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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

Spin-Orbit Torques and Magnetization Switching in (Bi,Sb)2Te3/Fe3GeTe2 Heterostructures Grown by Molecular Beam Epitaxy.

Topological insulators (TIs) hold promise for manipulating the magnetization of a ferromagnet (FM) through the spin-orbit torque (SOT) mechanism. However, integrating TIs with conventional FMs often leads to significant device-to-device variations and a broad distribution of SOT magnitudes. In this work, we present a scalable approach to grow a full van der Waals FM/TI heterostructure by molecular beam epitaxy, combining the charge-compensated TI (Bi,Sb)2Te3 with 2D FM Fe3GeTe2 (FGT). Harmonic magnetotransport measurements reveal that the SOT efficiency exhibits a non-monotonic temperature dependence and experiences a substantial enhancement with a reduction of the FGT thickness to 2 monolayers. Our study further demonstrates that the magnetization of ultrathin FGT films can be switched with a current density of Jc ∼ 1010 A/m2, with minimal device-to-device variations compared to previous investigations involving traditional FMs.

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.

Multiple Valley Modulations in Noncollinear Antiferromagnets.

Two-dimensional valleys and magnetism are rising areas with intriguing properties and practical uses in advanced information technology. By coupling valleys to collinear magnetism, valley degeneracy is lifted in a large number of magnetic valley materials to exploit the valley degree of freedom. Beyond collinear magnetism, new coupling modes between valley and magnetism are few but highly desirable. By tight-binding calculations of a breathing Kagome lattice, we demonstrate a tunable valley structure and valley-contrasting physical properties in noncollinear antiferromagnets. Distinct from collinear magnetism, noncollinear antiferromagnetic order enables valley splittings even without spin-orbit coupling. Both the canting and azimuthal angles of magnetic moments can be used as experimentally accessible knobs to tune valley splittings. Our first-principles calculations of the Fe3C6O6-silicene-Fe3C6O6 heterostructure also exhibit tunable valley splittings in noncollinear antiferromagnetism, agreeing with our tight-binding results. Our work paves avenues for designing novel magnetic valley materials and energy-efficient valleytronic devices based on noncollinear magnetism.

Transverse Spin-Orbit Interaction of Light.

Light carries both longitudinal and transverse spin angular momentum. The spin can couple with its orbital counterpart, known as the spin-orbit interaction (SOI) of light. Complementary to the longitudinal SOI known previously, here we show that transverse SOI of light is inherent in the Helmholtz equation when transverse spinning light propagates in curved paths. It lifts the degeneracy of dispersion relations of light for opposite transverse spin states, analogous to the Dresselhaus effect. Transverse SOI is ubiquitous in nanophotonic systems where transverse spin and optical path bending are inevitable. It can explain anomalous effects like the dispersion relation of surface plasmon polaritons on curved paths and the energy level of whispering gallery modes. Our results reveal the analogies of spin photonics and spintronics and offer a new degree of freedom for integrated photonics, spin photonics, and astrophysics.

Field-Free Spin-Orbit Torque Switching in Janus Chromium Dichalcogenides.

We predict a very large spin-orbit torque (SOT) capability of magnetic chromium-based transition-metal dichalcogenide (TMD) monolayers in their Janus forms CrXTe, with X = S, Se. The structural inversion symmetry breaking, inherent to Janus structures is responsible for a large SOT response generated by giant Rashba splitting, equivalent to that obtained by applying a transverse electric field of ∼100 V nm-1 in non-Janus CrTe2, completely out of experimental reach. By performing transport simulations on carefully derived Wannier tight-binding models, Janus systems are found to exhibit an SOT performance comparable to the most efficient two-dimensional materials, while additionally allowing for field-free perpendicular magnetization switching, due to their reduced in-plane symmetry. Altogether, our findings evidence that magnetic Janus TMDs stand as suitable candidates for ultimate SOT-MRAM devices in an ultracompact self-induced SOT scheme.

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.

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.

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.