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The interfacial Dzyaloshinskii-Moriya interaction (DMI) can be exploited in magnetic thin films to realize lateral chirally coupled systems, providing a way to couple different sections of a magnetic racetrack and realize interconnected networks of magnetic logic gates. Here, we systematically investigate the interplay between spin-orbit torques, chiral coupling and the device design in domain wall racetracks. We show that the current-induced domain nucleation process can be tuned between single-domain nucleation and repeated nucleation of alternate domains by changing the orientation of an in-plane patterned magnetic region within an out-of-plane magnetic racetrack. Furthermore, by combining experiments and micromagnetic simulations, we show that the combination of damping-like and field-like spin-orbit torques with DMI results in selective domain wall injection in one of two arms of a Y-shaped devices depending on the current density. Such an element constitutes the basis of domain wall based demultiplexer, which is essential for distributing a single input to any one of the multiple outputs in logic circuits. Our results provide input for the design of reliable and multifunctional domain-wall circuits based on chirally coupled interfaces.

Arrays of coupled nanomagnets have wide-ranging fundamental and practical applications in artificial spin ices, neuromorphic computing and spintronics. However, lacking in these fields are nanomagnets with perpendicular magnetic anisotropy with sufficient magnetostatic interaction. This would not only open up new possibilities for artificial spin ice geometries but also enable novel coupling methods for applications. Here we demonstrate a method to engineer the energy landscape of artificial spin lattices with perpendicular magnetic anisotropy. With this, we are able to realize for the first time magnetostatically-coupled 2D lattices of out-of-plane Ising spins that spontaneously order at room temperature on timescales that can be precisely engineered. We show how this property, together with straightforward electrical interfacing, make this system a promising platform for reservoir computing. Our results open the way to investigate the thermodynamics of out-of-plane magnetostatically coupled nanomagnet arrays with novel spin ice geometries, as well as to exploit such nanomagnet arrays in unconventional computing, taking advantage of the adjustable temporal dynamics and strong coupling between nanomagnets.

Imaging of nanoscale magnetic textures within extended material systems is of critical importance both to fundamental research and technological applications. Whilst high resolution magnetic imaging of thin nanoscale samples is well-established with electron and soft X-ray microscopy, the extension to micrometer-thick systems with hard X-rays currently limits high resolution imaging to rare-earth magnets. Here we overcome this limitation by establishing soft X-ray magnetic imaging of micrometer-thick systems using the pre-edge phase X-ray Magnetic Circular Dichroism signal, thus making possible the study of a wide range of magnetic materials. By performing dichroic spectro-ptychography, we demonstrate high spatial resolution imaging of magnetic samples up to 1.7 {\mu}m thick, an order of magnitude higher than conventionally possible with absorption-based techniques. This new regime of magnetic imaging makes possible the study of extended non rare-earth systems that have until now been inaccessible, from magnetic textures for future spintronic applications to non-rare-earth permanent magnets.

Two-dimensional arrays of magnetically coupled nanomagnets provide a mesoscopic platform for exploring collective phenomena as well as realizing a broad range of spintronic devices. In particular, the magnetic coupling plays a critical role in determining the nature of the cooperative behaviour and providing new functionalities in nanomagnet-based devices. Here, we create coupled Ising-like nanomagnets in which the coupling between adjacent nanomagnetic regions can be reversibly converted between parallel and antiparallel through solid-state ionic gating. This is achieved with the voltage-control of magnetic anisotropies in a nanosized region where the symmetric exchange interaction favours parallel alignment and the antisymmetric exchange interaction, namely the Dzyaloshinskii-Moriya interaction, favours antiparallel alignment. Applying this concept to a two-dimensional lattice, we demonstrate a voltage-controlled phase transition in artificial spin ices. Furthermore, we achieve an addressable control of the individual couplings and realize an electrically programmable Ising network, which opens up new avenues to design nanomagnet-based logic devices and neuromorphic computers

Strong, adjustable magnetic couplings are of great importance to all devices based on magnetic materials. Controlling the coupling between adjacent regions of a single magnetic layer, however, is challenging. In this work, we demonstrate strong exchange-based coupling between arbitrarily shaped regions of a single ferrimagnetic layer. This is achieved by spatially patterning the compensation temperature of the ferrimagnet by either oxidation or He+ irradiation. The coupling originates at the lateral interface between regions with different compensation temperature and scales inversely with their width. We show that this coupling generates large lateral exchange coupling fields and we demonstrate its application to control the switching of magnetically compensated dots with an electric current.

The establishment of chiral coupling in thin magnetic films with inhomogeneous anisotropy has led to the development of artificial systems of fundamental and technological interest. The chiral coupling itself is enabled by the Dzyaloshinskii-Moriya interaction (DMI) enforced by the patterned noncollinear magnetization. Here, we create a domain wall track with out-of-plane magnetization coupled on each side to a narrow parallel strip with in-plane magnetization. With this we show that the chiral torques emerging from the DMI at the boundary between the regions of noncollinear magnetization in a single magnetic layer can be used to bias the domain wall velocity. To tune the chiral torques, the design of the magnetic racetracks can be modified by varying the width of the tracks or the width of the transition region between noncollinear magnetizations, reaching effective chiral magnetic fields of up to 7.8 mT. Furthermore, we show how the magnitude of the chiral torques can be estimated by measuring asymmetric domain wall velocities, and demonstrate spontaneous domain wall motion propelled by intrinsic torques even in the absence of any external driving force.

The imaging of magneto-dynamical processes has been, so far, mostly a two-dimensional business, due to the constraints of the available experimental techniques. In this manuscript, building on the recent developments of soft X-ray magnetic laminography, we present an experimental setup where magneto-dynamical processes can be resolved in all three spatial dimensions and in time, with the possibility to freely tune the frequency of the dynamical process. We then employ this setup to investigate the three-dimensional dynamics of two resonant magneto-dynamical modes in a CoFeB microstructure occurring at different frequencies, namely the fundamental vortex gyration mode and a magnetic field-induced domain wall excitation mode. This new technique provides much needed capabilities for the experimental investigation of the magnetization dynamics of three-dimensional magnetic systems.

The development of spintronic oscillators is driven by their potential applications in radio frequency telecommunication and neuromorphic computing. In this work, we propose a spintronic oscillator based on the chiral coupling in thin magnetic films with patterned anisotropy. With an in-plane magnetized disk imprinted on an out-of-plane magnetized slab, the oscillator takes a polar vortex-like magnetic structure in the disk stabilized by a strong Dzyaloshinskii-Moriya interaction. By means of micromagnetic simulations, we investigate its oscillatory properties under applied spin current and, by placing an ensemble of oscillators in the near vicinity, we demonstrate their synchronization with different resonant frequencies. Finally, we show their potential application in neuromorphic computing using a network with six oscillators.

We investigate the inversion process of magnetic domain walls (DWs) propagating through synthetic noncollinear magnetic textures, whereby an up/down DW can be transformed into a down/up DW and vice versa. We exploit the lateral coupling between out-of-plane and in-plane magnetic regions induced by the interfacial Dzyaloshinskii-Moriya interaction in Pt/Co/AlOx trilayers to realize both field-driven and current-driven magnetic DW inverters. The inverters consist of narrow in-plane magnetic regions embedded in out-of-plane DW racetracks. Magnetic imaging and micromagnetic simulations provide insight into the DW inversion mechanism, showing that DW inversion proceeds by annihilation of the incoming domain on one side of the in-plane region and nucleation of a reverse domain on the opposite side. By changing the shape of the in-plane magnetic region, we show that the DW inversion efficiency can be tuned by adjusting the ratio between the chiral coupling energy at the inverter boundary and the energy cost of nucleating a reverse domain. Finally, we realize an asymmetric DW inverter that has nonreciprocal inversion properties and demonstrate that such a device can operate as a DW diode. Our results provide input for the versatile manipulation of DWs in magnetic racetracks and the design of efficient DW devices for nonvolatile magnetic logic schemes.

Despite their simple formulation, short range classical antiferromagnetic Ising models on frustrated lattices give rise to exotic phases of matter, in particular due to their macroscopic ground state degeneracy. Recent experiments on artificial spin systems comprising arrays of chirally coupled nanomagnets provide a significant strengthening of the nearest neighbour couplings compared to systems with dipolar-coupled nanomagnets. This opens the way to design artificial spin systems emulating Ising models with nearest neighbour couplings. In this paper, we compare the results of an extensive investigation with tensor network and Monte Carlo simulations of the nearest- and further-neighbour ($J_1-J_2-J_{3||}$) kagome Ising antiferromagnet with the experimental spin-spin correlations of a kagome lattice of chirally coupled nanomagnets. Even though the ratios between the further neighbour couplings and the nearest neighbour coupling estimated from micromagnetic simulations are much smaller than for dipolar-coupled nanomagnets, we show that they still play an essential role in the selection of the correlations., Comment: 27 pages, 33 figures. v3: Corrected two typos: frequency in the demagnetisation protocol, thickness of the unit cell in the micromagnetic simulations

We show that the coupling between two ferromagnetic layers separated by a nonmagnetic spacer can be used to control the depinning of domain walls and induce unidirectional domain wall propagation. We investigated CoFeB/Ti/CoFeB trilayers where the easy axis of the magnetization of the top CoFeB layer is out-of-plane and that of the bottom layer is in-plane. Using Magneto-optic Kerr effect microscopy, we find that the depinning of a domain wall in the perpendicularly magnetized CoFeB layer is influenced by the orientation of the magnetization of the in-plane layer, which gives rise to a field-driven asymmetric domain expansion. This effect occurs due to the magnetic coupling between the internal magnetization of the domain wall and the magnetization of the in-plane CoFeB layer, which breaks the symmetry of up-down and down-up homochiral N\'eel domain walls in the perpendicular CoFeB layer. Micromagnetic simulations support these findings by showing that the interlayer coupling either opposes or favors the Dzyaloshinskii-Moriya interaction in the domain wall, thereby generating an imbalance in the depinning fields. This effect also allows for artificially controlling the chirality and dynamics of domain walls in magnetic layers lacking a strong Dzyaloshinskii-Moriya interaction., Comment: 21 pages, 6 figures

The ability to engineer the interactions in assemblies of nanoscale magnets is central to the development of artificial spin systems and spintronic technologies. Following the emergence of the Dzyaloshinskii-Moriya interaction (DMI) in thin film magnetism, new routes have been opened to couple the nanomagnets via strong chiral interactions, which is complementary to the established dipolar and exchange coupling mechanisms. In this Perspective, we review recent progress in the engineering of synthetic magnets coupled by the interlayer and intralayer DMI. We show how multilayer chiral magnetic structures and two-dimensional synthetic antiferromagnets, skyrmions, and artificial spin systems can be realized by simultaneous control of the DMI and magnetic anisotropy. In addition, we show that, with the combination of DMI and current-induced spin-orbit torques, field-free switching of synthetic magnetic elements is obtained as well as all-electric domain wall logic circuits.

Memory and logic devices that encode information in magnetic domains rely on the controlled injection of domain walls to reach their full potential. In this work, we exploit the chiral coupling induced by the Dzyaloshinskii-Moriya interaction between in-plane and out-of-plane magnetized regions of a Pt/Co/AlO\textsubscript{x} trilayer in combination with current-driven spin-orbit torques to control the injection of domain walls into magnetic conduits. We demonstrate that the current-induced domain nucleation is strongly inhibited for magnetic configurations stabilized by the chiral coupling and promoted for those that have the opposite chirality. These configurations allow for efficient domain wall injection using current densities of the order of $4\times$\SI{e11}{A m^{-2}}, which are lower than those used in other injection schemes. Furthermore, by setting the orientation of the in-plane magnetization using an external field, we demonstrate the use of a chiral domain wall injector to create a controlled sequence of alternating domains in a racetrack structure driven by a steady stream of unipolar current pulses.

The ability to experimentally map the three-dimensional structure and dynamics in bulk and patterned three-dimensional ferromagnets is essential both for understanding fundamental micromagnetic processes, as well as for investigating technologically-relevant micromagnets whose functions are connected to the presence and dynamics of fundamental micromagnetic structures, such as domain walls and vortices. Here, we demonstrate time-resolved magnetic laminography, a technique which offers access to the temporal evolution of a complex three-dimensional magnetic structure with nanoscale resolution. We image the dynamics of the complex three-dimensional magnetization state in a two-phase bulk magnet with a lateral spatial resolution of 50 nm, mapping the transition between domain wall precession and the dynamics of a uniform magnetic domain that is attributed to variations in the magnetization state across the phase boundary. The capability to probe three-dimensional magnetic structures with temporal resolution paves the way for the experimental investigation of novel functionalities arising from dynamic phenomena in bulk and three-dimensional patterned nanomagnets., Comment: Nat. Nanotechnol. (2020)

Designing and constructing model systems that embody the statistical mechanics of frustration is now possible using nanotechnology. We have arranged nanomagnets on a two-dimensional square lattice to form an artificial spin ice, and studied its fractional excitations, emergent magnetic monopoles, and how they respond to a driving field using X-ray magnetic microscopy. We observe a regime in which the monopole drift velocity is linear in field above a critical field for the onset of motion. The temperature dependence of the critical field can be described by introducing an interaction term into the Bean-Livingston model of field-assisted barrier hopping. By analogy with electrical charge drift motion, we define and measure a monopole mobility that is larger both for higher temperatures and stronger interactions between nanomagnets. The mobility in this linear regime is described by a creep model of zero-dimensional charges moving within a network of quasi-one-dimensional objects., Comment: 10 pages, 5 figures

Chiral domain walls in ultrathin perpendicularly magnetised layers have a N\'{e}el structure stabilised by a Dzyaloshinskii-Moriya interaction (DMI) that is generated at the interface between the ferromagnet and a heavy metal. Different heavy metals are required above and below a ferromagnetic film in order to generate the structural inversion asymmetry needed to ensure that the DMI arising at the two interfaces does not cancel. Here we report on the magnetic properties of epitaxial Pt/Co/Au$_x$Pt$_{1-x}$ trilayers grown by sputtering onto sapphire substrates with 0.6 nm thick Co. As $x$ rises from 0 to 1 a structural inversion asymmetry is generated. We characterise the epilayer structure with x-ray diffraction and cross-sectional transmission electron microscopy, revealing (111) stacking. The saturation magnetization falls as the proximity magnetisation in Pt is reduced, whilst the perpendicular magnetic anisotropy $K_\mathrm{u}$ rises. The micromagnetic DMI strength $D$ was determined using the bubble expansion technique and also rises from a negligible value when $x=0$ to $\sim 1$ mJ/m$^2$ for $x = 1$. The depinning field at which field-driven domain wall motion crosses from the creep to the depinning regime rises from $\sim 40$ to $\sim 70$ mT, attributed to greater spatial fluctuations of the domain wall energy with increasing Au concentration. Meanwhile, the increase in DMI causes the Walker field to rise from $\sim 10$ to $\sim 280$ mT, meaning that only in the $x = 1$ sample is the steady flow regime accessible. The full dependence of domain wall velocity on driving field bears little resemblance to the prediction of a simple one-dimensional model, but can be described very well using micromagnetic simulations with a realistic model of disorder. These reveal a rise in Gilbert damping as $x$ increases.

Magnetic domain walls are objects whose dynamics is inseparably connected to their structure. In this work we investigate magnetic bilayers, which are engineered such that a coupled pair of domain walls, one in each layer, is stabilized by a cooperation of Dzyaloshinskii-Moriya interaction and flux-closing mechanism. The dipolar field mediating the interaction between the two domain walls, links not only their position but also their structure. We show that this link has a direct impact on their magnetic field induced dynamics. We demonstrate that in such a system the coupling leads to an increased domain wall velocity with respect to single domain walls. Since the domain wall dynamics is observed in a precessional regime, the dynamics involves the synchronization between the two walls, to preserve the flux closure during motion. Properties of these coupled oscillating walls can be tuned by an additional in-plane magnetic field enabling a rich variety of states, from perfect synchronization to complete detuning.

Collective spin ensembles known as skyrmion bubbles can exist in ultrathin magnetic film heterostructures and promise miniscule diameters and low-power all-electrical manipulation. The nucleation, identification and manipulation of skyrmions is of great interest, in part, because of their non-trivial topology. Here we ascertain the topology of 100 nm isolated hedgehog skyrmion bubbles and probe their response to external fields at room temperature in [ Pt \ Co (0.8 nm) \ Ir ] films. We find that structural disorder can stabilize skyrmion bubble states which exhibit creep-like domain wall motion. This makes the extraction of DMI from observations difficult and could explain the larger than predicted bubble sizes observed in interfacial DMI films. Intriguingly, we report on a critical size for hedgehog skyrmions, above which the bubbles lose circular symmetry and take up an irregular shape. Combining Lorentz TEM and fully three dimensional multi-layered simulations, we demonstrate the unique behavior of these topologically non-trivial spin textures., Comment: 12 pages, 5 figures

Magnetic skyrmions are textures behaving as quasiparticles which are topologically different from other states. Their discovery in systems with broken inversion symmetry sparked the search for materials containing such magnetic phase at room temperature. Their topological properties combined with the chirality-related spin-orbit torques make them interesting objects to control the magnetization at nanoscale. Here we show that a pair of coupled skyrmions with the same topological charge and opposite chiralities can be stabilized in a symmetric magnetic bilayer system by combining Dzyaloshinskii-Moriya interaction (DMI) and dipolar coupling effects. This effect opens a new path for skyrmion stabilization with much lower DMI. We then demonstrate in a single device with two different electrodes that such skyrmions can be efficiently and independently written and shifted by electric current at large velocities. The skyrmionic nature of the observed quasiparticles is further confirmed by using the gyrotropic force as a topological filter. These results set the ground for emerging spintronic technologies where issues concerning skyrmion stability, nucleation, and propagation are paramount.

Under the correct conditions, Dzyaloshinskii-Moriya interactions (DMI) can lead to topologically protected spin textures such as skyrmions. The application of DMI for spin-based computation and memory technologies is promising and requires a detailed consideration of the role intrinsic energies have on stabilizing the diverse textures observed thus far. Here we experimentally investigate the effect of dipolar energy from interlayer coupling on the remanent spin textures found at room temperature for interfacial DMI multilayers of [ Pt \ Co \ Ir ]$_{\times N}$. The total dipolar energy is modified by increasing the number of layer repetitions N which result in different phases of chiral magnetic textures. We use the phase transitions to estimate the DMI energy present in the ultrathin films to be D = 2.1 $\pm$ 0.1 mJ m$^{-2}$. Unlike traditional perpendicular magnetic anisotropy films, these multilayer films with finite DMI exhibit isolated hedgehog skyrmion bubbles as well as sub 100 nm labyrinth domains with cycloidal homochiral N\'eel walls which are dependent on DMI as well as the total dipolar energy., Comment: 10 pages, 5 figures

Next-generation concepts for solid-state memory devices are based on current-driven domain wall propagation, where the wall velocity governs the device performance. It has been shown that the domain wall velocity and the direction of travel is controlled by the nature of the wall and its chirality. This chirality is attributed to effects emerging from the lack of inversion symmetry at the interface between a ferromagnet and a heavy metal, leading to an interfacial Dzyaloshinskii-Moriya interaction that can control the shape and chirality of the magnetic domain wall. Here we present direct imaging of domain walls in Pt/Co/AlO$_x$ films using Lorentz transmission electron microscopy, demonstrating the presence of homochiral, and thus topologically protected, N\'{e}el walls. Such domain walls are good candidates for dense data storage, bringing the bit size down close to the limit of the domain wall width.