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.

Generalized scaling of spin qubit coherence in over 12,000 host materials.

SignificanceAtomic defects in solid-state materials are promising candidates as quantum bits, or qubits. New materials are actively being investigated as hosts for new defect qubits; however, there are no unifying guidelines that can quantitatively predict qubit performance in a new material. One of the most critical property of qubits is their quantum coherence. While cluster correlation expansion (CCE) techniques are useful to simulate the coherence of electron spins in defects, they are computationally expensive to investigate broad classes of stable materials. Using CCE simulations, we reveal a general scaling relation between the electron spin coherence time and the properties of qubit host materials that enables rapid and quantitative exploration of new materials hosting spin defects.

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.

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.

Magnetization dynamics and its scattering mechanism in thin CoFeB films with interfacial anisotropy.

Studies of magnetization dynamics have incessantly facilitated the discovery of fundamentally novel physical phenomena, making steady headway in the development of magnetic and spintronics devices. The dynamics can be induced and detected electrically, offering new functionalities in advanced electronics at the nanoscale. However, its scattering mechanism is still disputed. Understanding the mechanism in thin films is especially important, because most spintronics devices are made from stacks of multilayers with nanometer thickness. The stacks are known to possess interfacial magnetic anisotropy, a central property for applications, whose influence on the dynamics remains unknown. Here, we investigate the impact of interfacial anisotropy by adopting CoFeB/MgO as a model system. Through systematic and complementary measurements of ferromagnetic resonance (FMR) on a series of thin films, we identify narrower FMR linewidths at higher temperatures. We explicitly rule out the temperature dependence of intrinsic damping as a possible cause, and it is also not expected from existing extrinsic scattering mechanisms for ferromagnets. We ascribe this observation to motional narrowing, an old concept so far neglected in the analyses of FMR spectra. The effect is confirmed to originate from interfacial anisotropy, impacting the practical technology of spin-based nanodevices up to room temperature.

Evidence for Ferromagnetic Clusters in the Colossal-Magnetoresistance Material EuB_{6}.

We combined scanning tunneling microscopy and locally resolved magnetic stray field measurements on the ferromagnetic semimetal EuB_{6}, which exhibits a complex ferromagnetic order and a colossal magnetoresistance effect. In a zero magnetic field, scanning tunneling spectroscopy visualizes the existence of local inhomogeneities in the electronic density of states, which we interpret as the localization of charge carriers due to the formation of magnetic polarons. Micro-Hall magnetometry measurements of the total stray field emanating from the end of a rectangular-shaped platelike sample reveals evidence for magnetic clusters also in finite magnetic fields. In contrast, the signal detected below the faces of the magnetized sample measures a local stray field indicating the formation of pronounced magnetic inhomogeneities consistent with large clusters of percolated magnetic polarons.

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.

Electric-Field Modulation of Damping Constant in a Ferromagnetic Semiconductor (Ga,Mn)As.

The modulation of the Gilbert damping constant α in (Ga,Mn)As by the application of an electric field is detected by ferromagnetic resonance measurements, where α increases with decreasing hole concentration. The smaller modulation of other magnetic parameters, such as magnetic anisotropy fields and Landé g factor, suggests that the modulation of α is governed by other effects rather than the spin-orbit coupling. Comparison of the conductivity dependence of α with that of the magnetization indicates that the magnetic disorder induced by carrier localization plays a major role in determining the magnitude of α in (Ga,Mn)As.

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.

Current-induced torques in magnetic materials.

The magnetization of a magnetic material can be reversed by using electric currents that transport spin angular momentum. In the reciprocal process a changing magnetization orientation produces currents that transport spin angular momentum. Understanding how these processes occur reveals the intricate connection between magnetization and spin transport, and can transform technologies that generate, store or process information via the magnetization direction. Here we explain how currents can generate torques that affect the magnetic orientation and the reciprocal effect in a wide variety of magnetic materials and structures. We also discuss recent state-of-the-art demonstrations of current-induced torque devices that show great promise for enhancing the functionality of semiconductor devices.

Effects of water nanodroplets on skin moisture and viscoelasticity during air-conditioning.

BACKGROUND/PURPOSE: In air-conditioned rooms, dry air exacerbates some skin diseases, for example, senile xerosis, atopic dermatitis, and surface roughness. Humidifiers are used to improve air dryness, which often induces excess humidity and thermal discomfort. To address this issue, we investigated the effects of water nanodroplets (mist) on skin hydration, which may increase skin hydration by penetrating into the interstitial spaces between corneocytes of the stratum corneum (SC) without increasing air humidity. METHODS: We examined biophysical parameters, including skin conductance and transepidermal water loss (TEWL), and biomechanical parameters of skin distension/retraction before and after suction at the forehead, lateral canthus, and cheek, with or without mist, in a testing environment (24°C, 35% relative humidity) for 120 min. RESULTS: In the group without mist, TEWL values significantly decreased at all the sites after 1 h compared with the initial values. However, in the presence of mist, TEWL values were maintained at the initial values through the test, yielding significant differences vs. the group without mist. There were no significant differences between mist and mist-free groups in terms of skin conductance. Skin distension was significantly increased in the group with mist compared with that in the group without mist at the forehead and cheek, suggesting a softening effect of mist. CONCLUSION: Skin deformation of the face was improved by mist, suggesting hydration of the SC by mist. The change in TEWL was influenced by mist, suggesting supply of water to the skin, particularly the SC, by mist. These data indicated that a mist of water nanodroplets played an important role in softening skin in an air-conditioned room without increasing excess humidity.

A cross-sectional survey investigating care of the primary dentition by paediatric dental specialists in Japan and the UK.

OBJECTIVE: The aim of this study was to compare treatment decisions in primary dentistry between Japanese and UK-based paediatric dental specialists. METHODS: Four clinical scenarios involving a 6-year-old boy were used to ascertain the clinical opinions of participants. The scenarios presented: (i) a single distal cavity, vital and without pain; (ii) a distal occlusal cavity, vital and without pain; (iii) a large distal occlusal cavity, non-vital and without pain, and (iv) a large distal occlusal cavity, non-vital and painful. Participants were 104 Japanese and 115 UK-based paediatric dental specialists. RESULTS: In the first scenario, some UK specialists showed a preference for vital pulpotomy with a stainless steel crown (10.3% compared with 0.9% in Japan). In the second scenario, Japanese participants were more likely than UK participants to offer traditional restorative care (73.6% vs. 24.1%). In the third scenario, 54.7% of Japanese specialists chose to open the pulp chamber, whereas 51.8% of UK specialists selected non-vital pulpotomy with stainless steel crown. In the final scenario, 74.0% of Japanese specialists chose to open the pulp chamber, whereas 51.8% of UK specialists chose not to offer any treatment other than extraction. CONCLUSIONS: Japanese and UK specialists in paediatric dental care choose different interventions for the same clinical problems.

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.