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Two kinds of phenomena with the same essence may be correlative. Exploring this correlation can help us generate new ideas. Light can carry three types of angular momentum: The rotating electromagnetic field with circularly polarized will produce spin angular momentum (SAM); The vortex light with helical wavefronts will carry intrinsic orbital angular momentum (IOAM); Light, not traveling through the coordinate origin, will carry extrinsic orbital angular momentum (EOAM). The interaction between SAM and EOAM will produce a spin Hall effect of light. The interaction between SAM and IOAM will lead to mutual conversion between them. SAM and EOAM, as well as SAM and IOAM, can also form spin–orbit entangled states. Therefore, the spin–orbit interaction and corresponding entangled states of light must have some correlations. This work studied the relationship between the spin Hall effect and the spin–orbit entangled state, and the relationship between the conversion efficiency of spin–orbit angular momentum and the spin–orbit entangled state. This work can provide new enlightenment to the study of entangled states, which can help the cross-disciplinary application of quantum entanglement with other knowledge. [ABSTRACT FROM AUTHOR]

The inverse spin Hall effect is a critical method for detecting spin Hall conductivity. Unearthing the physical relationship between electronic structure and spin Hall conductivity is conducive to establishing an intrinsic link between microstructure and macroscopic phenomena. Here, we report MnBi2Te4 as an ideal candidate: a stable, inversion symmetry-broken magnetic topological insulator for investigating the intrinsic correlation between spin Hall conductivity signal reversal and electronic structure. The valence band exhibits a significant Rashba spin splitting, with a magnitude reaching up to 4.61 eV/Å. We identify robust topological properties independent of Rashba and Lifshitz spin-splitting types. Moreover, transitioning the spin-splitting type not only widens the bulk band gap, enhancing the spin Hall conductivity plateau, but also triples the intrinsic spin Hall conductivity value. We propose the inverse spin Hall effect that is tunable by spin-splitting types, thereby advancing the research on the microscopic electronic mechanisms of spin current detection. The spin Hall effect facilitates the generation and detection of spin currents and is expected to play an important role in future spintronic devices. Here, the authors theoretically investigate the presence of Rashba spin splitting for MnBi2Te4 and the relationship with an inverse spin Hall effect also present in the system. [ABSTRACT FROM AUTHOR]

The inverse spin Hall effect is a critical method for detecting spin Hall conductivity. Unearthing the physical relationship between electronic structure and spin Hall conductivity is conducive to establishing an intrinsic link between microstructure and macroscopic phenomena. Here, we report MnBi2Te4 as an ideal candidate: a stable, inversion symmetry-broken magnetic topological insulator for investigating the intrinsic correlation between spin Hall conductivity signal reversal and electronic structure. The valence band exhibits a significant Rashba spin splitting, with a magnitude reaching up to 4.61 eV/Å. We identify robust topological properties independent of Rashba and Lifshitz spin-splitting types. Moreover, transitioning the spin-splitting type not only widens the bulk band gap, enhancing the spin Hall conductivity plateau, but also triples the intrinsic spin Hall conductivity value. We propose the inverse spin Hall effect that is tunable by spin-splitting types, thereby advancing the research on the microscopic electronic mechanisms of spin current detection. The spin Hall effect facilitates the generation and detection of spin currents and is expected to play an important role in future spintronic devices. Here, the authors theoretically investigate the presence of Rashba spin splitting for MnBi2Te4 and the relationship with an inverse spin Hall effect also present in the system. [ABSTRACT FROM AUTHOR]

Topological semimetals have recently garnered widespread interest in the quantum materials research community due to their symmetry-protected surface states with dissipationless transport which have potential applications in next-generation low-power electronic devices. One such material, , exhibits Dirac nodal arcs and although the topological properties of single crystals have been investigated, there have been no reports in crystalline thin film geometry. We examined the growth of heterostructures on a range of single crystals by optimizing the electron beam evaporation of Pt and Sn and studied the effect of vacuum thermal annealing on phase and crystallinity. The electrical resistivity was fitted to a modified Bloch–Grüneisen model with a residual resistivity of 79.43(1) cm at 2K and a Debye temperature of 200K. Nonlinear Hall resistance indicated the presence of more than one carrier type with an effective carrier mobility of 33.6 and concentration of 1.41 at 300 K. X-ray photoemission spectra were in close agreement with convolved density of states and a work function of 4.7(2) eV was determined for the (010) surface. This study will facilitate measurements that require heterostructure geometry, such as spin and topological Hall effect, and will facilitate potential device incorporation in future quantum technologies. [ABSTRACT FROM AUTHOR]

Topological semimetals have recently garnered widespread interest in the quantum materials research community due to their symmetry-protected surface states with dissipationless transport which have potential applications in next-generation low-power electronic devices. One such material, , exhibits Dirac nodal arcs and although the topological properties of single crystals have been investigated, there have been no reports in crystalline thin film geometry. We examined the growth of heterostructures on a range of single crystals by optimizing the electron beam evaporation of Pt and Sn and studied the effect of vacuum thermal annealing on phase and crystallinity. The electrical resistivity was fitted to a modified Bloch–Grüneisen model with a residual resistivity of 79.43(1) cm at 2K and a Debye temperature of 200K. Nonlinear Hall resistance indicated the presence of more than one carrier type with an effective carrier mobility of 33.6 and concentration of 1.41 at 300 K. X-ray photoemission spectra were in close agreement with convolved density of states and a work function of 4.7(2) eV was determined for the (010) surface. This study will facilitate measurements that require heterostructure geometry, such as spin and topological Hall effect, and will facilitate potential device incorporation in future quantum technologies. [ABSTRACT FROM AUTHOR]

The Berry phase is a fundamental concept in quantum mechanics with profound implications for understanding topological properties of quantum systems. This tutorial provides a comprehensive introduction to the Berry phase, beginning with the essential mathematical framework required to grasp its significance. We explore the intrinsic link between the emergence of a non-trivial Berry phase and the presence of topological characteristics in quantum systems, showing the connection between the Berry phase and the band structure as well as the phase's gauge-invariant nature during cyclic evolutions. The tutorial delves into various topological effects arising from the Berry phase, such as the quantum, anomalous, and spin Hall effects, which exemplify how these quantum phases manifest in observable phenomena. We then extend our discussion to cover the transport properties of topological insulators, elucidating their unique behaviour rooted in the Berry phase physics. This tutorial aims at equipping its readers with a robust understanding of the basic theory underlying the Berry phase and of its pivotal role in the realm of topological quantum phenomena. [ABSTRACT FROM AUTHOR]

The photonic spin Hall effect (PSHE) at the optical interface is a polarization-dependent phenomenon of incident light. The described methodology is a novel strategy for controlling the active polarization mode of the enhanced PSHE. The PSHE is enhanced for both horizontal (H) and vertical (V) polarized light in the ∼ 1.5 mm to the submillimeter range. The enhanced PSHE has been measured for the reflected light from the modified Kretschmann configuration. An additional thin dielectric (glass) layer on the ultrathin metal (Ag, Al) layer provides simultaneous surface plasmon resonance (SPR) and wave-guiding effects. Furthermore, we demonstrated that by changing the physical parameter of the structure, we could tune the enhancement of PSHE along with the control on polarization mode. This research paves the way for new photonic devices with ultra-high sensitivity for metrological applications. Furthermore, depending on the light spin, this work enables a degree of freedom in the choosing of input light polarization for numerous potential applications. [ABSTRACT FROM AUTHOR]

We derive the axial projection of the spin angular momentum (SAM) vector for a vector Gaussian beam with 1D periodic amplitude modulation. Such a beam has zero SAM in the source plane and its polarization is inhomogeneous linear. We demonstrate that when such a beam propagates, its periodic modulation effectively splits the beam into two, having elliptic polarization of opposite handedness. Therefore, the spin Hall effect is shown to arise, since the cross section of the beam contains alternating domains with nonzero spin of opposite sign. For generating such a field, a metasurface can be employed, whose transmittance is changing with one coordinate periodically. [ABSTRACT FROM AUTHOR]

We investigate the spin angular momentum of a superposition of two vector light beams with rotational symmetry. One beam is cylindrically polarized and another is linearly polarized. Radial form of these beams can be arbitrary (Laguerre-Gaussian, Bessel-Gaussian, or some other). For such a superposition, an analytical expression is derived for the spin angular momentum and two its properties are obtained. At first, we found that altering the coefficients does not affect the form of the spin angular momentum distribution, while the intensity distribution is changed. At second, we found that maximal spin angular momentum is generated if both beams are of equal power. [ABSTRACT FROM AUTHOR]

The sharp focusing of the superposition of a plane wave with the linear polarisation (LP) and an optical vortex with topological charge (TC) m and with the same LP directed along the horizontal axis is considered. Applying the Richards–Wolf formalism, analytical formulas are derived for the intensity and the spin angular momentum (SAM) lengthwise component in the focal plane. It is demonstated that for odd and even TCs m the SAM and the intensity have different symmetries: for even m they are symmetric about both Cartesian axes, and for odd m they are symmetric only about the vertical axis. The intensity pattern has 2m local maxima in the focal plane. The intensity on the optical axis for any TC m is nonzero. The pattern of the lengthwise SAM (spin density) in the focal plane has 2(m + 2) subwavelength areas in the half of which the SAM has positive value while in others it has negative value. The centers of these areas alternately lie on a circle of a certain radius with a center on the optical axis. This spin pattern with different signs shows the spin Hall effect in the focal plane. The total negative and positive spin in the focal plane are mutually compensated and equal to zero. [ABSTRACT FROM AUTHOR]

Antiferromagnetic magnons possess a distinctive feature absent in their ferromagnetic counterparts: the presence of two distinct handedness modes, the right-handed (RH) and left-handed (LH) precession modes. The magnon handedness determines the sign of spin polarization carried by the propagating magnon, which is indispensable for harnessing the diverse functionalities in magnonic devices, such as data encoding, magnon polarization-based logic systems, and quantum applications involving magnons. However, the control of coherently propagating magnon handedness in antiferromagnets has remained elusive. Here we demonstrate the manipulation and electrical readout of propagating magnon handedness in perpendicularly magnetized synthetic antiferromagnets (SAF). We find that the antiferromagnetic magnon handedness can be directly identified by measuring the inverse spin Hall effect (ISHE) voltage, which arises from the spin pumping effect caused by the propagating antiferromagnetic magnons in the SAF structure. The RH and LH modes of the magnon can be distinguishable when the SAF structure is sandwiched by heavy metals with the same sign of spin Hall angle. This work unveils promising avenues for harnessing the unique properties of antiferromagnetic magnons. Antiferromagnetic magnons have two distinct chiralities, left handed and right handed. Here, Shiota and coauthors demonstrate both the manipulation and electrical readout of this handedness in a synthetic antiferromagnet. [ABSTRACT FROM AUTHOR]

The effect of the variation of the spin current on the magnetic susceptibility of a magnonic waveguide in the form of a "ferromagnet–normal metal" heterostructure is investigated. Based on the Landau–Lifshitz–Gilbert model with the current term in the Slonczewski–Berger form, which describes the magnetization dynamics including the spin moment transfer, expressions are obtained for the real and imaginary parts of the magnetic susceptibility in the geometry of surface spin waves in the damping mode. The resulting model correctly approximates experimental data demonstrating an increase in the amplitude of spin waves propagating in a YIG/Pt heterostructure. It is shown that an increase in the spin current leads to an increase in the resonance frequency of spin waves and in the magnetic susceptibility tensor components in resonance. The results of this study can be used to design waveguides for spin waves with controllable losses and high-sensitivity magnetic field sensors. [ABSTRACT FROM AUTHOR]

Light-matter interactions have emerged as a new research focus recently offering promises of unveiling novel physics and leading to applications under nonequilibrium conditions. The quantized Hall conductivities predicted by Floquet theory assuming a Fermi-Dirac distribution however deviate from experimental observations. To resolve these puzzles, we consider the effect of nonequilibrium electron occupation to study the anomalous, valley, and spin Hall effects of a prototype monolayer transition metal dichalcogenide MoS2. We find that spin Hall conductivity can be effectively suppressed approaching zero value by linearly polarized light under near resonant excitations. In contrast, it is substantially enhanced by circularly polarized light, originating from optical selection rules and topological phase transitions. Besides, the quantized anomalous Hall conductivity is much reduced if nonequilibrium occupations of Floquet bands are considered. Our study provides a novel avenue for engineering various Hall effects in two-dimensional materials using light, holding great promises for future device applications. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

The conversion efficiency from charge current to spin current via the spin Hall effect is evaluated by the spin Hall ratio (SHR). Through state-of-the-art ab initio calculations involving both charge conductivity and spin Hall conductivity, we report the SHRs of the III-V monolayer family, revealing an ultrahigh ratio of 0.58 in the hole-doped GaAs monolayer. In order to find more promising 2D materials, a descriptor for high SHR is proposed and applied to a high-throughput database, which provides the fully relativistic band structures and Wannier Hamiltonians of 216 exfoliable monolayer semiconductors and has been released to the community. Among potential candidates for high SHR, the MXene monolayer Sc2CCl2 is identified with the proposed descriptor and confirmed by computation, demonstrating the descriptor validity for high SHR materials discovery. [ABSTRACT FROM AUTHOR]

Centrosymmetric materials with site inversion asymmetries possess hidden spin polarization, which remains challenging to be converted into spin currents because the global inversion symmetry is still conserved. This study demonstrates the spin-polarized circular photocurrents in centrosymmetric transition metal dichalcogenide semiconductors at normal incidence without applying electric bias. The global inversion symmetry is broken by using a spatially-varying circularly polarized light beam, which could generate spin gradient owing to the hidden spin polarization. The dependence of the circular photocurrents on electrode configuration, illumination position, and beam spot size indicates an emergence of circulating electric current under spatially inhomogeneous light, which is associated with the deflection of spin-polarized current through the inverse spin Hall effect. The circular photocurrents is subsequently utilized to probe the spin polarization and the inverse spin Hall effect under different excitation wavelengths and temperatures. The results of this study demonstrate the feasibility of using centrosymmetric materials with hidden spin polarization and non-vanishing Berry curvature for spintronic device applications. The authors report the generation of circular photocurrents from multilayer 2H-phase transition metal dichalcogenides, including MoTe2, MoS2, and WSe2, which is attributed to the manifestation of hidden spin polarization and inverse spin Hall effect. [ABSTRACT FROM AUTHOR]

We consider the anomalous, spin, valley, and valley spin Hall effects in a pristine graphene-based van-der-Waals (vdW) heterostructure consisting of a bilayer graphene (BLG) sandwiched between a semiconducting van-der-Waals material with strong spin-orbit coupling (e.g., WS 2 ) and a ferromagnetic insulating vdW material (e.g. Cr 2 Ge 2 Te 6 ). Due to the exchange proximity effect from one side and spin-orbit proximity effect from the other side of graphene, such a structure is referred to as graphene based 'ex-so-tic' structure. First, we derive an effective Hamiltonian describing the low-energy states of the structure. Then, using the Green's function formalism, we obtain analytical results for the Hall conductivities as a function of the Fermi energy and gate voltage. For specific values of these parameters, we find a quantized valley Hall conductivity. [ABSTRACT FROM AUTHOR]

Recent theoretically predicted strong anisotropic spin Hall effect (SHE) or inverse SHE (ISHE) in chiral antiferromagnetic compounds Mn3X (X = Ge, Sn, Ga, Ir, Rh, and Pt) could potentially expand the horizons of the antiferromagnet spintronics; however, it has not been experimentally observed yet. For achieving this goal, we have first successfully fabricated high-quality Kagome phase Mn3Sn films with smooth surface by a combination of room-temperature magnetron sputtering and high-temperate annealing. These Mn3Sn films were proved to be epitaxially grown on MgO (110) single crystal substrate with a seldom reported ( 1 0 1 - 0 ) orientation that could serve as a good platform for the studies of the crystalline orientation-related anisotropic phenomenon. Then, by employing spin pumping-induced inverse spin Hall effect (SP-ISHE) voltage measurements, we have experimentally proved the existence of crystalline orientation-related anisotropic ISHE with an amplitude of more than 35% in our Mn3Sn films. [ABSTRACT FROM AUTHOR]

Vortex light, characterized by an intrinsic orbital angular momentum aligned with its propagation direction, is described through vortex electromagnetic waves. Similar to the gravitational spin Hall effect (SHE), vortex light is expected to exhibit intrinsic orbital angular momentum dependent trajectories and deviations from the null geodesic plane when propagating through a gravitational field, a phenomenon termed the gravitational orbital Hall effect (OHE). In this work, we model the vortex light as vortex Laguerre–Gaussian electromagnetic wave packets and analyze its motion by solving covariant Maxwell equations within the Lense–Thirring metric. Our findings reveal that the trajectory of vortex light with an intrinsic orbital angular momentum deviates from the null geodesic in two ways. It deviates both perpendicular to, and within, the null geodesic plane. This behavior contrasts with the gravitational SHE, where spin-polarized light primarily deviates perpendicular to the null geodesic plane. Moreover, the relationship between the deviation and intrinsic orbital angular momentum differs significantly from that between the deviation and spin. These results suggest a unique interaction between intrinsic orbital angular momentum and gravity, distinct from the spin-gravity coupling, indicating that the gravitational OHE of light might not be precisely predicted by merely substituting spin with intrinsic orbital angular momentum in the gravitational SHE of light. [ABSTRACT FROM AUTHOR]

In this study, we propose and simulate a magnetoplasmonics heterostructure that utilizes spin–orbit fields to generate an internal magnetic field and create a significant magneto-optical effect. Our approach offers a new way to overcome the challenges of using permanent magnets or magnetic coils in conventional magnetoplasmonics, such as high-power consumption and non-scalability. We demonstrate that it is possible to create an appropriate amount of magnetic field using spin–orbit fields induced by the spin-Hall effect, such that the consumption power becomes reasonable and the dimensions could be miniaturized. This approach will be an important development in the field of magneto-optics, as it can lead to enhanced transverse magneto-optical Kerr effect in the present of surface plasmon polaritons. The proposed nanostructure consists of a ferromagnetic film adjacent to a heavy metal layer, both sandwiched between two noble metal films, and deposited on a dielectric prism. The strength of the Kerr signal strongly depends on the thickness of the ferromagnetic layer, with the maximum effect observed at a thickness of 5nm. This concept has potential for various nanophotonic and spintronic applications, particularly for developing high-speed active plasmonic devices for ultrafast light modulation. [ABSTRACT FROM AUTHOR]

Angular-dependent magneto-optical Kerr effect (MOKE) and coplanar waveguide ferromagnetic resonance (CPW-FMR) measurements were performed to unravel the nature of anisotropy present in Ni 80 Fe 20 (Py) thin film. The "in-plane" angular variation of coercive field ( H c IP ) and resonance field ( H r IP ) confirms the magnetic anisotropy is negligible, where the spins are confined to the plane of the Py film. The variation of resonance field in "out-of-plane" geometry, H r OP , strongly indicates the presence of "out-of-plane" uniaxial anisotropy in the Py thin film. Also, the inverse spin Hall effect (ISHE) technique is employed to measure spin pumping-induced DC voltage, V ISHE , generated across the Py/Pt bilayer. The line shape analysis method has been utilized to distinguish ISHE and spin rectification contributions. The measured V ISHE at low (4 GHz) and high (35 GHz) frequencies confirm the pure spin current injected through the Py-Pt interface due to spin pumping using CPW-FMR setup, which has a direct bearing on the realization of quantum metrology through the spin current quantity. [ABSTRACT FROM AUTHOR]

The concept of ferroelectricity is now often extended to include continuous inversion symmetry-breaking transitions in various metals and doped semiconductors. Paraelectric metals near ferroelectric quantum criticality, which we term 'quantum paraelectric metals,' possess soft transverse optical phonons which can have Rashba-type coupling to itinerant electrons in the presence of spin-orbit coupling. We find through the Kubo formula calculation that such Rashba electron-phonon coupling has a profound impact on electron spin transport. While the spin Hall effect arising from non-trivial electronic band structures has been studied extensively, we find here the presence of the Rashba electron-phonon coupling can give rise to spin current, including spin Hall current, in response to an inhomogeneous electric field even with a completely trivial band structure. Furthermore, this spin conductivity displays unconventional characteristics, such as quadrupolar symmetry associated with the wave vector of the electric field and a thermal activation behavior characterized by scaling laws dependent on the phonon frequency to temperature ratio. These findings shed light on exotic electronic transport phenomena originating from ferroelectric quantum criticality, highlighting the intricate interplay of charge and spin degrees of freedom. [ABSTRACT FROM AUTHOR]

This study presents a novel method leveraging surface wave-assisted photonic spin Hall effect (PSHE) to construct physical unclonable functions (PUFs). PUFs exploit inherent physical variations to generate unique Challenge–Response pairs, which are critical for hardware security and arise from manufacturing discrepancies, device characteristics, or timing deviations. We explore PSHE generation-based PUF design, expanding existing design possibilities. With recent applications in precise sensing and computing, PSHE offers promising performance metrics for our proposed PUFs, including an inter-Hamming distance of 47.50% , an average proportion of unique responses of 62.5% , and a Pearson correlation coefficient of − 0.198. The PUF token demonstrates robustness to simulated noise. Additionally, we evaluate security using a machine learning-based attack model, employing a multi-layer perceptron (MLP) regression model with a randomized search method. The average accuracy of successful attack prediction is 9.70% for the selected dataset. Our novel PUF token exhibits high non-linearity due to the PSHE effect, resilience to MLP-based attacks, and sensitivity to process variation. [ABSTRACT FROM AUTHOR]

The article presents the results of a qualitative study of the model of a modern magnetic memory cell, in which the spin Hall effect is used for recording. Cells of square cross-section with longitudinal anisotropy of the active layer are considered. Based on the Landau-Lifshitz-Gilbert vector equation, a mathematical model for controlling the process of writing zero and one into a cell is constructed. In the approximation of a uniform distribution of magnetization, a system of equations is derived that describes the dynamics of magnetization under the action of a magnetic field and spin current. The parameters of the qualitatively equivalent dynamics of the model are determined. It has been established that at zero currents and fields in both cases there are two main stable equilibrium positions. These equilibria, depending on the mutual orientation of the magnetization vector of the active and reference layers, correspond to zero and one, written in the cell. The transition from one cell state to another is described by solving a system of differential equations. A bifurcation diagram of a dynamical system in the variables "field–current" is constructed. It is shown that with a given configuration of the memory element, external influences transfer the magnetization to an intermediate state in the plane of the free layer, which, when the current and field are turned off, leads to writing zero or one to the memory cell. The critical switching current is estimated as a function of the applied external magnetic field. [ABSTRACT FROM AUTHOR]

Electrons in metals can show a giant anomalous Hall effect (AHE) when interacting with characteristic spin texture. The AHE has been discussed in terms of scalar-spin-chirality (SSC) in long-range-ordered noncollinear spin textures typified by Skyrmion. The SSC becomes effective even in the paramagnetic state with thermal fluctuations, but the resultant AHE has been limited to be very small. Here, we report the observation of large AHE caused by the spin fluctuation near the devil's staircase transition in a collinear antiferromagnetic metal SrCo6O11. The AHE is prominent near and above the transition temperature at moderate magnetic fields, where the anomalous Hall angle becomes the highest level among known oxide collinear ferromagnets/antiferromagnets (>2%). Furthermore, the anomalous Hall conductivity is quadratically scaled to the conductivity. These results imply that the thermally induced solitonic spin defects inherent to the devil's staircase transition promote SSC-induced skew scattering. [ABSTRACT FROM AUTHOR]

The solid thin films of Py/Pt and Py/W heterostructures have been studied using the ferromagnetic resonance method. The temperature dependences of the Gilbert damping parameter and voltage of the inverse spin Hall effect (ISHE) have been obtained in the 5–290 K temperature range. An abnormal increase in the Gilbert damping parameter in the vicinity of 50 K and a change in the voltage of ISHE has been found. It has been concluded that an increase in the Gilbert damping parameter is of spin-orbital nature. [ABSTRACT FROM AUTHOR]

This paper investigates the relationship among interlayer exchange coupling (IEC), Dzyaloshinskii–Moriya interaction (DMI), and multilevel magnetization switching within a Co/Pt/Co heterostructure, where varying Pt thicknesses enable control over the coupling strength. Employing Brillouin Light Scattering to quantify the effective DMI, we explore its potential role in magnetization dynamics and multilevel magnetization switching. Experimental findings show four distinct resistance states under an external magnetic field and spin Hall effect related spin current. We explain this phenomenon based on the asymmetry between Pt/Co and Co/Pt interfaces and the interlayer coupling, which, in turn, influences the DMI and subsequently impacts the magnetization dynamics. Numerical simulations, including macrospin, 1D domain wall, and simple spin wave models, further support the experimental observations of multilevel switching and help uncover the underlying mechanisms. Our proposed explanation, supported by magnetic domain observation using polar-magnetooptical Kerr microscopy, offers insights into both the spatial distribution of magnetization and its dynamics for different IECs, thereby shedding light on its interplay with DMI, which may lead to potential applications in storage devices. [ABSTRACT FROM AUTHOR]

The spin Hall (SH) effect, the conversion of the electric current to the spin current along the transverse direction, relies on the relativistic spin-orbit coupling (SOC). Here, we develop a microscopic theory on the mechanisms of the SH effect in magnetic metals, where itinerant electrons are coupled with localized magnetic moments via the Hund exchange interaction and the SOC. Both antiferromagnetic metals and ferromagnetic metals are considered. It is shown that the SH conductivity can be significantly enhanced by the spin fluctuation when approaching the magnetic transition temperature of both cases. For antiferromagnetic metals, the pure SH effect appears in the entire temperature range, while for ferromagnetic metals, the pure SH effect is expected to be replaced by the anomalous Hall effect below the transition temperature. We discuss possible experimental realizations and the effect of the quantum criticality when the antiferromagnetic transition temperature is tuned to zero temperature. [ABSTRACT FROM AUTHOR]

The spin Hall effect (SHE) allows efficient generation of spin polarization or spin current through charge current and plays a crucial role in the development of spintronics. While SHE typically occurs in non-magnetic materials and is time-reversal even, exploring time-reversal-odd (T-odd) SHE, which couples SHE to magnetization in ferromagnetic materials, offers a new charge-spin conversion mechanism with new functionalities. Here, we report the observation of giant T-odd SHE in Fe3GeTe2/MoTe2 van der Waals heterostructure, representing a previously unidentified interfacial magnetic spin Hall effect (interfacial-MSHE). Through rigorous symmetry analysis and theoretical calculations, we attribute the interfacial-MSHE to a symmetry-breaking induced spin current dipole at the vdW interface. Furthermore, we show that this linear effect can be used for implementing multiply-accumulate operations and binary convolutional neural networks with cascaded multi-terminal devices. Our findings uncover an interfacial T-odd charge-spin conversion mechanism with promising potential for energy-efficient in-memory computing. Charge-to-spin conversion allows for the generation and control of spin polarization via a charge current. Typically, this is done with non-magnetic materials with large spin-orbit interactions such as Platinum. Herein, Dai et al demonstrate an intriguing charge-to-spin mechanism, a magnetic spin Hall effect, in a van der Waals heterostructure. [ABSTRACT FROM AUTHOR]

In this work, a transverse spin-dependent shift of the horizontal photonic spin Hall effect at a fixed wavelength (0.6328 μm) is simulated for cancer cell detection based on refractive index, chemical potential, and electrical voltage variations applied to a plasmonic sensor with five layers (Ge20Ga5Sb10S65 chalcogenide prism, silver, gold, grapheme, and cancerous medium). When the conventional weak measurement is applied and when the chemical potential is increased from 0.3 eV to 8 eV, the chemical and voltage resolutions are 3.87 × 10–7 eV, 13.3327 μV for n5 = 1.38 RIU (cancerous skin cell), 5.17 × 10–7 eV, 17.7889 μV for n5 = 1.392 RIU (cancerous cervical cell), 4.95 × 10–7 eV, 17.0249 μV for n5 = 1.390 RIU (cancerous blood cell), and 5.50 × 10–7 eV, 18.9514 μV for n5 = 1.395 RIU (cancerous adrenal gland cell), respectively. The values of the chemical and voltage resolutions (1.90 × 10–7 eV, 6.5560 μV for n5 = 1.36 RIU and normal skin cell) are better than for the case when the spin Hall effect is not applied (0.00513 eV, 0.1766 V). The voltage resolutions calculated with the conventional weak measurement method are comparable or considerably better to the best experimental values which can resolve voltage differences as small as 15 μV. [ABSTRACT FROM AUTHOR]

A quantum theory of electron spin transport in conductive magnets is developed. The theory describes a large number of effects that arise due to spin-orbit scattering of conduction electrons on crystal lattice defects, such as the spin Hall effect, the inverse spin Hall effect, and the anomalous Hall effect. The transport through the contact of two different conductive magnetics is also considered; the phenomenological boundary conditions for the charge and spin flows are formulated, which make it possible to take into account the spin flip at the interface. The developed electron spin transport theory is used to describe the spin-orbitronics of the "helimagnet metal/non-magnetic metal" heterojunction. The spatial distribution of the polarization of the spin current injected into the helimagnet is found, and the characteristic decay lengths of different components of the polarization vector of the spin current are determined. [ABSTRACT FROM AUTHOR]

THz generation from femtosecond photoexcited spintronic heterostructures has become a versatile tool for investigating ultrafast spin-transport and transient charge-current in a non-contact and non-invasive manner. The equivalent effect from the orbital degree of freedom is still in the primitive stage. Here, we experimentally demonstrate orbital-to-charge current conversion in metallic heterostructures, consisting of a ferromagnetic layer adjacent to either a light or a heavy metal layer, through detection of the emitted THz pulses. Our temperature-dependent experiments help to disentangle the orbital and spin components that are manifested in the respective Hall-conductivities, contributing to THz emission. NiFe/Nb shows the strongest inverse orbital Hall effect with an experimentally extracted value of effective intrinsic Hall-conductivity, ( σ S O H int ) e f f ~ 195 Ω − 1 c m − 1 , while CoFeB/Pt shows maximum contribution from the inverse spin Hall effect. In addition, we observe a nearly ten-fold enhancement in the THz emission due to pronounced orbital-transport in W-insertion heavy metal layer in CoFeB/W/Ta heterostructure as compared to CoFeB/Ta bilayer counterpart. By optically driving the magnetization in a magnetic system, terahertz emission can be induced from an adjacent normal metal, as a result of spin-to-charge conversion. Here, Kumar and Kumar successfully show the equivalent effect arising from orbital-to-charge conversion. [ABSTRACT FROM AUTHOR]

In this work, we present the results of a systematic experimental study of linear and parametric spin wave resonant excitation accompanied by spin currents (spin pumping) in a multifrequency composite bulk acoustic wave resonator with a ZnO-YIG-GGG-YIG/Pt structure. The features of magnetic dynamics excitation in YIG films due to magnetoelastic coupling with acoustic thickness modes of various polarizations are studied. Acoustic spin waves and spin pumping are detected by simultaneous frequency-field mapping of the inverse spin Hall effect voltage and the resonant frequencies of thickness extensional modes. In the parametric range of frequencies and fields, acoustic spin pumping induced by both shear and longitudinal polarization modes was observed. Linear acoustic spin waves are excited only by shear thickness extensional modes because longitudinal acoustic waves do not couple with the magnetic subsystem in linear regime. [ABSTRACT FROM AUTHOR]

In chiral materials, spins and chirality are coupled via spin-orbit interaction, provoking a fast-growing field of chiral spintronics. Compared with the widely explored chiral molecules, exploration of chirality-dependent spin effects in crystals and supramolecules remain limited. Here we assemble chiral superatomic crystals MXTe4 (M = transition metal; X = Ga or Ge) using telluride tetrahedra clusters as building blocks. Distinct from atomic crystals, these assembled monolayers have tunable symmetries and electronic characteristics by tilting the tetrahedral units through the variation of inter-cluster interaction. Dresselhaus-type spin textures and anisotropic spin Hall effect with inversed sign of spin current under opposite geometrical handedness are demonstrated in these chiral monolayers by symmetry analysis and verified by ab initio calculations. These results provide an innovative paradigm for assembling superatomic crystals with designated symmetry and hierarchical structures to access the chirality-driven quantum effects. [ABSTRACT FROM AUTHOR]

Utilizing micromagnetic modeling, we have explained the unprobed characteristics of 360° full cycle in-plane magnetization rotation and the resulting propagation of a magnetization wave along a ferromagnet nanowire. The magnetization wave, which is generated by setting off spin oscillation at one end of a ferromagnetic strip, propagates till the end of the wire. A perpendicular spin torque oscillator (STO) could generate magnetization rotation at one end of the ferromagnetic strip that is also part of the STO. Our results demonstrate that the oscillation frequency of the spins along the wire maintains excellent fidelity while the spatial wavelength of the magnetic wave increases. The driving mechanism behind the propagation of the wave is found to be exchange-springs, which enables the propagation of the wave without the need for a 'carrier' force, such as spin-transfer torque (STT) or spin Hall effect (SHE). Furthermore, we demonstrate that the gradient of the exchange energy drives the magnetic wave forward, while the in and out of plane anisotropy fields govern the shape of spin oscillation trajectories along the wire. Additionally, we show that stopping the oscillation at the STO end causes the wave to cease propagation after relaxation, and altering the STO rotational chirality leads to merging and annihilating domain walls of opposite winding numbers. [ABSTRACT FROM AUTHOR]

In this research, we investigated tight focusing of vector beams with negative orders. It is theoretically proven that the lengthwise component of the spin angular momentum is equal zero near the focal area only for the first order of the incident beam. It was shown using numerical simulations and Debye integrals that local subwavelength regions with circular and elliptic polarization of opposite signs are formed in front of and behind the focal plane. [ABSTRACT FROM AUTHOR]

Spin angular momenta play important roles in light–matter interactions, leading to the emergence of the spin Hall effect and topological quasiparticles in modern optics. The typical approach is to decompose the spins of plane electromagnetic waves into longitudinal and transverse components, yet this description is not easily transferable to more structured electromagnetic environments. Here, we developed a field theory to reveal the physical origin and topological properties of longitudinal and transverse spins for arbitrary electromagnetic waves (including water waves and acoustic waves) in both near-field and free space. For electromagnetic waves carrying intrinsic helicity, we observed the emergence of helicity-dependent transverse spin possessing helicity-dependent spin-momentum locking. To verify that the number of spin-momentum locking states coincides with the spin Chern number, we experimentally measured the three-dimensional spin angular momentum densities of Bloch-type optical skyrmions. Our findings yield valuable insight for constructing spin-based field theory and exploiting optical topological quasiparticle-based applications. The task of mapping solid-state spin-orbit coupling (SOC) into photonic systems has sparked intense research efforts. The authors propose a unified theory to study SOC in photonic and classical wave systems, that is validated numerically and through ad hoc experiments with Bloch-type photonic skyrmions, showing excellent agreement between the two. [ABSTRACT FROM AUTHOR]

In non-interacting systems, bands from non-trivial topology emerge strictly at half-filling and exhibit either the quantum anomalous Hall or spin Hall effects. Here we show using determinantal quantum Monte Carlo and an exactly solvable strongly interacting model that these topological states now shift to quarter filling. A topological Mott insulator is the underlying cause. The peak in the spin susceptibility is consistent with a possible ferromagnetic state at T = 0. The onset of such magnetism would convert the quantum spin Hall to a quantum anomalous Hall effect. While such a symmetry-broken phase typically is accompanied by a gap, we find that the interaction strength must exceed a critical value for this to occur. Hence, we predict that topology can obtain in a gapless phase but only in the presence of interactions in dispersive bands. These results explain the recent quarter-filled quantum anomalous Hall effects seen in moiré systems. Moire bilayers support quantum spin Hall (QSH) and quantum anomalous Hall (QAH) states, but a unified explanation is missing. Mai et al. show that by including interactions in typical models, the QSH state shifts from 1/2 to 1/4 filling and gives way to the QAH state at low temperature. [ABSTRACT FROM AUTHOR]

Cubic materials host high crystal symmetry and hence are not expected to support anisotropy in transport phenomena. In contrast to this common expectation, here we report an anomalous anisotropy of spin current can emerge in the (001) film of Mn3Pt, a noncollinear antiferromagnetic spin source with face-centered cubic structure. Such spin current anisotropy originates from the intertwined time reversal-odd (T -odd) and time reversal-even (T -even) spin Hall effects. Based on symmetry analyses and experimental characterizations of the current-induced spin torques in Mn3Pt-based heterostructures, we find that the spin current generated by Mn3Pt (001) exhibits exotic dependences on the current direction for all the spin components, deviating from that in conventional cubic systems. We also demonstrate that such an anisotropic spin current can be used to realize low-power spintronic applications such as the efficient field-free switching of the perpendicular magnetizations. Symmetry is an essential ingredient that governs numerous physical phenomena, including spin transport. Following this principle, spin current sources with a highly symmetric cubic structure are not expected to support anisotropic spin currents. Here, the authors demonstrate an anomalous spin current anisotropy in a cubic noncollinear antiferromagnet Mn3Pt by exploiting the combination of conventional and magnetic spin-hall effects. [ABSTRACT FROM AUTHOR]

The effervescent area of spintronics has produced different fields of research; among them is the field of interface phenomena capable of revealing the most intriguing effects of materials physics. We report here a phenomenon, which appears in response to the spin Hall effect and represents the anti-polarization of the spin current due to the coupling between interfacial magnetic anisotropies. Such a phenomenon produces a Hermitian spin current. The observation of this new phenomenon was performed on permalloy/cobalt bilayers and proven unequivocally. [ABSTRACT FROM AUTHOR]

The discovery of magnetic order in atomically-thin van der Waals materials has strengthened the alliance between spintronics and two-dimensional materials. An important use of magnetic two-dimensional materials in spintronic devices, which has not yet been demonstrated, would be for coherent spin injection via the spin-pumping effect. Here, we report spin pumping from Cr2Ge2Te6 into Pt or W and detection of the spin current by inverse spin Hall effect. The magnetization dynamics of the hybrid Cr2Ge2Te6/Pt system are measured, and a magnetic damping constant of ~ 4–10 × 10−4 is obtained for thick Cr2Ge2Te6 flakes, a record low for ferromagnetic van der Waals materials. Moreover, a high interface spin transmission efficiency (a spin mixing conductance of 2.4 × 1019/m2) is directly extracted, which is instrumental in delivering spin-related quantities such as spin angular momentum and spin-orbit torque across an interface of the van der Waals system. The low magnetic damping that promotes efficient spin current generation together with high interfacial spin transmission efficiency suggests promising applications for integrating Cr2Ge2Te6 into low-temperature two-dimensional spintronic devices as the source of coherent spin or magnon current. Spin-pumping experimental technique where a DC or AC spin current is generated, and typically transferred to a heavy metal layer where it can be detected via electrical measurements. While well established in conventional materials, coherent spin-pumping in van der Waals magnetic materials is challenging due to the low damping and high-quality interface requirements. Here, Xu et al demonstrate coherent spin pumping in the van der Waals magnet Cr2Ge2Te6. [ABSTRACT FROM AUTHOR]

This manuscript presents a dielectric resonator structure with altered dispersion characteristics to enhance the photonic spin Hall effect (PSHE). The structural parameters are optimized to enhance the PSHE at 632.8 nm operating wavelength. The thickness-dependent angular dispersion analysis is carried out to optimize the structure and obtain the exceptional points. The PSHE-induced spin splitting shows a high sensitivity to the optical thickness of the defect layer. This gives a maximum PSHE-based transverse displacement (PSHE-TD) of around 56.66 times the operating wavelength at an incidence angle of 61.68°. Moreover, the structure's capability as a PSHE-based refractive index sensor is also evaluated. The analytical results demonstrate an average sensitivity of around 33,720 μm/RIU. The structure exhibits around five times higher PSHE-TD and approximately 150% improvement in sensitivity than the recently reported values in lossy mode resonance structures. Due to the purely dielectric material-assisted PhC resonator configurations and significantly higher PSHE-TD, the development of low-cost PSHE-based devices for commercial applications is envisaged. [ABSTRACT FROM AUTHOR]

We report the impact of the tungsten crystal structure on the spin transport properties of permalloy/tungsten bilayers grown by sputtering on (100) silicon. The microstructure of the tungsten layer was modified using a reactive N 2 /argon mixture during the fabrication process. The analysis combines ferromagnetic resonance and inverse spin Hall effect (ISHE) experiments. A correlation with the electrical and structural characterization indicates that an initial β -W stabilization notably improves the measured ISHE signal. Nevertheless a subsequent increment of the N 2 pressure degrades the signal, probably due to higher interstitial nitrogen and degradation of the interface quality. The interplay between the resistivity and disorder gives an optimal growth condition to enhance the tungsten spin current sensing property. [ABSTRACT FROM AUTHOR]

The Orbital Hall effect, which originates from materials with weak spin-orbit coupling, has attracted considerable interest for spin-orbitronic applications. Here, we demonstrate the inverse effect of the orbital Hall effect and observe orbitronic terahertz emission in the Ti and Mn materials. Through spin-orbit transition in the ferromagnetic layer, the generated orbital current can be converted to charge current in the Ti and Mn layers via the inverse orbital Hall effect. Furthermore, the inserted W layer provides an additional conversion of the orbital-charge current in the Ti and Mn layers, significantly enhancing the orbitronic terahertz emission. Moreover, the orbitronic terahertz emission can be manipulated by cooperating with the inverse orbital Hall effect and the inverse spin Hall effect in the different sample configurations. Our results not only discover the physical mechanism of condensed matter physics but also pave the way for designing promising spin-orbitronic devices and terahertz emitters. [ABSTRACT FROM AUTHOR]

Spin-orbit torques (SOTs) have opened a novel way to manipulate the magnetization using in-plane current, with a great potential for the development of fast and low power information technologies. It has been recently shown that two-dimensional electron gases (2DEGs) appearing at oxide interfaces provide a highly efficient spin-to-charge current interconversion. The ability to manipulate 2DEGs using gate voltages could offer a degree of freedom lacking in the classical ferromagnetic/spin Hall effect bilayers for spin-orbitronics, in which the sign and amplitude of SOTs at a given current are fixed by the stack structure. Here, we report the non-volatile electric-field control of SOTs in an oxide-based Rashba-Edelstein 2DEG. We demonstrate that the 2DEG is controlled using a back-gate electric-field, providing two remanent and switchable states, with a large resistance contrast of 1064%. The SOTs can then be controlled electrically in a non-volatile way, both in amplitude and in sign. This achievement in a 2DEG-CoFeB/MgO heterostructures with large perpendicular magnetization further validates the compatibility of oxide 2DEGs for magnetic tunnel junction integration, paving the way to the advent of electrically reconfigurable SOT MRAMS circuits, SOT oscillators, skyrmion and domain-wall-based devices, and magnonic circuits. A central goal of spintronics is electric control of magnetism. One particularly promising method makes use of spin-orbit torques which arise due to the combination of electric current, and the intrinsic spin-orbit effect in a material. Here, Grezes et al demonstrate non-volatile electrical control of the spin-orbit torque generated at the interface between an oxide and a metal. [ABSTRACT FROM AUTHOR]

Metasurfaces have attracted significant interest due to their compact, artificial interfaces with exceptional optical properties. Dielectric platforms, in particular, hold promise for nonlinear nanophotonics, enabling applications such as ultrafast optical switching and high harmonic generation, which are central to developing nonlinear metaoptics. While most research has focused on single metasurfaces, stacking optical metasurfaces is a long-term goal, although it presents substantial fabrication challenges. Pancharatnam-Berry (PB) phase-based metasurfaces provide efficient wavefront control but typically require precise polarization management. These metasurfaces are particularly valuable for manipulating circularly polarized (CP) electromagnetic waves, with applications in chiral molecule interactions and optical communication. However, traditional materials-based devices suffer from bulkiness and low efficiency. PB metasurfaces, which efficiently control CP waves across different frequency domains, are becoming increasingly important. This review covers their working principles, methods for constructing high-efficiency PB metasurfaces in both reflection and transmission geometries, and their applications in meta-lensing, meta-holography, and surface coupling, concluding with perspectives on their future development. The photonic spin Hall effect (SHE), arising from the spin–orbit interaction of photons, can be precisely controlled using metasurfaces. These devices manipulate the SHE, which results in spin-dependent splitting in both position and momentum space. Integrating PB phases through space-variant polarization manipulations in metasurfaces provides new methods for fabricating spin-Hall devices. This review highlights the role of photonic SHE in metasurfaces and explores the prospects it offers for advancing spin photonics. [ABSTRACT FROM AUTHOR]

Antiferromagnetic materials have been proposed as new types of narrowband THz spintronic devices owing to their ultrafast spin dynamics. Manipulating coherently their spin dynamics, however, remains a key challenge that is envisioned to be accomplished by spin-orbit torques or direct optical excitations. Here, we demonstrate the combined generation of broadband THz (incoherent) magnons and narrowband (coherent) magnons at 1 THz in low damping thin films of NiO/Pt. We evidence, experimentally and through modeling, two excitation processes of spin dynamics in NiO: an off-resonant instantaneous optical spin torque in (111) oriented films and a strain-wave-induced THz torque induced by ultrafast Pt excitation in (001) oriented films. Both phenomena lead to the emission of a THz signal through the inverse spin Hall effect in the adjacent heavy metal layer. We unravel the characteristic timescales of the two excitation processes found to be < 50 fs and > 300 fs, respectively, and thus open new routes towards the development of fast opto-spintronic devices based on antiferromagnetic materials. Antiferromagnets are promising candidates to build terahertz spintronic devices. However, manipulating and detecting their terahertz spin dynamics remains key challenges. Here, Rongione et al. demonstrate both broadband and narrowband terahertz emission from an antiferromagnet/heavy metal heterostructure using spin-phonon interactions. [ABSTRACT FROM AUTHOR]

We report on the observation of sign reversal of vortex-Nernst effect in epitaxial NbN/Fe bilayers deposited on MgO (001) substrates. Strong coupling between vortex magnetisation and ferromagnetic magnetisation at the NbN/Fe bilayer interface is presented. In NbN/Fe bilayer thin films an apparent sign reversal of vortex-Nernst signal under a temperature gradient with magnetic field and temperature is observed when the thickness of Fe is increased up to 5 nm. This reversal of the vortex-Nernst effect is associated with the enhancement of the spin Seebeck effects (SSE) near Tc due to coherence peak effect (CPE) and strong coupling of vortex magnetisation and ferromagnetic magnetisation at the interface of the NbN/Fe bilayer. The observed large SSE via inverse spin Hall effect (ISHE) is due to the CPE below and close to TC, highlighting the high spin to charge conversion efficiency of NbN in this region. This work may contribute to the development of superconducting spintronic devices by engineering the coupling of the superconductor/ferromagnet interface. [ABSTRACT FROM AUTHOR]

Nonequilibrium quantum states can be controlled via the driving field in periodically driven systems. Such control, which is called Floquet engineering, has opened various phenomena, such as the light-induced anomalous Hall effect. There are expected to be some essential differences between the anomalous Hall and spin Hall effects of periodically driven systems because of the difference in time-reversal symmetry. However, these differences remain unclear due to the lack of Floquet engineering of the spin Hall effect. Here we show that when the helicity of circularly polarized light is changed in a periodically driven t2g-orbital metal, the spin current generated by the spin Hall effect remains unchanged, whereas the charge current generated by the anomalous Hall effect is reversed. This difference is protected by the symmetry of a time reversal operation. Our results offer a way to distinguish the spin current and charge current via light and could be experimentally observed in pump-probe measurements of periodically driven Sr2RuO4. Non-equilibrium states can be induced in a given system using periodic driving and the underlying physics understood using Floquet theory. Here, the authors model a periodically driven t2g-orbital metal and demonstrate how the spin Hall and anomalous Hall effects are realized and can be distinguished by their response to circularly polarized light with different helicities. [ABSTRACT FROM AUTHOR]

Spin injection using ferromagnetic semiconductors at room temperature is a building block for the realization of spin-functional semiconductor devices. Nevertheless, this has been very challenging due to the lack of reliable room-temperature ferromagnetism in well-known group IV and III-V based semiconductors. Here, we demonstrate room-temperature spin injection by using spin pumping in a BiSb/(Ga,Fe)Sb heterostructure, where (Ga,Fe)Sb is a ferromagnetic semiconductor (FMS) with high Curie temperature (TC) and BiSb is a topological insulator (TI). Despite the very small magnetization of (Ga,Fe)Sb at room temperature (45 emu/cc), we detected spin injection from (Ga,Fe)Sb by utilizing the large inverse spin Hall effect (ISHE) in BiSb. Our study provides the first demonstration of spin injection at room temperature from a FMS. [ABSTRACT FROM AUTHOR]