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.

Three-Dimensional Vortex Gyration Dynamics Unraveled by Time-Resolved Soft X-ray Laminography with Freely Selectable Excitation Frequencies.

The imaging of magneto-dynamical processes has been, so far, mostly a two-dimensional business, also due to the constraints of the available experimental techniques. In this paper, 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 at arbitrary frequencies. We employ this setup to investigate two resonant dynamical modes of a CoFeB microstructure, namely, the fundamental vortex gyration mode and a magnetic field-induced domain wall excitation mode. For the former, we observe a large variation of the gyration dynamics across the thickness of the core, coexisting with a breathing mode of the vortex core. For the latter, we observe a uniform displacement of the domain walls across the thickness of the microstructure. The imaging of these two modes establishes the possibility to freely select the excitation frequency for soft X-ray time-resolved laminography, allowing for the investigation of resonant magneto-dynamical processes.

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.

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.

Tuning spin-orbit torques at magnetic domain walls in epitaxial Pt/Co/Pt1-x Au x trilayers.

Magnetic domain walls (DWs) in perpendicularly magnetised thin films are attractive for racetrack memories, but technological progress still requires further reduction of the operationing currents. To efficiently drive these objects by the means of electric current, one has to optimize the damping-like torque which is caused by the spin Hall effect (SHE). This not only requires a high net spin Hall angle but also the presence of a Dzyaloshinskii-Moriya interaction (DMI) to produce magnetic textures sensitive to this type of the torque. In this work, we explore the coexistence and importance of these two phenomena in epitaxial Pt/Co/Pt1-x Au x films in which we control the degree of inversion symmetry-breaking between the two interfaces by varying x. Gold is used as a material with negligible induced magnetic moment and SHE and the interface between Co/Au as a source of a small DMI. We find no current-induced DW motion in the symmetric Pt/Co/Pt (x = 0) trilayer. By fitting a one-dimensional model to the DW velocity as a function of drive current density and in-plane applied field in samples with non-zero values of x, we find that both net DMI strength and spin Hall angle rise monotonically as Au is introduced. They reach values of 0.75 ± 0.05 mJ m-2 and 0.10 ± 0.01, respectively, for Pt/Co/Au (x = 1).

Velocity Enhancement by Synchronization of Magnetic Domain Walls.

Magnetic domain walls are objects whose dynamics is inseparably connected to their structure. In this Letter, 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.

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.

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.

Author Correction: Thermally and field-driven mobility of emergent magnetic charges in square artificial spin ice.

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

Thermally and field-driven mobility of emergent magnetic charges in square artificial spin ice.

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.

Chirally coupled nanomagnets.

Magnetically coupled nanomagnets have multiple applications in nonvolatile memories, logic gates, and sensors. The most effective couplings have been found to occur between the magnetic layers in a vertical stack. We achieved strong coupling of laterally adjacent nanomagnets using the interfacial Dzyaloshinskii-Moriya interaction. This coupling is mediated by chiral domain walls between out-of-plane and in-plane magnetic regions and dominates the behavior of nanomagnets below a critical size. We used this concept to realize lateral exchange bias, field-free current-induced switching between multistate magnetic configurations as well as synthetic antiferromagnets, skyrmions, and artificial spin ices covering a broad range of length scales and topologies. Our work provides a platform to design arrays of correlated nanomagnets and to achieve all-electric control of planar logic gates and memory devices.