Integer factorization using stochastic magnetic tunnel junctions.

Conventional computers operate deterministically using strings of zeros and ones called bits to represent information in binary code. Despite the evolution of conventional computers into sophisticated machines, there are many classes of problems that they cannot efficiently address, including inference, invertible logic, sampling and optimization, leading to considerable interest in alternative computing schemes. Quantum computing, which uses qubits to represent a superposition of 0 and 1, is expected to perform these tasks efficiently1-3. However, decoherence and the current requirement for cryogenic operation4, as well as the limited many-body interactions that can be implemented, pose considerable challenges. Probabilistic computing1,5-7 is another unconventional computation scheme that shares similar concepts with quantum computing but is not limited by the above challenges. The key role is played by a probabilistic bit (a p-bit)-a robust, classical entity fluctuating in time between 0 and 1, which interacts with other p-bits in the same system using principles inspired by neural networks8. Here we present a proof-of-concept experiment for probabilistic computing using spintronics technology, and demonstrate integer factorization, an illustrative example of the optimization class of problems addressed by adiabatic9 and gated2 quantum computing. Nanoscale magnetic tunnel junctions showing stochastic behaviour are developed by modifying market-ready magnetoresistive random-access memory technology10,11 and are used to implement three-terminal p-bits that operate at room temperature. The p-bits are electrically connected to form a functional asynchronous network, to which a modified adiabatic quantum computing algorithm that implements three- and four-body interactions is applied. Factorization of integers up to 945 is demonstrated with this rudimentary asynchronous probabilistic computer using eight correlated p-bits, and the results show good agreement with theoretical predictions, thus providing a potentially scalable hardware approach to the difficult problems of optimization and sampling.

Coherent antiferromagnetic spintronics.

Antiferromagnets have attracted extensive interest as a material platform in spintronics. So far, antiferromagnet-enabled spin-orbitronics, spin-transfer electronics and spin caloritronics have formed the bases of antiferromagnetic spintronics. Spin transport and manipulation based on coherent antiferromagnetic dynamics have recently emerged, pushing the developing field of antiferromagnetic spintronics towards a new stage distinguished by the features of spin coherence. In this Review, we categorize and analyse the critical effects that harness the coherence of antiferromagnets for spintronic applications, including spin pumping from monochromatic antiferromagnetic magnons, spin transmission via phase-correlated antiferromagnetic magnons, electrically induced spin rotation and ultrafast spin-orbit effects in antiferromagnets. We also discuss future opportunities in research and applications stimulated by the principles, materials and phenomena of coherent antiferromagnetic spintronics.

Handedness anomaly in a non-collinear antiferromagnet under spin-orbit torque.

Non-collinear antiferromagnets are an emerging family of spintronic materials because they not only possess the general advantages of antiferromagnets but also enable more advanced functionalities. Recently, in an intriguing non-collinear antiferromagnet Mn3Sn, where the octupole moment is defined as the collective magnetic order parameter, spin-orbit torque (SOT) switching has been achieved in seemingly the same protocol as in ferromagnets. Nevertheless, it is fundamentally important to explore the unknown octupole moment dynamics and contrast it with the magnetization vector of ferromagnets. Here we report a handedness anomaly in the SOT-driven dynamics of Mn3Sn: when spin current is injected, the octupole moment rotates in the opposite direction to the individual moments, leading to a SOT switching polarity distinct from ferromagnets. By using second-harmonic and d.c. magnetometry, we track the SOT effect onto the octupole moment during its rotation and reveal that the handedness anomaly stems from the interactions between the injected spin and the unique chiral-spin structure of Mn3Sn. We further establish the torque balancing equation of the magnetic octupole moment and quantify the SOT efficiency. Our finding provides a guideline for understanding and implementing the electrical manipulation of non-collinear antiferromagnets, which in nature differs from the well-established collinear magnets.

Memristive control of mutual spin Hall nano-oscillator synchronization for neuromorphic computing.

Synchronization of large spin Hall nano-oscillator (SHNO) arrays is an appealing approach toward ultrafast non-conventional computing. However, interfacing to the array, tuning its individual oscillators and providing built-in memory units remain substantial challenges. Here, we address these challenges using memristive gating of W/CoFeB/MgO/AlOx-based SHNOs. In its high resistance state, the memristor modulates the perpendicular magnetic anisotropy at the CoFeB/MgO interface by the applied electric field. In its low resistance state the memristor adds or subtracts current to the SHNO drive. Both electric field and current control affect the SHNO auto-oscillation mode and frequency, allowing us to reversibly turn on/off mutual synchronization in chains of four SHNOs. We also demonstrate that two individually controlled memristors can be used to tune a four-SHNO chain into differently synchronized states. Memristor gating is therefore an efficient approach to input, tune and store the state of SHNO arrays for non-conventional computing models.

Chiral-spin rotation of non-collinear antiferromagnet by spin-orbit torque.

Electrical manipulation of magnetic materials by current-induced spin torque constitutes the basis of spintronics. Here, we show an unconventional response to spin-orbit torque of a non-collinear antiferromagnet Mn3Sn, which has attracted attention owing to its large anomalous Hall effect despite a vanishingly small net magnetization. In epitaxial heavy-metal/Mn3Sn heterostructures, we observe a characteristic fluctuation of the Hall resistance under the application of electric current. This observation is explained by a rotation of the chiral-spin structure of Mn3Sn driven by spin-orbit torque. We find that the variation of the magnitude of anomalous Hall effect fluctuation with sample size correlates with the number of magnetic domains in the Mn3Sn layer. In addition, the dependence of the critical current on Mn3Sn layer thickness reveals that spin-orbit torque generated by small current densities, below 20 MA cm-2, effectively acts on the chiral-spin structure even in Mn3Sn layers that are thicker than 20 nm. The results provide additional pathways for electrical manipulation of magnetic materials.

Theory of Emergent Inductance with Spin-Orbit Coupling Effects.

We extend the theory of emergent inductance, which has recently been discovered in spiral magnets, to arbitrary magnetic textures by taking into account spin-orbit couplings arising in the absence of spatial inversion symmetry. We propose a new concept of spin-orbit emergent inductance, which can be formulated as originating from a dynamical Aharonov-Casher phase of an electron in ferromagnets. The spin-orbit emergent inductance universally arises in the coexistence of magnetism and the spin-orbit couplings, even with spatially uniform magnetization, allowing its stable operation in wide ranges of temperature and frequency. Revisiting the widely studied systems involving ferromagnets with spatial inversion asymmetry, with the new perspective offered by our work, will lead to opening a new paradigm in the study of spin-orbit physics and the spintronics-based power management in ultrawideband frequency range.

Engineering Single-Shot All-Optical Switching of Ferromagnetic Materials.

Since it was recently demonstrated in a spin-valve structure, magnetization reversal of a ferromagnetic layer using a single ultrashort optical pulse has attracted attention for future ultrafast and energy-efficient magnetic storage or memory devices. However, the mechanism and the role of the magnetic properties of the ferromagnet as well as the time scale of the magnetization switching are not understood. Here, we investigate single-shot all-optical magnetization switching in a GdFeCo/Cu/[CoxNi1-x/Pt] spin-valve structure. We demonstrate that the threshold fluence for switching both the GdFeCo and the ferromagnetic layer depends on the laser pulse duration and the thickness and the Curie temperature of the ferromagnetic layer. We are able to explain most of the experimental results using a phenomenological model. This work provides a way to engineer ferromagnetic materials for energy efficient single-shot all-optical magnetization switching.

Visualizing Magnetic Structure in 3D Nanoscale Ni-Fe Gyroid Networks.

Arrays of interacting 2D nanomagnets display unprecedented electromagnetic properties via collective effects, demonstrated in artificial spin ices and magnonic crystals. Progress toward 3D magnetic metamaterials is hampered by two challenges: fabricating 3D structures near intrinsic magnetic length scales (sub-100 nm) and visualizing their magnetic configurations. Here, we fabricate and measure nanoscale magnetic gyroids, periodic chiral networks comprising nanowire-like struts forming three-connected vertices. Via block copolymer templating, we produce Ni75Fe25 single-gyroid and double-gyroid (an inversion pair of single-gyroids) nanostructures with a 42 nm unit cell and 11 nm diameter struts, comparable to the exchange length in Ni-Fe. We visualize their magnetization distributions via off-axis electron holography with nanometer spatial resolution and interpret the patterns using finite-element micromagnetic simulations. Our results suggest an intricate, frustrated remanent state which is ferromagnetic but without a unique equilibrium configuration, opening new possibilities for collective phenomena in magnetism, including 3D magnonic crystals and unconventional computing.

Roadmap of spin-orbit torques.

Spin-orbit torque (SOT) is an emerging technology that enables the efficient manipulation of spintronic devices. The initial processes of interest in SOTs involved electric fields, spin-orbit coupling, conduction electron spins and magnetization. More recently interest has grown to include a variety of other processes that include phonons, magnons, or heat. Over the past decade, many materials have been explored to achieve a larger SOT efficiency. Recently, holistic design to maximize the performance of SOT devices has extended material research from a nonmagnetic layer to a magnetic layer. The rapid development of SOT has spurred a variety of SOT-based applications. In this Roadmap paper, we first review the theories of SOTs by introducing the various mechanisms thought to generate or control SOTs, such as the spin Hall effect, the Rashba-Edelstein effect, the orbital Hall effect, thermal gradients, magnons, and strain effects. Then, we discuss the materials that enable these effects, including metals, metallic alloys, topological insulators, two-dimensional materials, and complex oxides. We also discuss the important roles in SOT devices of different types of magnetic layers, such as magnetic insulators, antiferromagnets, and ferrimagnets. Afterward, we discuss device applications utilizing SOTs. We discuss and compare three-terminal and two-terminal SOT-magnetoresistive random-access memories (MRAMs); we mention various schemes to eliminate the need for an external field. We provide technological application considerations for SOT-MRAM and give perspectives on SOT-based neuromorphic devices and circuits. In addition to SOT-MRAM, we present SOT-based spintronic terahertz generators, nano-oscillators, and domain wall and skyrmion racetrack memories. This paper aims to achieve a comprehensive review of SOT theory, materials, and applications, guiding future SOT development in both the academic and industrial sectors.

Magnetization switching by spin-orbit torque in an antiferromagnet-ferromagnet bilayer system.

Spin-orbit torque (SOT)-induced magnetization switching shows promise for realizing ultrafast and reliable spintronics devices. Bipolar switching of the perpendicular magnetization by the SOT is achieved under an in-plane magnetic field collinear with an applied current. Typical structures studied so far comprise a nonmagnet/ferromagnet (NM/FM) bilayer, where the spin Hall effect in the NM is responsible for the switching. Here we show that an antiferromagnet/ferromagnet (AFM/FM) bilayer system also exhibits a SOT large enough to switch the magnetization of the FM. In this material system, thanks to the exchange bias of the AFM, we observe the switching in the absence of an applied field by using an antiferromagnetic PtMn and ferromagnetic Co/Ni multilayer with a perpendicular easy axis. Furthermore, tailoring the stack achieves a memristor-like behaviour where a portion of the reversed magnetization can be controlled in an analogue manner. The AFM/FM system is thus a promising building block for SOT devices as well as providing an attractive pathway towards neuromorphic computing.

Atomic-Scale Structure and Local Chemistry of CoFeB-MgO Magnetic Tunnel Junctions.

Magnetic tunnel junctions (MTJs) constitute a promising building block for future nonvolatile memories and logic circuits. Despite their pivotal role, spatially resolving and chemically identifying each individual stacking layer remains challenging due to spatially localized features that complicate characterizations limiting understanding of the physics of MTJs. Here, we combine advanced electron microscopy, spectroscopy, and first-principles calculations to obtain a direct structural and chemical imaging of the atomically confined layers in a CoFeB-MgO MTJ, and clarify atom diffusion and interface structures in the MTJ following annealing. The combined techniques demonstrate that B diffuses out of CoFeB electrodes into Ta interstitial sites rather than MgO after annealing, and CoFe bonds atomically to MgO grains with an epitaxial orientation relationship by forming Fe(Co)-O bonds, yet without incorporation of CoFe in MgO. These findings afford a comprehensive perspective on structure and chemistry of MTJs, helping to develop high-performance spintronic devices by atomistic design.

Layer thickness dependence of the current-induced effective field vector in Ta|CoFeB|MgO.

Current-induced effective magnetic fields can provide efficient ways of electrically manipulating the magnetization of ultrathin magnetic heterostructures. Two effects, known as the Rashba spin orbit field and the spin Hall spin torque, have been reported to be responsible for the generation of the effective field. However, a quantitative understanding of the effective field, including its direction with respect to the current flow, is lacking. Here we describe vector measurements of the current-induced effective field in Ta|CoFeB|MgO heterostructrures. The effective field exhibits a significant dependence on the Ta and CoFeB layer thicknesses. In particular, a 1 nm thickness variation of the Ta layer can change the magnitude of the effective field by nearly two orders of magnitude. Moreover, its sign changes when the Ta layer thickness is reduced, indicating that there are two competing effects contributing to it. Our results illustrate that the presence of atomically thin metals can profoundly change the landscape for controlling magnetic moments in magnetic heterostructures electrically.

CMOS plus stochastic nanomagnets enabling heterogeneous computers for probabilistic inference and learning.

Extending Moore's law by augmenting complementary-metal-oxide semiconductor (CMOS) transistors with emerging nanotechnologies (X) has become increasingly important. One important class of problems involve sampling-based Monte Carlo algorithms used in probabilistic machine learning, optimization, and quantum simulation. Here, we combine stochastic magnetic tunnel junction (sMTJ)-based probabilistic bits (p-bits) with Field Programmable Gate Arrays (FPGA) to create an energy-efficient CMOS + X (X = sMTJ) prototype. This setup shows how asynchronously driven CMOS circuits controlled by sMTJs can perform probabilistic inference and learning by leveraging the algorithmic update-order-invariance of Gibbs sampling. We show how the stochasticity of sMTJs can augment low-quality random number generators (RNG). Detailed transistor-level comparisons reveal that sMTJ-based p-bits can replace up to 10,000 CMOS transistors while dissipating two orders of magnitude less energy. Integrated versions of our approach can advance probabilistic computing involving deep Boltzmann machines and other energy-based learning algorithms with extremely high throughput and energy efficiency.

Collective Spin-Wave Dynamics in Gyroid Ferromagnetic Nanostructures.

Expanding upon the burgeoning discipline of magnonics, this research elucidates the intricate dynamics of spin waves (SWs) within three-dimensional nanoenvironments. It marks a shift from traditionally used planar systems to exploration of magnetization configurations and the resulting dynamics within 3D nanostructures. This study deploys micromagnetic simulations alongside ferromagnetic resonance measurements to scrutinize magnetic gyroids, periodic chiral configurations composed of chiral triple junctions with a period in nanoscale. Our findings uncover distinctive attributes intrinsic to the gyroid network, most notably the localization of collective SW excitations and the sensitivity of the gyroid's ferromagnetic response to the orientation of the static magnetic field, a correlation closely tied to the crystallographic alignment of the structure. Furthermore, we show that for the ferromagnetic resonance, multidomain gyroid films can be treated as a magnonic material with effective magnetization scaled by its filling factor. The implications of our research carry the potential for practical uses such as an effective, metamaterial-like substitute for ferromagnetic parts and lay the groundwork for radio frequency filters. The growing areas of 3D magnonics and spintronics present exciting opportunities to investigate and utilize gyroid nanostructures for signal processing purposes.

Directed Self-Assembly of Diamond Networks in Triblock Terpolymer Films on Patterned Substrates.

Block copolymers (BCPs) are particularly effective in creating soft nanostructured templates for transferring complex 3D network structures into inorganic materials that are difficult to fabricate by other methods. However, achieving control of the local ordering within these 3D networks over large areas remains a significant obstacle to advancing material properties. Here, we address this challenge by directing the self-assembly of a 3D alternating diamond morphology by solvent vapor annealing of a triblock terpolymer film on a chemically patterned substrate. The hexagonal substrate patterns were designed to match a (111) plane of the diamond lattice. Commensurability between the sparse substrate pattern and the BCP lattice produced a uniformly ordered diamond network within the polymer film, as confirmed by a combination of atomic force microscopy and cross-sectional imaging using focused ion beam scanning electron microscopy. The successful replication of the complex and well-ordered 3D network structure in gold promises to advance optical metamaterials and has potential applications in nanophotonics.

Local bifurcation with spin-transfer torque in superparamagnetic tunnel junctions.

Modulation of the energy landscape by external perturbations governs various thermally-activated phenomena, described by the Arrhenius law. Thermal fluctuation of nanoscale magnetic tunnel junctions with spin-transfer torque (STT) shows promise for unconventional computing, whereas its rigorous representation, based on the Néel-Arrhenius law, has been controversial. In particular, the exponents for thermally-activated switching rate therein, have been inaccessible with conventional thermally-stable nanomagnets with decade-long retention time. Here we approach the Néel-Arrhenius law with STT utilising superparamagnetic tunnel junctions that have high sensitivity to external perturbations and determine the exponents through several independent measurements including homodyne-detected ferromagnetic resonance, nanosecond STT switching, and random telegraph noise. Furthermore, we show that the results are comprehensively described by a concept of local bifurcation observed in various physical systems. The findings demonstrate the capability of superparamagnetic tunnel junction as a useful tester for statistical physics as well as sophisticated engineering of probabilistic computing hardware with a rigorous mathematical foundation.

Unconventional Hall effect and its variation with Co-doping in van der Waals Fe3GeTe2.

Two-dimensional (2D) van der Waals (vdW) magnetic materials have attracted a lot of attention owing to the stabilization of long range magnetic order down to atomic dimensions, and the prospect of novel spintronic devices with unique functionalities. The clarification of the magnetoresistive properties and its correlation to the underlying magnetic configurations is essential for 2D vdW-based spintronic devices. Here, the effect of Co-doping on the magnetic and magnetotransport properties of Fe3GeTe2 have been investigated. Magnetotransport measurements reveal an unusual Hall effect behavior whose strength was considerably modified by Co-doping and attributed to arise from the underlying complicated spin textures. The present results provide a clue to tailoring of the underlying interactions necessary for the realization of a variety of unconventional spin textures for 2D vdW FM-based spintronics.

Electrically connected spin-torque oscillators array for 2.4 GHz WiFi band transmission and energy harvesting.

The mutual synchronization of spin-torque oscillators (STOs) is critical for communication, energy harvesting and neuromorphic applications. Short range magnetic coupling-based synchronization has spatial restrictions (few µm), whereas the long-range electrical synchronization using vortex STOs has limited frequency responses in hundreds MHz (<500 MHz), restricting them for on-chip GHz-range applications. Here, we demonstrate electrical synchronization of four non-vortex uniformly-magnetized STOs using a single common current source in both parallel and series configurations at 2.4 GHz band, resolving the frequency-area quandary for designing STO based on-chip communication systems. Under injection locking, synchronized STOs demonstrate an excellent time-domain stability and substantially improved phase noise performance. By integrating the electrically connected eight STOs, we demonstrate the battery-free energy-harvesting system by utilizing the wireless radio-frequency energy to power electronic devices such as LEDs. Our results highlight the significance of electrical topology (series vs. parallel) while designing an on-chip STOs system.

Giant voltage-controlled modulation of spin Hall nano-oscillator damping.

Spin Hall nano-oscillators (SHNOs) are emerging spintronic devices for microwave signal generation and oscillator-based neuromorphic computing combining nano-scale footprint, fast and ultra-wide microwave frequency tunability, CMOS compatibility, and strong non-linear properties providing robust large-scale mutual synchronization in chains and two-dimensional arrays. While SHNOs can be tuned via magnetic fields and the drive current, neither approach is conducive to individual SHNO control in large arrays. Here, we demonstrate electrically gated W/CoFeB/MgO nano-constrictions in which the voltage-dependent perpendicular magnetic anisotropy tunes the frequency and, thanks to nano-constriction geometry, drastically modifies the spin-wave localization in the constriction region resulting in a giant 42% variation of the effective damping over four volts. As a consequence, the SHNO threshold current can be strongly tuned. Our demonstration adds key functionality to nano-constriction SHNOs and paves the way for energy-efficient control of individual oscillators in SHNO chains and arrays for neuromorphic computing.

Energy Efficient Control of Ultrafast Spin Current to Induce Single Femtosecond Pulse Switching of a Ferromagnet.

New methods to induce magnetization switching in a thin ferromagnetic material using femtosecond laser pulses without the assistance of an applied external magnetic field have recently attracted a lot of interest. It has been shown that by optically triggering the reversal of the magnetization in a GdFeCo layer, the magnetization of a nearby ferromagnetic thin film can also be reversed via spin currents originating in the GdFeCo layer. Here, using a similar structure, it is shown that the magnetization reversal of the GdFeCo is not required in order to reverse the magnetization of the ferromagnetic thin film. This switching is attributed to the ultrafast spin current and can be generated by the GdFeCo demagnetization. A larger energy efficiency of the ferromagnetic layer single pulse switching is obtained for a GdFeCo with a larger Gd concentration. Those ultrafast and energy efficient switchings observed in such spintronic devices open a new path toward ultrafast and energy efficient magnetic memories.