Current-driven magnetic domain-wall logic.

Spin-based logic architectures provide nonvolatile data retention, near-zero leakage, and scalability, extending the technology roadmap beyond complementary metal-oxide-semiconductor logic1-13. Architectures based on magnetic domain walls take advantage of the fast motion, high density, non-volatility and flexible design of domain walls to process and store information1,3,14-16. Such schemes, however, rely on domain-wall manipulation and clocking using an external magnetic field, which limits their implementation in dense, large-scale chips. Here we demonstrate a method for performing all-electric logic operations and cascading using domain-wall racetracks. We exploit the chiral coupling between neighbouring magnetic domains induced by the interfacial Dzyaloshinskii-Moriya interaction17-20, which promotes non-collinear spin alignment, to realize a domain-wall inverter, the essential basic building block in all implementations of Boolean logic. We then fabricate reconfigurable NAND and NOR logic gates, and perform operations with current-induced domain-wall motion. Finally, we cascade several NAND gates to build XOR and full adder gates, demonstrating electrical control of magnetic data and device interconnection in logic circuits. Our work provides a viable platform for scalable all-electric magnetic logic, paving the way for memory-in-logic applications.

Publisher Correction: Nanomagnetic encoding of shape-morphing micromachines.

An Amendment to this paper has been published and can be accessed via a link at the top of the paper.

Nanomagnetic encoding of shape-morphing micromachines.

Shape-morphing systems, which can perform complex tasks through morphological transformations, are of great interest for future applications in minimally invasive medicine1,2, soft robotics3-6, active metamaterials7 and smart surfaces8. With current fabrication methods, shape-morphing configurations have been embedded into structural design by, for example, spatial distribution of heterogeneous materials9-14, which cannot be altered once fabricated. The systems are therefore restricted to a single type of transformation that is predetermined by their geometry. Here we develop a strategy to encode multiple shape-morphing instructions into a micromachine by programming the magnetic configurations of arrays of single-domain nanomagnets on connected panels. This programming is achieved by applying a specific sequence of magnetic fields to nanomagnets with suitably tailored switching fields, and results in specific shape transformations of the customized micromachines under an applied magnetic field. Using this concept, we have built an assembly of modular units that can be programmed to morph into letters of the alphabet, and we have constructed a microscale 'bird' capable of complex behaviours, including 'flapping', 'hovering', 'turning' and 'side-slipping'. This establishes a route for the creation of future intelligent microsystems that are reconfigurable and reprogrammable in situ, and that can therefore adapt to complex situations.

Three-dimensional magnetization structures revealed with X-ray vector nanotomography.

In soft ferromagnetic materials, the smoothly varying magnetization leads to the formation of fundamental patterns such as domains, vortices and domain walls. These have been studied extensively in thin films of thicknesses up to around 200 nanometres, in which the magnetization is accessible with current transmission imaging methods that make use of electrons or soft X-rays. In thicker samples, however, in which the magnetization structure varies throughout the thickness and is intrinsically three dimensional, determining the complex magnetic structure directly still represents a challenge. We have developed hard-X-ray vector nanotomography with which to determine the three-dimensional magnetic configuration at the nanoscale within micrometre-sized samples. We imaged the structure of the magnetization within a soft magnetic pillar of diameter 5 micrometres with a spatial resolution of 100 nanometres and, within the bulk, observed a complex magnetic configuration that consists of vortices and antivortices that form cross-tie walls and vortex walls along intersecting planes. At the intersections of these structures, magnetic singularities-Bloch points-occur. These were predicted more than fifty years ago but have so far not been directly observed. Here we image the three-dimensional magnetic structure in the vicinity of the Bloch points, which until now has been accessible only through micromagnetic simulations, and identify two possible magnetization configurations: a circulating magnetization structure and a twisted state that appears to correspond to an 'anti-Bloch point'. Our imaging method enables the nanoscale study of topological magnetic structures in systems with sizes of the order of tens of micrometres. Knowledge of internal nanomagnetic textures is critical for understanding macroscopic magnetic properties and for designing bulk magnets for technological applications.

Spin-Wave Dynamics and Symmetry Breaking in an Artificial Spin Ice.

Artificial spin ices are periodic arrangements of interacting nanomagnets which allow investigating emergent phenomena in the presence of geometric frustration. Recently, it has been shown that artificial spin ices can be used as building blocks for creating functional materials, such as magnonic crystals. We investigate the magnetization dynamics in a system exhibiting anisotropic magnetostatic interactions owing to locally broken structural inversion symmetry. We find a rich spin-wave spectrum and investigate its evolution in an external magnetic field. We determine the evolution of individual modes, from building blocks up to larger arrays, highlighting the role of symmetry breaking in defining the mode profiles. Moreover, we demonstrate that the mode spectra exhibit signatures of long-range interactions in the system. These results contribute to the understanding of magnetization dynamics in spin ices beyond the kagome and square ice geometries and are relevant for the realization of reconfigurable magnonic crystals based on spin ices.

Spin-Wave Emission from Vortex Cores under Static Magnetic Bias Fields.

We studied the influence of a static in-plane magnetic field on the alternating-field-driven emission of nanoscale spin waves from magnetic vortex cores. Time-resolved scanning transmission X-ray microscopy was used to image spin waves in disk structures of synthetic ferrimagnets and single ferromagnetic layers. For both systems, it was found that an increasing magnetic bias field continuously displaces the wave-emitting vortex core from the center of the disk toward its edge without noticeably altering the spin-wave dispersion relation. In the case of the single-layer disk, an anisotropic lateral expansion of the core occurs at higher magnetic fields, which leads to a directional rather than radial-isotropic emission and propagation of waves. Micromagnetic simulations confirm these findings and further show that focusing effects occur in such systems, depending on the shape of the core and controlled by the static magnetic bias field.

Electroless Deposition of Ni-Fe Alloys on Scaffolds for 3D Nanomagnetism.

3D magnetic nanostructures are of great interest due to the possibility to design novel properties and the benefits for both technological applications such as high-density data storage, as well as more fundamental studies. One of the main challenges facing the realization of these three-dimensional systems is their fabrication, which includes the deposition of magnetic materials on 3D surfaces. In this work, the electroless deposition of Ni-Fe on a 3D-printed, non-conductive microstructure is presented. The deposited films exhibit low coercivity, with the saturation magnetization and composition corresponding to the archetypal soft magnetic material permalloy. For fundamental studies of 3D micromagnetism, this new development in fabrication offers the possibility to combine the flexibility of 3D nanofabrication techniques such as two-photon lithography for the fabrication of 3D scaffolds with a homogeneous soft ferromagnetic thin film, and thus represents an important step toward exploring the rich physics of complex 3D magnetic architectures with tailored properties and the development of advanced applications.

Switchable adhesion of soft composites induced by a magnetic field.

Switchable adhesives have the potential to improve the manufacturing and recycling of parts, and to enable new modes of motility for soft robots. Here, we demonstrate magnetically-switchable adhesion of a two-phase composite to non-magnetic objects. The composite's continuous phase is a silicone elastomer, and the dispersed phase is a magneto-rheological fluid. The composite is simple to prepare, and to mold into different shapes. When a magnetic field is applied, the magneto-rheological fluid develops a yield stress, which dramatically enhances the composite's adhesive properties. We demonstrate up to a nine-fold increase of the pull-off force of non-magnetic objects in the presence of a 250 mT field.

Chiral Domain Wall Injector Driven by Spin-Orbit Torques.

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, which is induced by the Dzyaloshinskii-Moriya interaction, between in-plane and out-of-plane magnetized regions of a Pt/Co/AlOx 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 × 1011 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.

Emergent dynamic chirality in a thermally driven artificial spin ratchet.

Modern nanofabrication techniques have opened the possibility to create novel functional materials, whose properties transcend those of their constituent elements. In particular, tuning the magnetostatic interactions in geometrically frustrated arrangements of nanoelements called artificial spin ice can lead to specific collective behaviour, including emergent magnetic monopoles, charge screening and transport, as well as magnonic response. Here, we demonstrate a spin-ice-based active material in which energy is converted into unidirectional dynamics. Using X-ray photoemission electron microscopy we show that the collective rotation of the average magnetization proceeds in a unique sense during thermal relaxation. Our simulations demonstrate that this emergent chiral behaviour is driven by the topology of the magnetostatic field at the edges of the nanomagnet array, resulting in an asymmetric energy landscape. In addition, a bias field can be used to modify the sense of rotation of the average magnetization. This opens the possibility of implementing a magnetic Brownian ratchet, which may find applications in novel nanoscale devices, such as magnetic nanomotors, actuators, sensors or memory cells.

Generation of coherent extreme ultraviolet radiation from α-quartz using 50 fs laser pulses at a 1030 nm wavelength and high repetition rates.

Coherent extreme ultraviolet (EUV) radiation using high-harmonic generation (HHG) in α-quartz is demonstrated from 10 to 200 kHz, using 50 fs laser pulses at the center wavelength of 1030 nm. The EUV radiation extends beyond 25 eV in the nondamaging regime. The number of photons generated in a single harmonic order at 15.6 eV is measured to be ≈(3.5±2.5)×1010 per second which, to the best of our knowledge, is a first and record value reported to date using EUV HHG from solids. This Letter demonstrates one of the first all-solid-state EUV sources based on industrial-grade fiber lasers, enabling the possibility of bringing reliable EUV sources to the mass market.

Computational logic with square rings of nanomagnets.

Nanomagnets are a promising low-power alternative to traditional computing. However, the successful implementation of nanomagnets in logic gates has been hindered so far by a lack of reliability. Here, we present a novel design with dipolar-coupled nanomagnets arranged on a square lattice to (i) support transfer of information and (ii) perform logic operations. We introduce a thermal protocol, using thermally active nanomagnets as a means to perform computation. Within this scheme, the nanomagnets are initialized by a global magnetic field and thermally relax on raising the temperature with a resistive heater. We demonstrate error-free transfer of information in chains of up to 19 square rings and we show a high level of reliability with successful gate operations of ∼94% across more than 2000 logic gates. Finally, we present a functionally complete prototype NAND/NOR logic gate that could be implemented for advanced logic operations. Here we support our experiments with simulations of the thermally averaged output and determine the optimal gate parameters. Our approach provides a new pathway to a long standing problem concerning reliability in the use of nanomagnets for computation.

Element-specific X-ray phase tomography of 3D structures at the nanoscale.

Recent advances in fabrication techniques to create mesoscopic 3D structures have led to significant developments in a variety of fields including biology, photonics, and magnetism. Further progress in these areas benefits from their full quantitative and structural characterization. We present resonant ptychographic tomography, combining quantitative hard x-ray phase imaging and resonant elastic scattering to achieve ab initio element-specific 3D characterization of a cobalt-coated artificial buckyball polymer scaffold at the nanoscale. By performing ptychographic x-ray tomography at and far from the Co K edge, we are able to locate and quantify the Co layer in our sample to a 3D spatial resolution of 25 nm. With a quantitative determination of the electron density we can determine that the Co layer is oxidized, which is confirmed with microfluorescence experiments.

Domain-wall induced large magnetoresistance effects at zero applied field in ballistic nanocontacts.

We determine magnetoresistance effects in stable and clean Permalloy nanocontacts of variable cross section, fabricated by UHV deposition and in situ electromigration. To ascertain the magnetoresistance (MR) effects originating from a magnetic domain wall, we measure the resistance values with and without such a wall at zero applied field. In the ballistic transport regime, the MR ratio reaches up to 50% and exhibits a previously unobserved sign change. Our results can be reproduced by recent atomistic calculations for different atomic configurations of the nanocontact, highlighting the importance of the detailed atomic arrangement for the MR effect.

Electrically programmable magnetic coupling in an Ising network exploiting solid-state ionic gating.

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 behavior 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 the magnetic anisotropy in a nanosized region where the symmetric exchange interaction favors parallel alignment and the antisymmetric exchange interaction, namely the Dzyaloshinskii-Moriya interaction, favors antiparallel alignment of the nanomagnet magnetizations. 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.

Element-specific hysteresis loop measurements on Individual 35 nm islands with scanning transmission X-ray microscopy.

Using scanning transmission X-ray microscopy combined with X-ray magnetic circular dichroism, element-specific hysteresis loops with a 25 nm X-ray probe are obtained on 35 nm Fe/Gd multilayer nanoislands fabricated by extreme ultra-violet interference lithography. Local hysteresis loops measured for the individual islands and the antidot film between the islands display similar behavior resulting from the lateral confinement. Line scan measurements confirm ferrimagnetic coupling between Fe and Gd in the patterned region. The ability to measure magnetization reversal with X-rays at high spatial resolution will provide an important tool for future characterization of sub-50 nm nanostructures.

Route to tunable room temperature electric polarization in SrTiO3-CoFe2O4 heterostructures.

Utilizing the magnetostrictive properties of CoFe2O4, we demonstrate reversible room temperature control of the Ti electronic structure in SrTiO3-CoFe2O4 heterostructures, by inducing local and reversible strain in the SrTiO3. By means of X-ray absorption spectroscopy, we have ascertained the changes that take place in the energy levels of the Ti 3d orbitals under the influence of an external magnetic field. The observed Ti electronic state when the sample is subjected to moderately large external magnetic fields and the disappearance of the induced phase upon their removal indicates lattice distortions that are suggestive of the development of a net electric polarization.

Direct observation of spin correlations in an artificial triangular lattice Ising spin system with grazing-incidence small-angle neutron scattering.

The triangular lattice with Ising magnetic moments is an archetypical example of geometric frustration. In the case of dipolar-coupled out-of-plane moments, the geometric frustration results in a disordered classical spin-liquid state at higher temperatures while the system is predicted to transition to an anti-ferromagnetic stripe ground state at low temperatures. In this work we fabricate artificial triangular Ising spin systems without and with uniaxial in-plane compression to tune the nature and temperature of the correlations. We probe the energy scale and nature of magnetic correlations by grazing-incidence small-angle neutron scattering. In particular, we apply a newly-developed empirical structure-factor model to describe the measured short-range correlated spin-liquid state, and find good agreement with theoretical predictions. We demonstrate that grazing-incidence neutron scattering on our high-quality samples, in conjunction with detailed modeling of the scattering using the Distorted Wave Born Approximation, can be used to experimentally quantify the spin-liquid-like correlations in highly-frustrated artificial spin systems.

Relation between microscopic interactions and macroscopic properties in ferroics.

The driving force in materials to spontaneously form states with magnetic or electric order is of fundamental importance for basic research and device technology. The macroscopic properties and functionalities of these ferroics depend on the size, distribution and morphology of domains; that is, of regions across which such uniform order is maintained1. Typically, extrinsic factors such as strain profiles, grain size or annealing procedures control the size and shape of the domains2-5, whereas intrinsic parameters are often difficult to extract due to the complexity of a processed material. Here, we achieve this separation by building artificial crystals of planar nanomagnets that are coupled by well-defined, tuneable and competing magnetic interactions6-9. Aside from analysing the domain configurations, we uncover fundamental intrinsic correlations between the microscopic interactions establishing magnetically compensated order and the macroscopic manifestations of these interactions in basic physical properties. Experiment and simulations reveal how competing interactions can be exploited to control ferroic hallmark properties such as the size and morphology of domains, topological properties of domain walls or their thermal mobility.

Time-resolved imaging of three-dimensional nanoscale magnetization dynamics.

Understanding and control of the dynamic response of magnetic materials with a three-dimensional magnetization distribution is important both fundamentally and for technological applications. From a fundamental point of view, the internal magnetic structure and dynamics in bulk materials still need to be mapped1, including the dynamic properties of topological structures such as vortices2, magnetic singularities3 or skyrmion lattices4. From a technological point of view, the response of inductive materials to magnetic fields and spin-polarized currents is essential for magnetic sensors and data storage devices5. Here, we demonstrate time-resolved magnetic laminography, a pump-probe technique, which offers access to the temporal evolution of a three-dimensional magnetic microdisc with nanoscale resolution, and with a synchrotron-limited temporal resolution of 70 ps. We image the dynamic response to a 500 MHz magnetic field of the complex three-dimensional magnetization in a two-phase bulk magnet with a lateral spatial resolution of 50 nm. This is achieved with a stroboscopic measurement consisting of eight time steps evenly spaced over 2 ns. These measurements map the spatial transition between domain wall motion and the dynamics of a uniform magnetic domain that is attributed to variations in the magnetization state across the phase boundary. Our technique, which probes three-dimensional magnetic structures with temporal resolution, enables the experimental investigation of functionalities arising from dynamic phenomena in bulk and three-dimensional patterned nanomagnets6.