Universal intrinsic spin Hall effect

Full Electrical Manipulation of Perpendicular Magnetization in [111]-Orientated Pt/Co Heterostructure Enabled by Anisotropic Epitaxial Strain

The effective manipulation of perpendicular magnetization through spin-orbit torque (SOT) holds great promise for magnetic memory and spin-logic device. However, field-free SOT switching of perpendicular magnetization remains a challenge for conventional materials with high symmetry. This study elucidates a full electrical manipulation of the perpendicular magnetization in an epitaxial [111]-orientated Pt/Co heterostructure. A large anisotropic epitaxial strain induces a symmetry transition from the ideal C3v to C1v, attributed to the mismatch between [112] and [110] directions. The anisotropic strain also generates a noteworthy in-plane magnetization component along the [112] direction, further breaking magnetic symmetry. Notably, the high-temperature performance under 393 K highlights the robustness of strain-induced in-plane symmetry breaking. Furthermore, eight Boolean logic operations have been demonstrated within a single SOT device. This research presents a method for harnessing epitaxial strain to break in-plane symmetry, which may open a new avenue in practical SOT devices.

Rashba effect originates from the reduction of point-group symmetries

The Rashba effect in a nonmagnetic condensed-matter system is described by the reduction of point-group symmetries. The inversion, two-fold rotation, and reflection symmetries transforming the wavevector k to -k are identified as the origin of a degenerate state according to the time-reversal symmetry. The lack of these symmetries in a bulk system or the breaking of these in a surface system is then identified as the origin of a nondegenerate state. The surface systems Au(111), Au(110), and W(110) are assessed. The bulk system BiTeI is demonstrated for the existence of a nondegenerate state on the basis of first-principles calculations. The related issues of the heterostructure GaAs/AlGaAs and the spin Hall effect are also presented.

Orbital Pumping Incorporating Both Orbital Angular Momentum and Position

We develop a theory of adiabatic orbital pumping, highlighting qualitative differences from spin pumping. An oscillating magnetic field pumps not only orbital angular momentum current, but also orbital angular position current. The latter, which has no spin counterpart, underscores the incompleteness of existing orbital torque theories. Importantly, both types of orbital currents can be detected as transverse electric voltages, which contain considerable second-harmonic components unlike in spin pumping. Moreover, orbital currents can be pumped by lattice dynamics that carry phonon angular momentum, implying that orbital currents can, in turn, induce phonon angular momentum. Our Letter open up new possibilities for generating orbital currents and provides a broader understanding of the interplay between spin, orbital, and phonon dynamics.

Chiral-induced unidirectional spin-to-charge conversion

The observation of spin-dependent transmission of electrons through chiral molecules has led to the discovery of chiral-induced spin selectivity (CISS). The remarkably high efficiency of the spin polarizing effect has recently gained substantial interest due to the high potential for future sustainable hybrid chiral molecule magnetic applications. However, the fundamental mechanisms underlying the chiral-induced phenomena remain to be understood fully. In this work, we explore the impact of chirality on spin angular momentum in hybrid metal/chiral molecule thin-film heterostructures. For this, we inject a pure spin current via spin pumping and investigate the spin-to-charge conversion at the hybrid chiral interface. Notably, we observe a chiral-induced unidirectionality in the conversion. Furthermore, angle-dependent measurements reveal that the spin selectivity is maximum when the spin angular momentum is aligned with the molecular chiral axis. Our findings validate the central role of spin angular momentum for the CISS effect, paving the path toward three-dimensional functionalization of hybrid molecule-metal devices via chirality.

Chirality-Induced Majorana Zero Modes and Majorana Polarization

Realizing Majorana Fermions has always been regarded as a crucial and formidable task in topological superconductors. In this work, we report a physical mechanism and a material platform for realizing Majorana zero modes (MZMs). This material platform consists of open circular helix molecule (CHM) proximity coupled with an s-wave superconductor (under an external magnetic field) or interconnected-CHM chain coupled with a phase-bias s-wave superconducting heterostructure (without any external magnetic field). MZMs generated here are tightly associated with the structural chirality in CHMs. Notably, the left- and right-handedness results in completely opposite Majorana polarization (MP), leading us to refer to this phenomenon as chirality-induced MP (CIMP). Importantly, the local CIMP is closely linked to chirality-induced spin polarization, providing us with an effective way to regulate MZMs through the chirality-induced spin selectivity (CISS) effect. Furthermore, MZMs can be detected by the spin-polarized current measurements related to the CISS in chiral materials.

Spin-Hall conductivity and optical characteristics of noncentrosymmetric quantum spin Hall insulators: the case of PbBiI

Quantum spin Hall insulators have attracted significant attention in recent years. Understanding the optical properties and spin Hall effect in these materials is crucial for technological advancements. In this study, we present theoretical analyses to explore the optical properties, Berry curvature and spin Hall conductivity of pristine and perturbed PbBiI using the linear combination of atomic orbitals and the Kubo formula. The system is not centrosymmetric and it is hosting at the same time Rashba spin-splitting and quantized spin Hall conductivity. Our calculations reveal that the electronic structure can be modified using staggered exchange fields and electric fields, leading to changes in the optical properties. Additionally, the spin Berry curvature and spin Hall conductivity are investigated as a function of the energy and temperature. The results indicate that due to the small dynamical spin Hall conductivity, generating an ac spin current in the PbBiI requires the use of external magnetic fields or magnetic materials.

Spin Hall-induced bilinear magnetoelectric resistance

Magnetoresistance is a fundamental transport phenomenon that is essential for reading the magnetic states for various information storage, innovative computing and sensor devices. Recent studies have expanded the scope of magnetoresistances to the nonlinear regime, such as a bilinear magnetoelectric resistance (BMER), which is proportional to both electric field and magnetic field. Here we demonstrate that the BMER is a general phenomenon that arises even in three-dimensional systems without explicit momentum-space spin textures. Our theory suggests that the spin Hall effect enables the BMER provided that the magnitudes of spin accumulation at the top and bottom interfaces are not identical. The sign of the BMER follows the sign of the spin Hall effect of heavy metals, thereby evidencing that the BMER originates from the bulk spin Hall effect. Our observation suggests that the BMER serves as a general nonlinear transport characteristic in three-dimensional systems, especially playing a crucial role in antiferromagnetic spintronics.

Role of Disorder in the Intrinsic Orbital Hall Effect

The orbital Hall effect (OHE) has garnered much attention as a promising approach to realize highly efficient "orbitronic" devices with a wide range of materials. However, the existing theories that attempt to explain the experimental evidence focus on the intrinsic effect, neglecting the omnipresent disorder. Here, we formulate the impact of random defect scattering on the orbital Hall effect by a quantum Boltzmann equation and solve it for a generic two-band model including the in-scattering collision integral (vertex correction). In contrast to the common belief that the intrinsic OHE is robust against the disorder, we find that diffuse scattering by an arbitrarily weak disorder affects and can even fully suppress the intrinsic orbital Hall current, depending on the character of orbital states and the disorder.

Long-distance decay-less spin transport in indirect excitons in a van der Waals heterostructure

In addition to its fundamental interest, the long-distance spin transport is essential for spintronic devices. However, the spin relaxation caused by scattering of the particles carrying the spin limits spin transport. We explored spatially indirect excitons (IXs) in van der Waals heterostructures composed of atomically thin layers of transition-metal dichalcogenides as spin carries. We observed the long-distance spin transport: the spin polarized excitons travel over the entire sample,  ~10 micron away from the excitation spot, with no spin density decay. This transport is characterized by the 1/e decay distances reaching  ~100 micron. The 1/e decay distances are extracted from fits over the  ~10 micron sample size. The emergence of long-distance spin transport is observed at the densities and temperatures where the IX transport decay distances and, in turn, scattering times are strongly enhanced. The suppression of IX scattering suppresses the spin relaxation and enables the long-distance spin transport.

Even-integer quantum Hall effect in an oxide caused by a hidden Rashba effect

In the presence of a high magnetic field, quantum Hall systems usually host both even- and odd-integer quantized states because of lifted band degeneracies. Selective control of these quantized states is challenging but essential to understand the exotic ground states and manipulate the spin textures. Here we demonstrate the quantum Hall effect in Bi2O2Se thin films. In magnetic fields as high as 50 T, we observe only even-integer quantum Hall states, but there is no sign of odd-integer states. However, when reducing the thickness of the epitaxial Bi2O2Se film to one unit cell, we observe both odd- and even-integer states in this Janus (asymmetric) film grown on SrTiO3. By means of a Rashba bilayer model based on the ab initio band structures of Bi2O2Se thin films, we can ascribe the only even-integer states in thicker films to the hidden Rasbha effect, where the local inversion-symmetry breaking in two sectors of the [Bi2O2]2+ layer yields opposite Rashba spin polarizations, which compensate with each other. In the one-unit-cell Bi2O2Se film grown on SrTiO3, the asymmetry introduced by the top surface and bottom interface induces a net polar field. The resulting global Rashba effect lifts the band degeneracies present in the symmetric case of thicker films.

Sliding Ferroelectricity Engineered Coupling between Spin Hall Effect and Layertronics in 2D Lattice

Coupling the spin Hall effect with novel degrees of freedom of electrons is central to the rich phenomena observed in condensed-matter physics. Here, using symmetry analysis and a low-energy k·p model, we report the sliding ferroelectricity engineered coupling between spin Hall effect and emerging layertronics, thereby generating the layer spin Hall effect (LSHE), in a 2D lattice. The physics is rooted in a pair of T-symmetry connected valleys, which experience spin splitting accompanied by large Berry curvature under spin-orbit coupling. The interaction between the out-of-plane ferroelectricity and electronic properties gives rise to the layer-locked Berry curvature and thus layer-polarized spin Hall effect (LP-SHE) in the bilayers. Such LP-SHE is strongly coupled with sliding ferroelectricity, enabling it to be ferroelectrically reversible. Using first-principles calculations, the mechanism is further demonstrated in a series of real bilayer systems, including MoS2, MoTe2, WSe2, MoSi2P4, and MoSi2As4. These phenomena and insights open a new direction for spin Hall effect.

Noncollinear Electric Dipoles in a Polar Chiral Phase of CsSnBr3 Perovskite

Polar and chiral crystal symmetries confer a variety of potentially useful functionalities upon solids by coupling otherwise noninteracting mechanical, electronic, optical, and magnetic degrees of freedom. We describe two phases of the 3D perovskite, CsSnBr3, which emerge below 85 K due to the formation of Sn(II) lone pairs and their interaction with extant octahedral tilts. Phase II (77 K < T < 85 K, space group P21/m) exhibits ferroaxial order driven by a noncollinear pattern of lone pair-driven distortions within the plane normal to the unique octahedral tilt axis, preserving the inversion symmetry observed at higher temperatures. Phase I (T < 77 K, space group P21) additionally exhibits ferroelectric order due to distortions along the unique tilt axis, breaking both inversion and mirror symmetries. This polar and chiral phase exhibits second harmonic generation from the bulk and pronounced electrostriction and negative thermal expansion along the polar axis (Q22 ≈ 1.1 m4 C-2; αb = -7.8 × 10-5 K-1) through the onset of polarization. The structures of phases I and II were predicted by recursively following harmonic phonon instabilities to generate a tree of candidate structures and subsequently corroborated by synchrotron X-ray powder diffraction and polarized Raman and 81Br nuclear quadrupole resonance spectroscopies. Preliminary attempts to suppress unintentional hole doping to allow for ferroelectric switching are described. Together, the polar symmetry, small band gap, large spin-orbit splitting of Sn 5p orbitals, and predicted strain sensitivity of the symmetry-breaking distortions suggest bulk samples and epitaxial films of CsSnBr3 or its neighboring solid solutions as candidates for bulk Rashba effects.

In-Plane Anisotropy in the Layered Topological Insulator Ta2Ni3Te5 Investigated via TEM and Polarized Raman Spectroscopy

Layered Ta2M3Te5 (M = Pd, Ni) has emerged as a platform to study 2D topological insulators, which have exotic properties such as spin-momentum locking and the presence of Dirac fermions for use in conventional and quantum-based electronics. In particular, Ta2Ni3Te5 has been shown to have superconductivity under pressure and is predicted to have second-order topology. Despite being an interesting material with fascinating physics, the detailed crystalline and phononic properties of this material are still unknown. In this study, we use transmission electron microscopy (TEM) and polarized Raman spectroscopy (PRS) to reveal the anisotropic properties of exfoliated few-layer Ta2Ni3Te5. An electron diffraction and TEM study reveals structural anisotropy in the material, with a preferential crystal orientation along the [010] direction. Through Raman spectroscopy, we discovered 15 vibrational modes, 3 of which are ultralow-frequency modes, which show anisotropic response with sample orientation varying with the polarization of the incident beam. Using angle-resolved PRS, we assigned the vibrational symmetries of 11 modes to Ag and two modes to B3g. We also found that linear dichroism plays a role in understanding the Raman signature of this material, which requires the use of complex elements in the Raman tensors. The anisotropy of the Raman scattering also depends on the excitation energies. Our observations reveal the anisotropic nature of Ta2Ni3Te5, establish a quick and nondestructive Raman fingerprint for determining sample orientation, and represent a significant advance in the fundamental understanding of the two-dimensional topological insulator (2DTI) Ta2Ni3Te5 material.

Biaxial strain modulated electronic structures of layered two-dimensional MoSiGeN4 Rashba systems

The two-dimensional (2D) MA2Z4 family has received extensive attention in manipulating its electronic structure and achieving intriguing physical properties. However, engineering the electronic properties remains a challenge. Herein, based on first-principles calculations, we systematically investigate the effect of biaxial strains on the electronic structure of 2D Rashba MoSiGeN4 (MSGN), and further explore how the interlayer interactions affect the Rashba spin splitting (RSS) in such strained layered MSGN systems. After applying biaxial strains, the band gap decreases monotonically with increasing tensile strains but increases when the compressive strains are applied. An indirect-direct-indirect band gap transition is induced by applying a moderate compressive strain (<5%) in the MSGN systems. Due to the symmetry breaking and moderate spin-orbit coupling (SOC), the monolayer MSGN possesses an isolated RSS near the Fermi level, which could be effectively regulated to the Lifshitz-type spin splitting (LSS) by biaxial strain. For instance, the LSS ← RSS → LSS transformation of the Fermi surface is presented in the monolayer and a more complex and changeable LSS ← RSS → LSS → RSS evolution is observed in bilayer and trilayer MSGN systems as the biaxial strain varies from -8% to 12%, which actually depends on the appearance, variation, and vanish of the Mexican hat band in the absence of SOC under different strains. The contribution of the Mo-dz2 orbital hybridized with the N-pz orbital in the highest valence band plays a dominant role in band evolution under biaxial strains, where the RSS → LSS evolution corresponds to the decreased Mo-dz2 orbital contribution. Our study highlights the biaxial strain controllable RSS, in particular the introduction and even the evolution of LSS near the Fermi surface, which makes the strained MSGN systems promising candidates for future applications in spintronic devices.

Observation of Terahertz Spin Hall Conductivity Spectrum in GaAs with Optical Spin Injection

We report the first observation of the spin Hall conductivity spectrum in GaAs at room temperature. Our terahertz polarimetry with a precision of several μrads resolves the Faraday rotation of terahertz pulses arising from the inverse spin Hall effect of optically injected spin-polarized electrons. The obtained spin Hall conductivity spectrum exhibits an excellent quantitative agreement with theory, demonstrating a crossover in the dominant origin from impurity scattering in the dc regime to the intrinsic Berry-curvature mechanism in the terahertz regime. Our spectroscopic technique opens a new pathway to analyze anomalous transports related to spin, valley, or orbital degrees of freedom.

A versatile model with three-dimensional triangular lattice for unconventional transport and various topological effects

The finite Berry curvature in topological materials can induce many subtle phenomena, such as the anomalous Hall effect (AHE), spin Hall effect (SHE), anomalous Nernst effect (ANE), non-linear Hall effect (NLHE) and bulk photovoltaic effects. To explore these novel physics as well as their connection and coupling, a precise and effective model should be developed. Here, we propose such a versatile model-a 3D triangular lattice with alternating hopping parameters, which can yield various topological phases, including kagome bands, triply degenerate fermions, double Weyl semimetals and so on. We reveal that this special lattice can present unconventional transport due to its unique topological surface states and the aforementioned topological phenomena, such as AHE, ANE, NLHE and the topological photocurrent effect. In addition, we also provide a number of material candidates that have been synthesized experimentally with this lattice, and discuss two materials, including a non-magnetic triangular system for SHE, NLHE and the shift current, and a ferromagnetic triangular lattice for AHE and ANE. Our work provides an excellent platform, including both the model and materials, for the study of Berry-curvature-related physics.

Emergence of Weyl fermions by ferrimagnetism in a noncentrosymmetric magnetic Weyl semimetal

Condensed matter physics has often provided a platform for investigating the interplay between particles and fields in cases that have not been observed in high-energy physics. Here, using angle-resolved photoemission spectroscopy, we provide an example of this by visualizing the electronic structure of a noncentrosymmetric magnetic Weyl semimetal candidate NdAlSi in both the paramagnetic and ferrimagnetic states. We observe surface Fermi arcs and bulk Weyl fermion dispersion as well as the emergence of new Weyl fermions in the ferrimagnetic state. Our results establish NdAlSi as a magnetic Weyl semimetal and provide an experimental observation of ferrimagnetic regulation of Weyl fermions in condensed matter.

The tunable anisotropic Rashba spin-orbit coupling effect in Pb-adsorbed Janus monolayer WSeTe

The spin-splitting properties of Pb-adsorbed monolayer Janus WSeTe are investigated based on first-principles calculations. The adsorbed system shows large Rashba splitting (the Rashba parameter is up to 0.75 eV Å), and we find that different adsorption layers (Te/Se adsorption layers) exhibit different significant features under spin-orbit coupling. Zeeman splitting and Rashba splitting co-exist at the high symmetry Γ point of the Te adsorption layer, while the Se adsorption layer exhibits anisotropic Rashba spin-orbit coupling. It was determined using k·p perturbation theory that Pb atom adsorption reduces the initial symmetry of the 2H-WSeTe monolayer and induces a strong spin-orbit coupling effect, so as to induce the anisotropic Rashba effect. Furthermore, the tunability of Rashba splitting was demonstrated by varying the adsorption concentration, adjusting the adsorption distance, and applying biaxial strain. This predicted adsorption system has potential value in spintronic devices.

Nonlinear Topological Magnon Spin Hall Effect

When a magnon passes through two-dimensional magnetic textures, it will experience a fictitious magnetic field originating from the 3×3 skew-symmetric gauge fields. To date, only one of the three independent components of the gauge fields has been found to play a role in generating the fictitious magnetic field, while the other two are perfectly hidden. In this Letter, we show that they are concealed in the nonlinear magnon transport in magnetic textures. Without loss of generality, we theoretically study the nonlinear magnon-skyrmion interaction in antiferromagnets. By analyzing the scattering features of three-magnon processes between the circularly polarized incident magnon and breathing skyrmion, we predict a giant Hall angle of both the confluence and splitting modes. Furthermore, we find that the Hall angle reverses its sign when one switches the handedness of the incident magnons. We dub this the nonlinear topological magnon spin Hall effect. Our findings are deeply rooted in the bosonic nature of magnons that the particle number is not conserved, which has no counterpart in low-energy fermionic systems and may open the door for probing gauge fields by nonlinear means.

Photonic spin Hall effect in a graphene-incorporated quasi-PT symmetric system and the miniaturization of nanophotonic devices

By inserting the monolayer graphene between the balanced gain and loss layers, the graphene-incorporated quasi-parity-time (PT) symmetric structure is established. In this contribution, the introduction of graphene provides a new degree of freedom to manipulate the optical performance as well as the photonic spin Hall effect (SHE). The coherent perfect absorption (CPA)-laser mode still remains in the graphene-incorporated quasi-PT symmetric system, and the spin shift of transmitted light can be significantly enhanced (i.e., up to its upper limitation) in the vicinity of CPA-laser mode, which is 18 times larger than the value of a simple PT symmetric structure. In addition, the excitation of the CPA-laser mode and the huge spin shift of transmitted light can be achieved with the thin gain/loss layers, which will be conducive to the miniaturization of nanophotonic devices based on the photonic SHE in the future.

Superconducting, Topological, and Transport Properties of Kagome Metals CsTi3Bi5 and RbTi3Bi5

The recently discovered ATi3Bi5 (A=Cs, Rb) exhibit intriguing quantum phenomena including superconductivity, electronic nematicity, and abundant topological states. ATi3Bi5 present promising platforms for studying kagome superconductivity, band topology, and charge orders in parallel with AV3Sb5. In this work, we comprehensively analyze various properties of ATi3Bi5 covering superconductivity under pressure and doping, band topology under pressure, thermal conductivity, heat capacity, electrical resistance, and spin Hall conductivity (SHC) using first-principles calculations. Calculated superconducting transition temperature (Tc) of CsTi3Bi5 and RbTi3Bi5 at ambient pressure are about 1.85 and 1.92 K. When subject to pressure, Tc of CsTi3Bi5 exhibits a special valley and dome shape, which arises from quasi-two-dimensional compression to three-dimensional isotropic compression within the context of an overall decreasing trend. Furthermore, Tc of RbTi3Bi5 can be effectively enhanced up to 3.09 K by tuning the kagome van Hove singularities (VHSs) and flat band through doping. Pressures can also induce abundant topological surface states at the Fermi energy (EF) and tune VHSs across EF. Additionally, our transport calculations are in excellent agreement with recent experiments, confirming the absence of charge density wave. Notably, SHC of CsTi3Bi5 can reach up to 226ℏ ·(e· Ω ·cm)-1 at EF. Our work provides a timely and detailed analysis of the rich physical properties for ATi3Bi5, offering valuable insights for further experimental verifications and investigations in this field.

Nonequilibrium Magneto-Conductance as a Manifestation of Spin Filtering in Chiral Nanojunctions

It is generally accepted that spin-dependent electron transmission may appear in chiral systems, even without magnetic components, as long as significant spin-orbit coupling is present in some of its elements. However, how this chirality-induced spin selectivity (CISS) manifests in experiments, where the system is taken out of equilibrium, is still debated. Aided by group theoretical considerations and nonequilibrium DFT-based quantum transport calculations, here we show that when spatial symmetries that forbid a finite spin polarization in equilibrium are broken, a net spin accumulation appears at finite bias in an arbitrary two-terminal nanojunction. Furthermore, when a suitably magnetized detector is introduced into the system, the net spin accumulation, in turn, translates into a finite magneto-conductance. The symmetry prerequisites are mostly analogous to those for the spin polarization at any bias with the vectorial nature given by the direction of magnetization, hence establishing an interconnection between these quantities.

Generation of out-of-plane polarized spin current by spin swapping

The generation of spin currents and their application to the manipulation of magnetic states is fundamental to spintronics. Of particular interest are chiral antiferromagnets that exhibit properties typical of ferromagnetic materials even though they have negligible magnetization. Here, we report the generation of a robust spin current with both in-plane and out-of-plane spin polarization in epitaxial thin films of the chiral antiferromagnet Mn₃Sn in proximity to permalloy thin layers. By employing temperature-dependent spin-torque ferromagnetic resonance, we find that the chiral antiferromagnetic structure of Mn₃Sn is responsible for an in-plane polarized spin current that is generated from the interior of the Mn₃Sn layer and whose temperature dependence follows that of this layer's antiferromagnetic order. On the other hand, the out-of-plane polarized spin current is unrelated to the chiral antiferromagnetic structure and is instead the result of scattering from the Mn₃Sn/permalloy interface. We substantiate the later conclusion by performing studies with several other non-magnetic metals all of which are found to exhibit out-of-plane polarized spin currents arising from the spin swapping effect.

Nanoscale mapping of edge-state conductivity and charge-trap activity in topological insulators

We report the nanoscale mapping of topological edge-state conductivity and the effects of charge-traps on conductivity in a Bi₂Se₃ multilayer film under ambient conditions. In this strategy, we applied an electric field perpendicular to the surface plane of Bi₂Se₃via a conducting probe to directly map the charge-trap densities and conductivities with a nanoscale resolution. The results showed that edge regions had one-dimensional characteristics with higher conductivities (two orders) and lower charge-trap densities (four orders) than those of flat surface regions where their conductivities and charge-traps were dominated by bulk effects. Additionally, edges showed an enhanced conductivity with an elevated electric field, possibly due to the creation of new topological states by stronger spin-Hall effects. Importantly, we observed ultra-high photoconductivity predominantly on edge regions compared with that of flat surface regions, which was attributed to the excitation of edge-state carriers by light. Since our method provides an important insight into the charge transport in topological insulators, it could be a significant advancement in the development of error-tolerant topotronic devices.

A Group-Theoretic Approach to the Origin of Chirality-Induced Spin-Selectivity in Nonmagnetic Molecular Junctions

Spin-orbit coupling gives rise to a range of spin-charge interconversion phenomena in nonmagnetic systems where certain spatial symmetries are reduced or absent. Chirality-induced spin-selectivity (CISS), a term that generically refers to a spin-dependent electron transfer in nonmagnetic chiral systems, is one such case, appearing in a variety of seemingly unrelated situations ranging from inorganic materials to molecular devices. In particular, the origin of CISS in molecular junctions is a matter of an intense current debate. Here, we derive a set of geometrical conditions for this effect to appear, hinting at the fundamental role of symmetries beyond otherwise relevant quantitative issues. Our approach, which draws on the use of point-group symmetries within the scattering formalism for transport, shows that electrode symmetries are as important as those of the molecule when it comes to the emergence of a spin-polarization and, by extension, to the possible appearance of CISS. It turns out that standalone metallic nanocontacts can exhibit spin-polarization when relative rotations which reduce the symmetry are introduced. As a corollary, molecular junctions with achiral molecules can also exhibit spin-polarization along the direction of transport, provided that the whole junction is chiral in a specific way. This formalism also allows the prediction of qualitative changes of the spin-polarization upon substitution of a chiral molecule in the junction with its enantiomeric partner. Quantum transport calculations based on density functional theory corroborate all of our predictions and provide further quantitative insight within the single-particle framework.

Intrinsic Nonlinear Planar Hall Effect

We propose an intrinsic nonlinear planar Hall effect, which is of band geometric origin, independent of scattering, and scales with the second order of electric field and first order of magnetic field. We show that this effect is less symmetry constrained compared with other nonlinear transport effects and is supported in a large class of nonmagnetic polar and chiral crystals. Its characteristic angular dependence provides an effective way to control the nonlinear output. Combined with first-principles calculations, we evaluate this effect in the Janus monolayer MoSSe and report experimentally measurable results. Our work reveals an intrinsic transport effect, which offers a new tool for material characterization and a new mechanism for nonlinear device application.

Spin Hall effect from bipolaron dynamics in organics

Using an extended Su-Schrieffer-Heeger model and a nonadiabatic dynamics method, we investigate the dynamics of bipolarons in coupled nondegenerate organic chains including the spin-orbit coupling and interchain coupling. By tracing the time-dependent evolution of the charges and spins in each chain, an obvious oscillating spin Hall effect (SHE) from the bipolaron transport is revealed. The results are compared with that from polaron-dominated transport. A reduction of amplitude and an increase of oscillating frequency are observed for the SHE from the bipolaron transport. The mechanism is attributed to the enhanced skew scattering off the larger transient deformations of the chains in the case of the bipolaron. Spectrum analysis by fast Fourier transform of the SHE signal demonstrates a distinct shift of two characteristic peaks to a higher onset frequency compared to the polaron transport. The charge-spin conversion efficiency is also compared, where a larger conversion efficiency is obtained from the bipolaron transport due to the lower saturated velocity. The effects of the strength of the electric field and the interactions are discussed. This work reveals the role of the bipolaron in organic SHE and provides a feasible way to achieve larger conversion efficiency by controlling the species of carriers with the concentration of the dopant.

Generation and manipulation of pure spin current in a conducting loop coupled to an Aharonov-Bohm ring

In this work we put forward a new prescription for the generation and manipulation of non-decaying pure spin current (SC) in a Rashba spin-orbit (SO) coupled conducting loop which is attached to an Aharonov-Bohm (AB) ring. In presence of a single link between the rings, a SC is established in the flux-free ring, without accompanying any charge current (CC). The magnitude and direction of this SC are controlled by means of the AB flux, without tuning the SO coupling, which is the central aspect of our study. Employing a tight-binding framework we describe the two-ring quantum system, where the effect of magnetic flux is incorporated through Peierls phase factor. The specific roles of AB flux, SO coupling and the connectivity among the rings are critically investigated which yield several non-trivial signatures in energy band spectrum and pure SC. Along with SC, the phenomenon of flux-driven CC is also discussed, and at the end, different other effects like electron filling, system size and disorder are analyzed to make the present communication a self contained one. Our detailed investigation may provide some key aspects of designing efficient spintronic devices where SC can be guided in an other way.

Quantum Fluctuation of the Quantum Geometric Tensor and Its Manifestation as Intrinsic Hall Signatures in Time-Reversal Invariant Systems

In time-reversal invariant systems, all charge Hall effects predicted so far are extrinsic effects due to the dependence on the relaxation time. We explore intrinsic Hall signatures by studying the quantum noise spectrum of the Hall current in time-reversal invariant systems, and discover intrinsic thermal Hall noises in both linear and nonlinear regimes. As the band geometric characteristics, quantum geometric tensor and Berry curvature play critical roles in various Hall effects; so do their quantum fluctuations. It is found that the thermal Hall noise in linear order of the electric field is purely intrinsic, and the second-order thermal Hall noise has both intrinsic and extrinsic contributions. In particular, the intrinsic part of the second-order thermal Hall noise is a manifestation of the quantum fluctuation of the quantum geometric tensor, which widely exists as long as Berry curvature is nonzero. These intrinsic thermal Hall noises provide direct measurable means to band geometric information, including Berry curvature related quantities and quantum fluctuation of quantum geometric tensor.

Topological superconductivity and large spin Hall effect in the kagome family Ti6X4 (X = Bi, Sb, Pb, Tl, and In)

Topological superconductors (TSC) become a focus of research due to the accompanying Majorana fermions. However, the reported TSC are extremely rare. Recent experiments reported kagome TSC AV3Sb5 (A = K, Rb, and Cs) exhibit unique superconductivity, topological surface states (TSS), and Majorana bound states. More recently, the first titanium-based kagome superconductor CsTi3Bi5 with nontrivial topology was successfully synthesized as a perspective TSC. Given that Cs contributes little to electronic structures of CsTi3Bi5 and binary compounds may be easier to be synthesized, here, by first-principle calculations, we predict five stable nonmagnetic kagome compounds Ti6X4 (X = Bi, Sb, Pb, Tl, and In) which exhibit superconductivity with critical temperature Tc = 3.8 K - 5.1 K, nontrivialZ 2 band topology, and TSS close to the Fermi level. Additionally, large intrinsic spin Hall effect is obtained in Ti6X4, which is caused by gapped Dirac nodal lines due to a strong spin-orbit coupling. This work offers new platforms for TSC and spintronic devices.

Enhancing the Spin-Orbit Torque Efficiency by the Insertion of a Sub-nanometer β-W Layer

Spin-orbit torque (SOT) efficiency is one of the key issues of spintronics. However, enhancing the SOT efficiency is usually limited by the positive correlation between resistivity and the spin Hall ratio, where a high resistivity often accompanies a large spin Hall ratio. Here, we demonstrate that sub-nanometer β-W intercalation has a considerable impact on the SOT efficiency in α-W (6 nm)/Co (8 nm)/Pt (3 nm) samples. The damping-like SOT efficiency per unit current density, ξ_DL^j, of α-W (5.7 nm)/β-W (0.3 nm)/Co (8 nm)/Pt (3 nm) shows a ∼ 296% enhancement compared to that of the α-W/Co/Pt system. Meanwhile, a resistivity similar to that of α-W and the spin Hall ratio larger than β-W induce a giant damping-like SOT efficiency per applied electric field, ξ_DL^E, which is about 12.1 times larger than that of β-W. Our findings will benefit the SOT devices by reducing energy consumption.

Spin-Hall conductivity and Hall angle in a two-dimensional system with impurities in the presence of spin–orbit interactions

We investigate the spin-torque-dependent Spin Hall phenomenon in a two-dimensional tight-binding system in the presence of Rashba and Dresselhaus spin–orbit interactions and random static impurities. We employ the Matsubara Green function techniques to calculate the relaxation time caused by the scattering of electrons by impurities. The longitudinal and transverse conductivities are next calculated with the help of the Kubo formalism. We have also calculated the spin Hall angle for the present model and studied its dependence on spin–orbit interactions and impurity strength. Finally, we explore the effect of interplay between the Rashba and Dresselhaus interactions on the spin-Hall effect.

Robust pure spin current induced by the photogalvanic effect in half-silicane with spatial inversion symmetry

The spin-dependent photogalvanic (PG) effect in low-dimensional spin semiconductors has attracted great interest recently. Here, we have studied the spin semiconducting feature and spin-dependent photocurrent in a two-dimensional (2D) silicene-based device with spatial inversion symmetrical half-hydrogenation, in which half of the silicene is hydrogenated on the upper surface and half is hydrogenated on the lower surface. Because of the unique spin semiconductor properties and symmetry of the system, pure spin current can be robustly produced in both the zigzag and armchair directions for linearly and elliptically polarized light. The behavior of the spin-dependent photoresponse in the spin PG effect is highly anisotropic and can be tuned by the polarization/phase angles or photon energy (E_ph). Moreover, the produced pure spin current in such a half-silicane device with spatial inversion symmetry via the PG effect is several orders of magnitude larger than that obtained in metal/semiconductor/metal systems. These findings suggest a promising approach for generating pure spin current by the PG effect and provide a new possibility for the application of 2D half-silicane in spintronics.

Topological Spin Texture of Chiral Edge States in Photonic Two-Dimensional Quantum Walks

Topological insulators host topology-linked boundary states, whose spin and charge degrees of freedom could be exploited to design topological devices with enhanced functionality. We experimentally observe that dissipationless chiral edge states in a spin-orbit coupled anomalous Floquet topological phase exhibit topological spin texture on boundaries, realized via a two-dimensional quantum walk. Our experiment shows that, for a walker traveling around a closed loop along the boundary in real space, its spin evolves and winds through a great circle on the Bloch sphere, which implies that edge-spin texture has nontrivial winding. This topological spin winding is protected by a chiral-like symmetry emerging for the low-energy Hamiltonian. Our experiment confirms that two-dimensional anomalous Floquet topological systems exhibit topological spin texture on the boundary, which could inspire novel topology-based spintronic phenomena and devices.

Spin Swapping Effect of Band Structure Origin in Centrosymmetric Ferromagnets

We theoretically demonstrate the spin swapping effect of band structure origin in centrosymmetric ferromagnets. It is mediated by an orbital degree of freedom but does not require inversion asymmetry or impurity spin-orbit scattering. Analytic and tight-binding models reveal that it originates mainly from k points where bands with different spins and different orbitals are nearly degenerate, and thus it has no counterpart in normal metals. First-principle calculations for centrosymmetric 3d transition-metal ferromagnets show that the spin swapping conductivity of band structure origin can be comparable in magnitude to the intrinsic spin Hall conductivity of Pt. Our theory generalizes transverse spin currents generated by ferromagnets and emphasizes the important role of the orbital degree of freedom in describing spin-orbit-coupled transport in centrosymmetric materials.

Momentum-Space Spin Antivortex and Spin Transport in Monolayer Pb

Nontrivial momentum-space spin texture of electrons can be induced by spin-orbit coupling and underpins various spin transport phenomena, such as current-induced spin polarization and the spin Hall effect. In this work, we find a nontrivial spin texture, spin antivortex, can appear at certain momenta on the Γ-K line in a 2D monolayer Pb on top of SiC. Different from spin vortex due to the band degeneracy in the Rashba model, the existence of this spin antivortex is guaranteed by the Poincaré-Hopf theorem and thus topologically stable. Accompanied with this spin antivortex, a Lifshitz transition of Fermi surfaces occurs at certain momenta on the K-M line, and both phenomena are originated from the anticrossing between the j=1/2 and j=3/2 bands. A rapid variation of the response coefficients for both the current-induced spin polarization and spin Hall conductivity is found when the Fermi energy is tuned around the spin antivortex. Our work demonstrates the monolayer Pb as a potentially appealing platform for spintronic applications.

Regulating Interfacial Spin Hall Conductivity with Ferroelectricity

We report a new physical phenomenon of active and enhanced control of the spin Hall conductivity (SHC) in a family of metal-ferroelectric multilayers. Rather than the direction of the built-in electric field, such ferroelectric regulation of SHC originates from the drastic change of the interfacial electronic state along with its intrinsic Berry phase near the Fermi level due to the distinct hybridization between the metal film and substrate when the ferroelectric polarization reverses. Using Pt/PbZrTiO₃ multilayers as a representative model, we demonstrate the controllability of a large magnitude and even the sign of SHC in the Pt film at the two interfaces with an antitype conducting carrier in a ferroelectric substrate. The interfacial Rashba effect plays a role in contributing to the change of SHC through spin-projected band analysis. The present work makes a fundamental theoretical discovery and opens up a new direction to manipulate spin-charge conversion of thin-film layered structures by ferroelectricity, which is crucial for designing future electric and spintronic devices.

Rashba splitting in organic-inorganic lead-halide perovskites revealed through two-photon absorption spectroscopy

The Rashba splitting in hybrid organic-inorganic lead-halide perovskites (HOIP) is particularly promising and yet controversial, due to questions surrounding the presence or absence of inversion symmetry. Here we utilize two-photon absorption spectroscopy to study inversion symmetry breaking in different phases of these materials. This is an all-optical technique to observe and quantify the Rashba effect as it probes the bulk of the materials. In particular, we measure two-photon excitation spectra of the photoluminescence in 2D, 3D, and anionic mixed HOIP crystals, and show that an additional band above, but close to the optical gap is the signature of new two-photon transition channels that originate from the Rashba splitting. The inversion symmetry breaking is believed to arise from ionic impurities that induce local electric fields. The observation of the Rashba splitting in the bulk of HOIP has significant implications for the understanding of their spintronic and optoelectronic device properties.

Suppression of spin rectification effects in spin pumping experiments

Spin pumping (SP) is a well-established method to generate pure spin currents allowing efficient spin injection into metals and semiconductors avoiding the problem of impedance mismatch. However, to disentangle pure spin currents from parasitic effects due to spin rectification effects (SRE) is a difficult task that is seriously hampering further developments. Here we propose a simple method that allows suppressing SRE contribution to inverse spin Hall effect (ISHE) voltage signal avoiding long and tedious angle-dependent measurements. We show an experimental study in the well-known Py/Pt system by using a coplanar waveguide (CPW). Results obtained demonstrate that the sign and size of the measured transverse voltage signal depends on the width of the sample along the CPW active line. A progressive reduction of this width evidences that SRE contribution to the measured transverse voltage signal becomes negligibly small for sample width below 200 μm. A numerical solution of the Maxwell equations in the CPW-sample setup, by using the Landau-Lifshitz equation with the Gilbert damping term (LLG) as the constitutive equation of the media, and with the proper set of boundary conditions, confirms the obtained experimental results.

Spin-Orbit Coupling in 2D Semiconductors: A Theoretical Perspective

This theoretical Perspective reviews spin-orbit coupling (SOC), including the Rashba effect and Dresselhaus effect, in two-dimensional (2D) semiconductors. We first introduce the origin of the Rashba effect and Dresselhaus effect using the Hamiltonian models; we then summarize 2D Rashba semiconductors predicted by first-principles density functional theory (DFT) calculations, including AB binary monolayers, Janus monolayers, 2D perovskites, and so on. We also review various manipulating techniques of the Rashba effect on 2D semiconductors, such as external electric field, strain engineering, charge doping, interlayer interactions, proximity effect of substrates, and external magnetic field. We then briefly summarize the applications of SOC, including the generation, detection, and manipulation of spin currents in spin Hall effect transistors and spin field effect transistors. Finally, we conclude this Perspective and propose three promising research fields of SOC in low-dimensional semiconductors, including the nonlinear SOC Hamiltonian model, 2D ferroelectric SOC semiconductors, and 1D Rashba model and semiconductors. This theoretical Perspective enriches the fundamental understanding of SOC in 2D semiconductors and will help in the design of new types of spintronic devices in future experiments.

Non-monotonic variation of the Kramers point band gap with increasing magnetic doping in BiTeI

Polar Rashba-type semiconductor BiTeI doped with magnetic elements constitutes one of the most promising platforms for the future development of spintronics and quantum computing thanks to the combination of strong spin-orbit coupling and internal ferromagnetic ordering. The latter originates from magnetic impurities and is able to open an energy gap at the Kramers point (KP gap) of the Rashba bands. In the current work using angle-resolved photoemission spectroscopy (ARPES) we show that the KP gap depends non-monotonically on the doping level in case of V-doped BiTeI. We observe that the gap increases with V concentration until it reaches 3% and then starts to mitigate. Moreover, we find that the saturation magnetisation of samples under applied magnetic field studied by superconducting quantum interference device (SQUID) magnetometer has a similar behaviour with the doping level. Theoretical analysis shows that the non-monotonic behavior can be explained by the increase of antiferromagnetic coupled atoms of magnetic impurity above a certain doping level. This leads to the reduction of the total magnetic moment in the domains and thus to the mitigation of the KP gap as observed in the experiment. These findings provide further insight in the creation of internal magnetic ordering and consequent KP gap opening in magnetically-doped Rashba-type semiconductors.

Applications of nanomagnets as dynamical systems: II

In Part I of this topical review, we discussed dynamical phenomena in nanomagnets, focusing primarily on magnetization reversal with an eye to digital applications. In this part, we address mostly wave-like phenomena in nanomagnets, with emphasis on spin waves in myriad nanomagnetic systems and methods of controlling magnetization dynamics in nanomagnet arrays which may have analog applications. We conclude with a discussion of some interesting spintronic phenomena that undergird the rich physics exhibited by nanomagnet assemblies.

Orbital torque in magnetic bilayers

The orbital Hall effect describes the generation of the orbital current flowing in a perpendicular direction to an external electric field, analogous to the spin Hall effect. As the orbital current carries the angular momentum as the spin current does, injection of the orbital current into a ferromagnet can result in torque on the magnetization, which provides a way to detect the orbital Hall effect. With this motivation, we examine the current-induced spin-orbit torques in various ferromagnet/heavy metal bilayers by theory and experiment. Analysis of the magnetic torque reveals the presence of the contribution from the orbital Hall effect in the heavy metal, which competes with the contribution from the spin Hall effect. In particular, we find that the net torque in Ni/Ta bilayers is opposite in sign to the spin Hall theory prediction but instead consistent with the orbital Hall theory, which unambiguously confirms the orbital torque generated by the orbital Hall effect. Our finding opens a possibility of utilizing the orbital current for spintronic device applications, and it will invigorate researches on spin-orbit-coupled phenomena based on orbital engineering.

PT-Symmetry-Enabled Spin Circular Photogalvanic Effect in Antiferromagnetic Insulators

The short timescale spin dynamics in antiferromagnets is an attractive feature from the standpoint of ultrafast spintronics. Yet generating highly polarized spin current at room temperature remains a fundamental challenge for antiferromagnets. We propose a spin circular photogalvanic effect (spin CPGE), in which circularly polarized light can produce a highly spin-polarized current at room temperature, through an "injection-current-like" mechanism in parity-time (PT)-symmetric antiferromagnetic (AFM) insulators. We demonstrate this effect by first-principles simulations of bilayer CrI_{3} and room-temperature-AFM hematite. The spin CPGE is significant, and the magnitude of spin photocurrent is comparable with the widely observed charge photocurrent in ferroelectric materials. Interestingly, this spin photocurrent is not sensitive to spin-orbit interactions, which were regarded as fundamental mechanisms for generating spin current. Given the fast response of light-matter interactions, large energy scale, and insensitivity to spin-orbit interactions, our work gives hope to realizing fast-dynamic and temperature-robust pure spin current in a wide range of PT-symmetric AFM materials, including topological axion insulators and weak-relativistic magnetic insulators.

Relation between spin current and spin torque in Rashba ferromagnets

We establish a brief relation between spin current and spin torque, including spin-orbit torque and spin transfer torque in 2D Rashba ferromagnets with nonuniform magnetic texture. Both electrically and thermally induced charge, heat, and spin current are investigated by the Luttinger's mechanical method, and we derive the contributions of magnetization corresponding to the thermal spin current and the thermal spin torque. The novel transport currents are also found in this paper when the interplay between spin-orbit coupling and nonuniform magnetic texture is taken into account.

Berry curvature induced magnetotransport in 3D noncentrosymmetric metals

We study the magnetoelectric and magnetothermal transport properties of noncentrosymmetric metals using semiclassical Boltzmann transport formalism by incorporating the effects of Berry curvature (BC) and orbital magnetic moment (OMM). These effects impart quadratic-Bdependence to the magnetoelectric and magnetothermal conductivities, leading to intriguing phenomena such as planar Hall effect, negative magnetoresistance (MR), planar Nernst effect and negative Seebeck effect. The transport coefficients associated with these effects show the usual oscillatory behavior with respect to the angle between the applied electric field and magnetic field. The bands of noncentrosymmetric metals are split by Rashba spin-orbit coupling except at a band touching point (BTP). For Fermi energy below (above) the BTP, giant (diminished) negative MR is observed. This difference in the nature of MR is related to the magnitudes of the velocities, BC and OMM on the respective Fermi surfaces, where the OMM plays the dominant role. The absolute MR and planar Hall conductivity show a decreasing (increasing) trend with Rashba coupling parameter for Fermi energy below (above) the BTP.

Prediction of giant and ideal Rashba-type splitting in ordered alloy monolayers grown on a polar surface

A large and ideal Rashba-type spin-orbit splitting is desired for the applications of materials in spintronic devices and the detection of Majorana fermions in solids. Here, we propose an approach to achieve giant and ideal spin-orbit splittings through a combination of ordered surface alloying and interface engineering, that is, growing alloy monolayers on an insulating polar surface. We illustrate this unique strategy by means of first-principle calculations of buckled hexagonal monolayers of SbBi and PbBi supported on Al₂O₃(0001). Both systems display ideal Rashba-type states with giant spin-orbit splittings, characterized with energy offsets over 600 meV and momentum offsets over 0.3 Å⁻¹, respectively. Our study thus points to an effective way of tuning spin-orbit splitting in low-dimensional materials to draw immediate experimental interest.

Spin-Charge Interconversion in KTaO3 2D Electron Gases

Oxide interfaces exhibit a broad range of physical effects stemming from broken inversion symmetry. In particular, they can display non-reciprocal phenomena when time reversal symmetry is also broken, e.g., by the application of a magnetic field. Examples include the direct and inverse Edelstein effects (DEE, IEE) that allow the interconversion between spin currents and charge currents. The DEE and IEE have been investigated in interfaces based on the perovskite SrTiO₃ (STO), albeit in separate studies focusing on one or the other. The demonstration of these effects remains mostly elusive in other oxide interface systems despite their blossoming in the last decade. Here, the observation of both the DEE and IEE in a new interfacial two-dimensional electron gas (2DEG) based on the perovskite oxide KTaO₃ is reported. 2DEGs are generated by the simple deposition of Al metal onto KTaO₃ single crystals, characterized by angle-resolved photoemission spectroscopy and magnetotransport, and shown to display the DEE through unidirectional magnetoresistance and the IEE by spin-pumping experiments. Their spin-charge interconversion efficiency is then compared with that of STO-based interfaces, related to the 2DEG electronic structure, and perspectives are given for the implementation of KTaO₃ 2DEGs into spin-orbitronic devices is compared.

Pure spin photocurrent in non-centrosymmetric crystals: bulk spin photovoltaic effect

Spin current generators are critical components for spintronics-based information processing. In this work, we theoretically and computationally investigate the bulk spin photovoltaic (BSPV) effect for creating DC spin current under light illumination. The only requirement for BSPV is inversion symmetry breaking, thus it applies to a broad range of materials and can be readily integrated with existing semiconductor technologies. The BSPV effect is a cousin of the bulk photovoltaic (BPV) effect, whereby a DC charge current is generated under light. Thanks to the different selection rules on spin and charge currents, a pure spin current can be realized if the system possesses mirror symmetry or inversion-mirror symmetry. The mechanism of BSPV and the role of the electronic relaxation time [Formula: see text] are also elucidated. We apply our theory to several distinct materials, including monolayer transition metal dichalcogenides, anti-ferromagnetic bilayer MnBi2Te4, and the surface of topological crystalline insulator cubic SnTe.

Efficient Time-Domain Approach for Linear Response Functions

We derive the general Kubo formula in a form that solely utilizes the time evolution of displacement operators. The derivation is based on the decomposition of the linear response function into its time-symmetric and time-antisymmetric parts. We relate this form to the well-known fluctuation-dissipation formula and discuss theoretical and numerical aspects of it. The approach is illustrated with an analytical example for magnetic resonance as well as a numerical example where we analyze the electrical conductivity tensor and the Chern insulating state of the disordered Haldane model. We introduce a highly efficient time-domain approach that describes the quantum dynamics of the resistivity of this model with an at least 1000-fold better performance in comparison to existing time-evolution schemes.