g-factor symmetry and topology in semiconductor band states.

The [Formula: see text] tensor, which determines the reaction of Kramers-degenerate states to an applied magnetic field, is of increasing importance in the current design of spin qubits. It is affected by details of heterostructure composition, disorder, and electric fields, but it inherits much of its structure from the effect of the spin-orbit interaction working at the crystal-lattice level. Here, we uncover interesting symmetry and topological features of [Formula: see text] for important valence and conduction bands in silicon, germanium, and gallium arsenide. For all crystals with high (cubic) symmetry, we show that large departures from the nonrelativistic value [Formula: see text] are guaranteed by symmetry. In particular, considering the spin part [Formula: see text], we prove that the scalar function [Formula: see text] must go to zero on closed surfaces in the Brillouin zone, no matter how weak the spin-orbit coupling is. We also prove that for wave vectors [Formula: see text] on these surfaces, the Bloch states [Formula: see text] have maximal spin-orbital entanglement. Using tight-binding calculations, we observe that the surfaces [Formula: see text] exhibit many interesting topological features, exhibiting Lifshitz critical points as understood in Fermi-surface theory.

Defected twisted ring topology for autonomous periodic flip-spin-orbit soft robot.

Periodic spin-orbit motion is ubiquitous in nature, observed from electrons orbiting nuclei to spinning planets orbiting the Sun. Achieving autonomous periodic orbiting motions, along circular and noncircular paths, in soft mobile robotics is crucial for adaptive and intelligent exploration of unknown environments-a grand challenge yet to be accomplished. Here, we report leveraging a closed-loop twisted ring topology with a defect for an autonomous soft robot capable of achieving periodic spin-orbiting motions with programmed circular and re-programmed irregular-shaped trajectories. Constructed by bonding a twisted liquid crystal elastomer ribbon into a closed-loop ring topology, the robot exhibits three coupled periodic self-motions in response to constant temperature or constant light sources: inside-out flipping, self-spinning around the ring center, and self-orbiting around a point outside the ring. The coupled spinning and orbiting motions share the same direction and period. The spinning or orbiting direction depends on the twisting chirality, while the orbital radius and period are determined by the twisted ring geometry and thermal actuation. The flip-spin and orbiting motions arise from the twisted ring topology and a bonding site defect that breaks the force symmetry, respectively. By utilizing the twisting-encoded autonomous flip-spin-orbit motions, we showcase the robot's potential for intelligently mapping the geometric boundaries of unknown confined spaces, including convex shapes like circles, squares, triangles, and pentagons and concaves shapes with multi-robots, as well as health monitoring of unknown confined spaces with boundary damages.

Polyvalent s-block elements: A missing link challenges the periodic law of chemistry for the heavy elements.

The Periodic Law of Chemistry is one of the great discoveries in cultural history. Elements behaving chemically similar are empirically merged in groups G of a Periodic Table, each element with G valence electrons per neutral atom, and with upper limit G for the oxidation and valence numbers. Here, we report that among the usually mono- or di-valent s-block elements (G = 1 or 2), the heaviest members (87Fr, 88Ra, 119E, and 120E) with atomic numbers Z = 87, 88, 119, 120 form unusual 5- or 6-valent compounds at ambient conditions. Together with well-reported basic changes of valence at the end of the 6d-series, in the whole 7p-series, and for 5g6f-elements, it indicates that at the bottom of common Periodic Tables, the classic Periodic Law is not as straightforward as commonly expected. Specifically, we predict the feasible experimental synthesis of polyvalent [RaL-n] (n = 4, 6) compounds.

Compass-like manipulation of electronic nematicity in Sr3Ru2O7.

Electronic nematicity has been found in a wide range of strongly correlated electron materials, resulting in the electronic states having-4.5pc]Please note that the spelling of the following author name(s) in the manuscript differs from the spelling provided in the article metadata: Izidor Benedicic. The spelling provided in the manuscript has been retained; please confirm. a symmetry that is lower than that of the crystal that hosts them. One of the most astonishing examples is [Formula: see text], in which a small in-plane component of a magnetic field induces significant resistivity anisotropy. The direction of this anisotropy follows the direction of the in-plane field. The microscopic origin of this field-induced nematicity has been a long-standing puzzle, with recent experiments suggesting a field-induced spin density wave driving the anisotropy. Here, we report spectroscopic imaging of a field-controlled anisotropy of the electronic structure at the surface of [Formula: see text]. We track the electronic structure as a function of the direction of the field, revealing a continuous change with the angle. This continuous evolution suggests a mechanism based on spin-orbit coupling resulting in compass-like control of the electronic bands. The anisotropy of the electronic structure persists to temperatures about an order of magnitude higher compared to the bulk, demonstrating novel routes to stabilize such phases over a wider temperature range.

Coexistence of Ferromagnetism and Superconductivity at KTaO3 Heterointerfaces.

The coexistence of superconductivity and ferromagnetism is a long-standing issue in superconductivity due to the antagonistic nature of these two ordered states. Experimentally identifying and characterizing novel heterointerface superconductors that coexist with magnetism presents significant challenges. Here, we report the observation of two-dimensional long-range ferromagnetic order in a KTaO3 heterointerface superconductor, showing the coexistence of superconductivity and ferromagnetism. Remarkably, our direct current superconducting quantum interference device measurements reveal an in-plane magnetization hysteresis loop persisting above room temperature. Moreover, first-principles calculations and X-ray magnetic circular dichroism measurements provide decisive insights into the origin of the observed robust ferromagnetism, attributing it to oxygen vacancies that localize electrons in nearby Ta 5d states. Our findings suggest KTaO3 heterointerfaces as time-reversal symmetry breaking superconductors, injecting fresh momentum into the exploration of the intricate interplay between superconductivity and magnetism enhanced by the strong spin-orbit coupling inherent to the heavy Ta in 5d orbitals.

Room-Temperature Highly Efficient Nonvolatile Magnetization Switching by Current in van der Waals Fe3GaTe2 Devices.

The ability to manipulate magnetic states by a low electric current represents a fundamental desire in spintronics. In recent years, two-dimensional van der Waals (vdW) magnetic materials have attracted an extensive amount of attention due to their appreciable spin-orbit torque effect. However, for most known vdW ferromagnets, their relatively low Curie temperatures (TC) limit their applications. Consequently, low-power vdW spintronic devices that can operate at room temperature are in great demand. In this research, we fabricate nanodevices based on a solitary thin flake of vdW ferromagnet Fe3GaTe2, in which we successfully achieve nonvolatile and highly efficient magnetization switching by small currents at room temperature. Notably, the switching current density and the switching power dissipation are as low as 1.7 × 105 A/cm2 and 1.6 × 1013 W/m3, respectively, with an external magnetic field of 80 Oe; both are much reduced compared to those of conventional magnet/heavy metal heterostructure devices and other vdW devices.

Field-Free Manipulation of Two-Dimensional Ferromagnet CrTe2 by Spin-Orbit Torques.

Electrical manipulation of magnetic states in two-dimensional ferromagnetic systems is crucial in information storage and low-dimensional spintronics. Spin-orbit torque presents a rapid and energy-efficient method for electrical control of the magnetization. In this letter, we demonstrate a wafer-scale spin-orbit torque switching of two-dimensional ferromagnetic states. Using molecular beam epitaxy, we fabricate two-dimensional heterostructures composed of low crystal-symmetry WTe2 and ferromagnet CrTe2 with perpendicular anisotropy. By utilizing out-of-plane spins generated from WTe2, we achieve field-free switching of the CrTe2 perpendicular magnetization. The threshold switching current density in CrTe2/WTe2 is 1.2 × 106 A/cm2, 20 times smaller than that of the CrTe2/Pt control sample even with an external magnetic field. In addition, the switching behavior can be modulated by external magnetic fields and crystal symmetry. Our findings demonstrate a controllable and all-electric manipulation of perpendicular magnetization in a two-dimensional ferromagnet, representing a significant advancement toward the practical implementation of low-dimensional spintronic devices.

Perfect Zeeman Anisotropy in Rotationally Symmetric Quantum Dots with Strong Spin-Orbit Interaction.

In nanoscale structures with rotational symmetry, such as quantum rings, the orbital motion of electrons combined with a spin-orbit interaction can produce a very strong and anisotropic Zeeman effect. Since symmetry is sensitive to electric fields, ring-like geometries provide an opportunity to manipulate magnetic properties over an exceptionally wide range. In this work, we show that it is possible to form rotationally symmetric confinement potentials inside a semiconductor quantum dot, resulting in electron orbitals with large orbital angular momentum and strong spin-orbit interactions. We find complete suppression of Zeeman spin splitting for magnetic fields applied in the quantum dot plane, similar to the expected behavior of an ideal quantum ring. Spin splitting reappears as orbital interactions are activated with symmetry-breaking electric fields. For two valence electrons, representing a common basis for spin-qubits, we find that modulating the rotational symmetry may offer new prospects for realizing tunable protection and interaction of spin-orbital states.

Tuning Displacement Fields in a Two-Dimensional Topological Insulator Using Nanopatterned Gates.

Epitaxial heterostructures with topological insulators enable novel quantum phases and practical device applications. Their topological electronic states are sensitive to the microscopic parameters, including structural inversion asymmetry (SIA), which is an inherent feature of many real heterostructures. Controlling SIA is challenging, because it requires the ability to tune the displacement field across the topological film. Here, using nanopatterned gates, we demonstrate a tunable displacement field in a heterostructure of the two-dimensional topological insulator cadmium arsenide. Transport studies in magnetic fields reveal an extreme sensitivity of the band inversion to SIA. We show that a relatively small displacement field (∼50 mV/nm) converts the crossing of the two zeroth Landau levels in magnetic field to an avoided crossing, signaling a change to trivial band order. This work demonstrates a universal methodology for tuning electronic states in topological thin films.

Field-Free Spin-Orbit Torque Magnetization Switching in a Single-Phase Ferromagnetic and Spin Hall Oxide.

Current-induced spin-orbit torque (SOT) offers substantial promise for the development of low-power, nonvolatile magnetic memory. Recently, a single-phase material concurrently exhibiting magnetism and the spin Hall effect has emerged as a scientifically and technologically interesting platform for realizing efficient and compact SOT systems. Here, we demonstrate external-magnetic-field-free switching of perpendicular magnetization in a single-phase ferromagnetic and spin Hall oxide SrRuO3. We delicately altered the local lattices of the top and bottom surface layers of SrRuO3, while retaining a quasi-homogeneous, single-crystalline nature of the SrRuO3 bulk. This leads to unbalanced spin Hall effects between the top and bottom layers, enabling net SOT performance within single-layer ferromagnetic SrRuO3. Notably, our SrRuO3 exhibits the highest SOT efficiency and lowest power consumption among all known single-layer systems under field-free conditions. Our method of artificially manipulating the local atomic structures will pave the way for advances in spin-orbitronics and the exploration of new SOT materials.

Neuromorphic Computing with Emerging Antiferromagnetic Ordering in Spin-Orbit Torque Devices.

Field-free switching (FFS) and spin-orbit torque (SOT)-based neuromorphic characteristics were realized in a W/Pt/Co/NiO/Pt heterostructure with a perpendicular exchange bias (HEB) for brain-inspired neuromorphic computing (NC). Experimental results using NiO-based SOT devices guided the development of fully spin-based artificial synapses and sigmoidal neurons for implementation in a three-layer artificial neural network. This system achieved impressive accuracies of 91-96% when applied to the Modified National Institute of Standards and Technology (MNIST) image data set and 78.85-81.25% when applied to Fashion MNIST images, due presumably to the emergence of robust NiO antiferromagnetic (AFM) ordering. The emergence of AFM ordering favored the FFS with an enhanced HEB, which suppressed the memristivity and reduced the recognition accuracy. This indicates a trade-off between the requirements for solid-state memory and those required for brain-inspired NC devices. Nonetheless, our findings revealed opportunities by which the two technologies could be aligned via controllable exchange coupling.

Initialization-Free and Magnetic Field-Free Spin-Orbit p-Bits with Backhopping-like Magnetization Switching for Probabilistic Applications.

Probabilistic bits (p-bits) with thermal- and spin torque-induced nondeterministic magnetization switching are promising candidates for performing probabilistic computing. Previously reported spin torque p-bits include volatile low-energy barrier nanomagnets (LBNMs) with spontaneously fluctuating magnetizations and initialization-necessary nonvolatile magnets. However, initialization-free nonvolatile spin torque p-bits are still lacking. Here, we demonstrate moderately thermal stable spin-orbit torque (SOT) p-bits with non-consecutively deposited Pt//Pt/Co/Pt stacks. Backhopping-like (BH) magnetization switching with a wide range current-tunable probability of final up and down magnetization states from 0% to 100% was achieved, regardless of the initial magnetization state, which was attributed to the interplay of SOT and thermal contributions. Integer factorization using such BH-SOT p-bits in zero magnetic field was demonstrated at times that are significantly shorter than those of existing nonvolatile STT or volatile LBNMs p-bits. Our realization of initialization-free and magnetic field-free moderately thermally stable BH-SOT p-bits opens up a new perspective for probabilistic spintronic applications.

An Antiferromagnetic Neuromorphic Memory Based on Perpendicularly Magnetized CoO.

Antiferromagnets (AFMs) are ideal materials to boost neuromorphic computing toward the ultrahigh speed and ultracompact integration regime. However, developing a suitable AFM neuromorphic memory remains an aspirational but challenging goal. In this work, we construct such a memory based on the CoO/Pt heterostructure, in which the collinear insulating AFM CoO shows a strong perpendicular anisotropy facilitating its electrical readout and writing. Utilizing the unique nonlinear response and bipolar fading memory properties of the device, we demonstrate a multidimensional reservoir computing beyond the traditional binary paradigm. These results are expected to pave the way toward next-generation fast and massive neuromorphic computing.

Observation of Long-Range Current-Induced Torque in Ni/Pt Bilayers.

The generation of current-induced torques through the spin Hall effect in Pt has been key to the development of spintronics. In prototypical ferromagnetic-metal/Pt devices, the characteristic length of the torque generation is known to be about 1 nm due to the short spin diffusion length of Pt. Here, we report the observation of a long-range current-induced torque in Ni/Pt bilayers. We demonstrate that when Ni is used as the ferromagnetic layer, the torque efficiency increases with the Pt thickness, even when it exceeds 10 nm. The torque efficiency is also enhanced by increasing the Ni thickness, providing evidence that the observed torque cannot be attributed to the spin Hall effect in the Pt layer. These findings, coupled with our semirealistic tight-binding calculations of the current-induced torque, suggest the possibility that the observed long-range torque is dominated by the orbital Hall effect in the Pt layer.

Granular Magnetization Switching in Pt/Co/Ti Structure with HfOx Insertion for In-Memory Computing Applications.

Exploring multiple states based on the domain wall (DW) position has garnered increased attention for in-memory computing applications, particularly focusing on the utilization of spin-orbit torque (SOT) to drive DW motion. However, devices relying on the DW position require efficient DW pinning. Here, we achieve granular magnetization switching by incorporating an HfOx insertion layer between the Co/Ti interface. This corresponds to a transition in the switching model from the DW motion to DW nucleation. Compared to the conventional Pt/Co/Ti structure, incorporation of the HfOx layer results in an enhanced SOT efficiency and a lower switching current density. We also realized stable multistate storage and synaptic plasticity by applying pulse current in the Pt/Co/HfOx/Ti device. The simulation of artificial neural networks (ANN) based on the device can perform digital recognition tasks with an accuracy rate of 91%. These results identify that DW nucleation with a Pt/Co/HfOx/Ti based device has potential applications in multistate storage and ANN.

Restricted Boltzmann Machines Implemented by Spin-Orbit Torque Magnetic Tunnel Junctions.

Artificial intelligence has surged forward with the advent of generative models, which rely heavily on stochastic computing architectures enhanced by true random number generators with adjustable sampling probabilities. In this study, we develop spin-orbit torque magnetic tunnel junctions (SOT-MTJs), investigating their sigmoid-style switching probability as a function of the driving voltage. This feature proves to be ideally suited for stochastic computing algorithms such as the restricted Boltzmann machines (RBM) prevalent in pretraining processes. We exploit SOT-MTJs as both stochastic samplers and network nodes for RBMs, enabling the implementation of RBM-based neural networks to achieve recognition tasks for both handwritten and spoken digits. Moreover, we further harness the weights derived from the preceding image and speech training processes to facilitate cross-modal learning from speech to image generation. Our results clearly demonstrate that these SOT-MTJs are promising candidates for the development of hardware accelerators tailored for Boltzmann neural networks and other stochastic computing architectures.

Unconventional Piezoelectricity of Two-Dimensional Materials Driven by the Hall Effect.

Piezoelectricity has been widely explored for nanoelectromechanical applications, yet its working modes are mainly limited in polar directions. Here we discover the intrinsic electro-mechanical response in crystal materials that is transverse to the conventional polarized direction, which is named unconventional piezoelectricity. A Hall-like mechanism is proposed to interpret unconventional piezoelectricity as charge polarization driven by a built-in electric field for systems with asymmetric Berry curvature distributions. Density functional theory simulations and statistical analyses justify such a mechanism and confirm that unconventional piezoelectricity is a general property for various two-dimensional materials with spin splitting or valley splitting. An empirical formula is derived to connect the conventional and unconventional piezoelectricity. The extended understanding of the piezoelectric tensor in quantum materials opens an opportunity for applications in multidirectional energy conversion, broadband operation, and multifunctional sensing.

Heat-Assisted Magnetization Switching in Flexible Spin-Orbit Torque Devices.

Heat-assisted magnetic anisotropy engineering has been successfully used in selective magnetic writing and microwave amplification due to a large interfacial thermal resistance between the MgO barrier and the adjacent ferromagnetic layers. However, in spin-orbit torque devices, the writing current does not flow through the tunnel barrier, resulting in a negligible heating effect due to efficient heat dissipation. Here, we report a dramatically reduced switching current density of ∼2.59 MA/cm2 in flexible spin-orbit torque heterostructures, indicating a 98% decrease in writing energy consumption compared with that on a silicon substrate. The reduced driving current density is enabled by the dramatically decreased magnetic anisotropy due to Joule dissipation and the lower thermal conductivity of the flexible substrate. The large magnetic anisotropy could be fully recovered after the impulse, indicating retained high stability. These results pave the way for flexible spintronics with the otherwise incompatible advantages of low power consumption and high stability.

Electrically Tunable, Rapid Spin-Orbit Torque Induced Modulation of Colossal Magnetoresistance in Mn3Si2Te6 Nanoflakes.

As a quasi-layered ferrimagnetic material, Mn3Si2Te6 nanoflakes exhibit magnetoresistance behavior that is fundamentally different from their bulk crystal counterparts. They offer three key properties crucial for spintronics. First, at least 106 times faster response compared to that exhibited by bulk crystals has been observed in current-controlled resistance and magnetoresistance. Second, ultralow current density is required for resistance modulation (∼5 A/cm2). Third, electrically gate-tunable magnetoresistance has been realized. Theoretical calculations reveal that the unique magnetoresistance behavior in the Mn3Si2Te6 nanoflakes arises from a magnetic field induced band gap shift across the Fermi level. The rapid current induced resistance variation is attributed to spin-orbit torque, an intrinsically ultrafast process (∼nanoseconds). This study suggests promising avenues for spintronic applications. In addition, it highlights Mn3Si2Te6 nanoflakes as a suitable platform for investigating the intriguing physics underlying chiral orbital moments, magnetic field induced band variation, and spin torque.

Giant Tunability of Intersubband Transitions and Quantum Hall Quartets in Few-Layer InSe Quantum Wells.

A two-dimensional (2D) quantum electron system is characterized by quantized energy levels, or subbands, in the out-of-plane direction. Populating higher subbands and controlling the intersubband transitions have wide technological applications such as optical modulators and quantum cascade lasers. In conventional materials, however, the tunability of intersubband spacing is limited. Here we demonstrate electrostatic population and characterization of the second subband in few-layer InSe quantum wells, with giant tunability of its energy, population, and spin-orbit coupling strength, via the control of not only layer thickness but also the out-of-plane displacement field. A modulation of as much as 350% or over 250 meV is achievable, underscoring the promise of InSe for tunable infrared and THz sources, detectors, and modulators.