulations. The mismatch of magnetization induces curling of magnetization around the axis in the modulations, in an attempt to screen the interfacial magnetic charges. The curling angle increases with modulation length, until a plateau is reached with nearly full charge screening for a specific length scale~$Δ_\mathrm{mod}$, larg…
The stochasticity of domain wall (DW) motion in magnetic nanowires has been probed by measuring slow fluctuations, or noise, in electrical resistance at small magnetic fields. By controlled injection of DWs into isolated cylindrical nanowires of nickel, we have been able to track the motion of the DWs between the electrical leads by discrete steps in the resistance. Closer inspection of the time-dependence of noise reveals a diffusive random walk of the DWs with an universal kinetic exponent. Our experiments outline a method with which electrical resistance is able to detect the kinetic state …
Perpendicularly magnetized nanowires exhibit distinct domain wall types depending on the geometry. Wide wires contain Bloch walls, narrow wires Néel walls. Here, the transition region is investigated by direct imaging of the wall structure using high-resolution spin-polarized scanning electron microscopy. An achiral intermediate wall type is discovered that is unpredicted by established theoretical models. With the help of micromagnetic simulations, the formation of this novel wall type is explained.
We study shot noise of the spin-polarized current in a diffusive ferromagnetic nanowire which contains a ballistic domain wall. We find that the existence of a short domain wall influences strongly the shot noise for sufficiently high spin-polarization of the wire. Compared to the situation of the absence of the domain wall, the shot noise can be reduced or enhanced depending on the length of the domain wall and its relative conductance.
We present a theoretical study of a nanowire made of a three-dimensional topological insulator. The bulk topological insulator is described by a continuum-model Hamiltonian, and the cylindrical-nanowire geometry is modelled by a hard-wall boundary condition. We provide the secular equation for the eigenergies of the systems (both for bulk and surface states) and the analytical form of the energy eigenfunctions. We describe how the surface states of the cylinder are modified by finite-size effects. In particular, we provide a $1/R$ expansion for the energy of the surface states up to second ord…
Zeroth-order complex dispersion relations of a cylindrical metallic nanowire have been solved out analytically with approximate methods. The analytical solutions are valid for the sections of the dispersion relations whose frequencies are close to the Surface Plasmon frequency. The back bending of the Surface Plasmon-Polaritons(SPPs) can be well described by the analytical solutions, confirming that the back bending is originated from the metal Ohmic loss. The utility of the back bending point in the dispersion relation for the measurement of the metallic Ohimc loss has also been suggested.
Nanoscale magnetic systems have been studied extensively in various geometries, such as wires of different cross-sections, arrays of wires, dots, rings, etc. Such systems have interesting physical properties and promising applications in advanced magnetic devices. Uniform magnetic nanowires are the basic structures which were broadly investigated. However, some of their dynamical properties, like: (anti)crossing between the spin wave modes and impact of the magnetic field on spin wave spectrum, still need to be exploited. We continue this research by investigation of the spin wave dynamics in …
We investigate current-driven domain wall (DW) propagation in magnetic nanowires in the framework of the modified Landau-Lifshitz-Gilbert equation with both adiabatic and nonadiabatic spin torque (NAST) terms. Contrary to the common opinion that NAST is indispensable for DW motion[1,2], we point out that adiabatic spin torque (AST) only is enough for current-driven DW motion in a cylindrical (uniaxial) nanowire. Apart from a discussion of the rigid DW motion from the energy and angular momentum viewpoint, we also propose an experimental scheme to measure the spin current polarization by combin…
Since its proposal, the idea to vastly increase data storage density with a magnetic non-volatile 3D shift-register has sustained interest in current-induced domain wall (DW) motion. So far, experimental efforts have focused on flat nanostrips, which exhibit a wide range of noteworthy effects, yet suffer from intrinsic DW instabilities limiting their mobility. In contrast, ferromagnetic cylindrical nanowires (NWs) can host a novel type of magnetic DW, namely the Bloch-point wall (BPW), which due to its specific 3D topology should not experience the same fundamental issue. This could give rise …
The nature of magnetization reversal in an isolated cylindrical nanomagnet has been studied employing time-resolved magnetoresistance measurement. We find that the reversal mode is highly stochastic, occurring either by multimode or single-step switching. Intriguingly, the stochasticity was found to depend on the alignment of the driving magnetic field to the long axis of the nanowires, where predominantly multimode switching gives way to single-step switching behavior as the field direction is rotated from parallel to transverse with respect to the nanowire axis.
Cylindrical nanowires made of soft magnetic materials, in contrast to thin strips, may host domain walls of two distinct topologies. Unexpectedly, we evidence experimentally the dynamic transformation of topology upon wall motion above a field threshold. Micromagnetic simulations highlight the underlying precessional dynamics for one way of the transformation, involving the nucleation of a Bloch-point singularity, however, fail to reproduce the reverse process. This rare discrepancy between micromagnetic simulations and experiments raises fascinating questions in material and computer science.
The pinning effect of the periodic diameter modulations on the domain wall propagation in FeCoCu individual nanowires is determined by Magnetic Force Microscopy, MFM. A main bistable magnetic configuration is firstly concluded from MFM images characterized by the spin reversal between two nearly single domain states with opposite axial magnetization. Complementary micromagnetic simulations confirm a vortex mediated magnetization reversal process. A refined MFM imaging procedure under variable applied field allows us to observe metastable magnetic states where the propagating domain wall is pin…
We have investigated dynamic behaviors of the magnetic domain wall under perpendicular magnetic field pulses in ferromagnetic nanowires using micromagnetic simulations. It has been found that the perpendicular magnetic field pulse can trigger the magnetic domain wall motion, where all the field torques are kept to be on the plane of nanowire strip. The magnetic domain wall speed faster than several hundreds meters per second is predicted without the Walker breakdown for the perpendicular magnetic driving field stronger than $200~\mathrm{mT}$. Interestingly, the dynamic behavior of the moving m…
The fascinating high-speed field-driven domain wall (DW) motion along ferrimagnetic nanowires near the angular momentum compensation point (AMCP) is solved based on the generic ferrimagnetic dynamics. The physics of the absences of precessional torque and infinite high Walker breakdown field at the AMCP is proved under general conditions. Based on the energy conservation principle, an almost exact DW velocity formula, valid beyond the Walker breakdown field, is obtained. Our results agree with all existing experiments and simulations. This theory provides useful guidances to DW manipulation.
Rectangular nanowires may have domain walls nucleated and moved through them to realize many devices. It has been shown that at a particular width and thickness of a nanowire with perpendicular anisotropy, there is a switch from the domain wall being of Bloch-type to it being of Néel-type. This critical shape can be found through micromagnetics simulations, but here we present an analytic calculation for the energies of both wall types involving two iterations for the demagnetizing energy density. The expressions developed are long, but have the advantage that by simply inputting material para…
Interactions between pairs of magnetic domain walls (DW) and pinning by radial constrictions were studied in cylindrical nanowires with surface roughness. It was found that a radial constriction creates a symmetric pinning potential well, with a change of slope when the DW is situated outside the notch. Surface deformation induces an asymmetry in the pinning potential as well as dynamical pinning. The depinning fields of the domain walls were found generally to decrease with increasing surface roughness. A DW pinned at a radial constriction creates a pinning potential well for a free DW in a p…
We investigate how to facilitate the injection of domain walls in chiral ferromagnetic nanowires by electrical means. We calculate the critical current density above which domain walls are injected into the nanowire depending on the material parameters and the source of interaction including spin-transfer torques as well as spin-orbit torques. We demonstrate that the Dzyaloshinskii-Moriya interaction can significantly reduce the required critical current to inject the types of domain walls favored by the Dzyaloshinskii-Moriya interaction. We find that in chiral magnets it is only possible to s…
We demonstrate that for multilayered magnetic nanowires, where the thickness and composition of the individual layers has been carefully chosen, domain walls can be pinned at non-topographic sites created purely by ion irradiation in a focused ion beam system. The pinning results from irradiation induced alloying leading to magnetic property modification only in the affected regions. Using Lorentz transmission electron microscopy, we have studied the pinning behavior of domain walls at the irradiation sites. Depending on the irradiation dose, a single line feature not only pinned the domain wa…
A next-generation memory device utilizing a three-dimensional nanowire system requires the reliable control of domain wall motion. In this letter, domain walls are studied in cylindrical nanowires consisting of alternating segments of cobalt and nickel. The material interfaces acting as domain wall pinning sites, are utilized in combination with current pulses, to control the position of the domain wall, which is monitored using magnetoresistance measurements. Magnetic force microscopy results further confirm the occurrence of current assisted domain wall depinning. Data bits are therefore shi…
We consider the dynamics of polarization of a single domain wall in a magnetic nanowire, which is strongly pinned by impurities. In this case the equation of motion for the polarization parameter does not include any other dynamical variables and is nonlinear due to magnetic anisotropy. We calculated numerically the magnetization dynamics for different choices of parameters under short current pulses inducing polarization switching. Our results show that the switching is most effective for very rapid current pulses. Damping also enhances the switching probability.
We present a circuit model to describe the electron transport through a domain wall in a ferromagnetic nanowire. The domain wall is treated as a coherent 4-terminal device with incoming and outgoing channels of spin up and down and the spin-dependent scattering in the vicinity of the wall is modelled using classical resistances. We derive the conductance of the circuit in terms of general conductance parameters for a domain wall. We then calculate these conductance parameters for the case of ballistic transport through the domain wall, and obtain a simple formula for the domain wall magnetores…
Existing data for soft magnetic materials of critical current for domain-wall motion, wall speed driven by a magnetic field, and wall electrical resistance, show that all three observable properties are related through a single parameter: the wall mobility $μ$. The reciprocal of $μ$ represents the strength of viscous friction between domain wall and conduction-electron gas. And $μ$ is a function of the wall width, which depends in turn on the aspect ratio t/w, where t and w are the thickness and width of the sample. Over four orders of magnitude of $μ$, the data for nanowires show $μ\propto (t…
We present fractional quantum Hall domain walls confined in a gate-defined wire structure. Our experiments utilize spatial oscillation of domain walls driven by radio frequency electric fields to cause nuclear magnetic resonance. The resulting spectra are discussed in terms of both large quadrupole fields created around the wire and hyperfine fields associated with the oscillating domain walls. This provides the experimental fact that the domain walls survive near the confined geometry despite of potential deformation, by which a localized magnetic resonance is allowed in electrical means.
One-dimensional (1D) sub-bands in cylindrical InAs nanowires (NWs) are electrically mapped as a function of NW diameter in the range of 15-35 nm. At low temperatures, stepwise current increases with the gate voltage are clearly observed and attributed to the electron transport through individual 1D sub-bands. The two-fold degeneracy in certain sub-band energies predicted by simulation due to structural symmetry is experimentally observed for the first time. The experimentally obtained sub-band energies match the simulated results, shedding light on both the energies of the sub-bands as well as…
We investigate the effect of curvature on the energy and stability of domain wall configurations in curved cylindrical nanotubes and nanowires. We use micromagnetic simulations to calculate the phase diagram for the transverse wall (TW) and vortex wall (VW) states in tubes, finding the ground state configuration and the metastability region where both types of walls can exist. The introduction of curvature shifts the range for which the TW is the ground state domain wall to higher diameters, and increases the range of metastability. We interpret this behavior to be primarily due to the curvatu…
Nominally identical permalloy nanowires, with widths down to 150 nm, were fabricated onto a single electron transparent Si$_{3}$N$_{4}$ membrane using electron beam lithography (EBL) and focused ion beam (FIB) milling. Transmission electron microscopy (TEM) experiments were performed to compare the nanostructures produced by these two techniques in what we believe is the first direct comparison of fabrication techniques for nominally identical nanowires. Both EBL and FIB methods produced high quality structures with edge roughness being of the order of the mean grain size 5 -10 nm observed in …
We represent the results of micromagnetic modeling and experimental magnetic force microscopy investigations of domain wall (DW) pinning-depinning effects in the hybrid systems consisting of ferromagnetic nanowire (NW) and two ferromagnetic nanoparticles (NPs). It was demonstrated that the special NW-NPs configuration including the NW with DW nucleating bulb at one end and two-NP gate enables the realization of controlled DW pinning-depinning based on switching of magnetization in NPs subsystem. The algorithm of external driving field manipulation and independent NPs switching, which allow one…
We report the results of experimental investigations of controlled domain wall (DW) pinning in a ferromagnetic nanowire (NW) by stray fields of two uniformly magnetized bistable ferromagnetic nanoparticles (NPs) placed on either side of the NW and elongated parallel to the NW axis. We show by magnetic force microscopy measurements that DW pinning strength essentially depends on the orientation of the NP magnetic moments relative to the NW magnetization and can reach 20 mT. We also performed micromagnetic simulations confirming the influence of the magnetostatic interaction of the DW with the N…
We present calculations of Majorana edge modes in cylindrical nanowires of a semiconductor material with proximity-induced superconductivity. We consider a Rashba field along the transverse direction and an applied magnetic field in arbitrary orientation. Our analysis is based on exact numerical diagonalizations for the finite cylinder and on the complex band structure for the semi-infinite one. Orbital effects are responsible for a strong anisotropy of the critical field for which the effective gap vanishes. Robust Majorana modes are induced by the parallel field component and we find regimes…
With downscaling of electronic circuits, components based on semiconductor quantum dots are assuming increasing relevance for future technologies. Their response under external stimuli intrinsically depend on their quantum properties. Here we investigate single-electron tunneling in hard-wall InAs/InP nanowires in the presence of an off-resonant microwave drive. Our heterostructured nanowires include InAs quantum dots (QDs) and exhibit different tunnel-current regimes. In particular, for source-drain bias up to few mV Coulomb diamonds spread with increasing contrast as a function of microwave …
We report current-induced domain wall motion (CIDWM) in Ta\Co20Fe60B20\MgO nanowires. Domain walls are observed to move against the electron flow when no magnetic field is applied, while a field along the nanowires strongly affects the domain wall motion direction and velocity. A symmetric effect is observed for up-down and down-up domain walls. This indicates the presence of right-handed domain walls, due to a Dzyaloshinskii-Moriya interaction (DMI) with a DMI coefficient D=+0.06 mJ/m2. The positive DMI coefficient is interpreted to be a consequence of boron diffusion into the tantalum buffer…
We investigated how the dynamics of a domain wall are affected by the presence of spin density waves in a ferromagnetic wire. Domain walls and other scattering centres can cause coherent spin density waves to propagate through a wire when a current is applied. In some cases the spin torque due to these scattered electrons can be enhanced such that it is on a par with the exchange and anisotropy energies controlling the shape and dynamics of the domain wall. In such a case we find that the spin density waves enhance the current induced domain wall motion, allowing for domain wall motion with sm…
We report the realization of a planar transverse domain wall (TDW) with arbitrary tilting angle in a magnetic biaxial nanowire under a transverse magnetic field (TMF) pulse with fixed strength and optimized orientation profile. We smooth any twisting in azimuthal angle plane of a TDW and thus completely decouple the polar and azimuthal degrees of freedom. The analytical differential equation that describes the polar angle distribution is then derived and the resulting solution is not a Walker-ansatz form. With this optimized TMF pulse comoving, the field-driven dynamics of the planar TDW is in…
Stability of the well-known Walker propagating domain wall (DW) solution of the Landau-Lifshitz-Gilbert equation is analytically investigated. Surprisingly, the Walker's rigid body propagating DW mode is not stable against the spin wave/wavepacket emission. In the low field region only stern spin waves are emitted while both stern and bow waves are generated under high fields. In a high enough field, but below the Walker breakdown field, the Walker solution could be convective/absolute unstable if the transverse magnetic anisotropy is larger than a critical value, corresponding to a significan…
The low-energy effective Hamiltonian of the strong `spin'-orbit coupled one-dimensional hole gas in a cylindrical Ge nanowire in the presence of a strong magnetic field is studied both numerically and analytically. Basing on the Luttinger-Kohn Hamiltonian in the spherical approximation, we show this strong `spin'-orbit coupled one-dimensional hole gas can be accurately described by an effective two-band Hamiltonian $H^{\rm ef}=\hbar^{2}k^{2}_{z}/(2m^{*}_{h})+ασ^{x}k_{z}+g^{*}_{h}μ_{B}Bσ^{z}/2$, as long as the magnetic field is purely longitudinal or purely transverse. The explicit magnetic fie…
The precise manipulation of transverse magnetic domain walls in finite/infinite nanowires with artificial defects under the influence of very short spin-polarized current pulses is investigated. We show that for a classical $3d$ ferromagnet material like Nickel, the exact positioning of the domain walls at room temperature is possible only for pulses with very short rise and fall time that move the domain wall reliably to nearest neighboring pinning position. The influence of the shape of the current pulse and of the transient effects on the phase diagram current-pulse length are discussed. We…
Domain walls in ferromagnetic nanowires are potential building-blocks of future technologies such as racetrack memories, in which data encoded in the domain walls are transported using spin-polarised currents. However, the development of energy-efficient devices has been hampered by the high current densities needed to initiate domain wall motion. We show here that a remarkable reduction in the critical current density can be achieved for in-plane magnetised coupled domain walls in CoFe/Ru/CoFe synthetic ferrimagnet tracks. The antiferromagnetic exchange coupling between the layers leads to si…
