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The photonic spin Hall effect (PSHE) in surface plasmon resonance (SPR) structures has great potential for various polarization-sensitive applications and devices. Here, using optical weak measurement, we observe spin-dependent and spin-independent angular shifts of the reflected beam, enhanced by SPR in a subwavelength nickel grating. An enhanced in-plane photonic spin Hall effect manifested in the angular splitting of circularly polarized photons with opposite helicity signs is demonstrated. We theoretically and experimentally demonstrate that angular in-plane shifts can be changed from spin-independent (Goos-Hanchen shift) to spin-dependent (PSHE) when the incident beam polarization state changes. The SPR-induced depolarization of light and the mixing of polarization states are analyzed. High purity of spin separation and a high degree of circular polarization are achieved with an optimal polarization state (preselection angle) and a resonance angle of incidence. The spineless spatial separation of two orthogonal components of the field with diagonal linear polarizations is demonstrated., Comment: 20 pages, 5 figures

We propose an intrinsic nonlinear spin Hall effect, which enables the generation of collinearly-polarized spin current in a large class of nonmagnetic materials with the corresponding linear response being symmetry-forbidden. This opens a new avenue for field-free switching of perpendicular magnetization, which is required for the next-generation information storage technology. We develop the microscopic theory of this effect, and clarify its quantum origin in band geometric quantities which can be enhanced by topological nodal features. Combined with first-principles calculations, we predict pronounced effects at room temperature in topological metals $\mathrm{PbTaSe_{2}}$ and PdGa. Our work establishes a fundamental nonlinear response in spin transport, and opens the door to exploring spintronic applications based on nonlinear spin Hall effect.

We study Dirac fermions in the presence of a space-dependent chiral gauge field and thermodynamic gradients, establishing a connection to the inverse spin Hall effect. The chiral gauge field induces a chiral magnetic field, resulting in a surface Fermi arc state and a chiral Landau level state which, although is delocalized in the bulk, we show to be more robust against impurities. By applying chemical potential and temperature gradients, we achieve nonzero charge currents, with each gradient leading to distinct Fermi level dependencies, both of which have been observed in a recent experiment. Unlike the conventional mixed axial-gravitational anomaly, our currents require a noncollinear chiral magnetic field and thermodynamic gradient. We further derive low-energy transport formulas and demonstrate the importance of carefully treating the ultraviolet cutoff for understanding our lattice calculations., Comment: 7 pages, 3 figures

Drude weight, historically associated with the longitudinal Drude conductivity, can be generalized to describe the transverse or Hall component of the extrinsic conductivity tensor. In particular, transverse Drude weights, such as band geometric quantities Berry curvature dipole and spin vorticity, manifest themselves through the \textit{extrinsic} second-order nonlinear Hall effect and \textit{extrinsic} linear spin Hall effect (SHE) in diffusive transport, respectively. In this work, we uncover a new class of intrinsic Hall effects in quantum transport regime, termed as quantum intrinsic Hall effect (QIHE), which is the manifestation of system symmetry through intrinsic transport phenomena. For a given Hamiltonian, its transport characteristics can be revealed either intrinsically through QIHE in ballistic regime or extrinsically via the transverse Drude weight in diffusive transport, where both intrinsic and extrinsic effects share the same salient transport features governed by symmetry of the Hamiltonian. The physical origin of QIHE is attributed to quantum boundary scattering of the measurement setup that respects the system symmetry, as exemplified by the contact resistance of a two-terminal ballistic conductor. We demonstrate our finding by studying the quantum ${\cal T}$-odd ($\mathcal{T}$, time-reversal) SHE in altermagnets. Our work paves a way towards the quantum transport manifestation of band geometric characteristics.

In this study, we derive the non-relativistic Hamiltonian for electrons within the Schwarzschild metric from covariant Dirac equations, using both the weak field approximation and the Foldy-Wouthuysen transformation. This Hamiltonian incorporates a gravitational spin-orbit coupling term, resulting in the gravitational spin Hall effect (SHE), which separates electrons by their spin. By solving the Schr\"odinger equation for these electrons, we investigate the gravitational SHE as they orbit a non-rotating gravitational source. Our findings reveal that the spin-dependent separation of electrons increases in proportion to their orbital periods, significantly improving the detectability of gravitational SHE. Specifically, for electrons in a low Earth orbit, the separation is estimated to be $3.0\times 10^{-12}\, \text{m}$ annually. These results indicate the practicality of detecting the gravitational SHE in electrons orbiting Earth, especially with prolonged orbital durations, underscoring the potential for quantum test of the Weak Equivalence Principle.

We theoretically describe and numerically investigate the operation of "vectorial" optical differentiation of a three-dimensional light beam, which consists in simultaneous computation of two partial derivatives of the incident beam profile with respect to two spatial coordinates in different transverse electric field components. It is implemented upon reflection of the beam from a layered structure by simultaneously utilizing the effect of optical resonance and the spin Hall effect of light. As an example of a layered structure performing this operation, we propose a three-layer metal-dielectric-metal (MDM) structure. We show that by choosing the parameters of the MDM structure, it is possible to achieve the so-called isotropic vectorial differentiation, for which the intensity of the reflected optical beam (squared electric field magnitude) is proportional to the squared absolute value of the gradient of the incident linearly polarized beam. The presented numerical simulation results demonstrate high-quality vectorial differentiation and confirm the developed theoretical description., Comment: 12 pages, 4 figures

In this study, we investigate the spin-charge current conversion characteristics of chemically disordered ferromagnetic single FePt thin films by spin-pumping ferromagnetic resonance experiments performed on both a resonance cavity and on patterned devices. We clearly observe a self-induced signal in a single FePt layer. The sign of a single FePt spin pumping voltage signal is consistent with a typical bilayer with a positive spin Hall angle layer such as that of Pt on top of a ferromagnet (FM), substrate//FM/Pt. Structural analysis shows a strong composition gradient due to natural oxidation at both FePt interfaces, with the Si substrate and with the air. The FePt-thickness dependence of the self-induced charge current produced allowed us to obtain $\lambda _ \text{FePt}=(1.5\pm 0.1)$ nm and self-induced $\theta_ \text{self-FePt}=0.047 \pm 0.003$, with efficiency for reciprocal effects applications $\theta _ \text{self-FePt} \times \lambda _ \text{FePt} = 0.071$ nm which is comparable to that of Pt, $\theta _ \text{SH-Pt} \times \lambda _ \text{Pt} = 0.2$ nm. Moreover, by studying bilayer systems such as Si//FePt/Pt and Si//Pt//FePt we independently could extract the individual contributions of the external inverse spin Hall effect of Pt and the self-induced inverse spin Hall effect of FePt. Notably, this method gives consistent values of charge currents produced due to only self-induced inverse spin Hall effect in FePt layers. These results advance our understanding of spin-to-charge interconversion mechanisms in composite thin films and pave the way for the development of next-generation spintronics devices based on self-torque., Comment: 13 pages, 7 figures

The spin-Hall effect underpins some of the most active topics in modern physics, including spin torques and the inverse spin-Hall effect, yet it lacks a proper theoretical description. This makes it difficult to differentiate the SHE from other mechanisms, as well as differentiate band structure and disorder contributions. Here, by exploiting recent analytical breakthroughs in the understanding of the intrinsic spin-Hall effect, we devise a density functional theory method for evaluating the conserved (proper) spin current in a generic system. Spin non-conservation makes the conventional spin current physically meaningless, while the conserved spin current has been challenging to evaluate since it involves the position operator between Bloch bands. The novel method we introduce here can handle band structures with arbitrary degeneracies and incorporates all matrix elements of the position operator, including the notoriously challenging diagonal elements, which are associated with Fermi surface, group velocity, and dipolar effects but often diverge if not treated correctly. We apply this method to the most important classes of spin-Hall materials: topological insulators, 2D quantum spin-Hall insulators, non-collinear antiferromagnets, and strongly spin-orbit coupled metals. We demonstrate that the torque dipole systematically suppresses contributions to the conventional spin current such that, the proper spin current is generally smaller in magnitude and often has a different sign. Remarkably, its energy-dependence is relatively flat and featureless, and its magnitude is comparable in all classes of materials studied. These findings will guide the experiment in characterizing charge-to-spin interconversion in spintronic and orbitronic devices. We also discuss briefly a potential generalisation of the method to calculate extrinsic spin currents generated by disorder scattering.

A single layer ferromagnetic film magnetized in the plane of an ac current flow, exhibits a characteristic Hall voltage with harmonic and second harmonic components, which is attributed to the presence of spin currents with polarization non-collinear with the magnetization. A set of 30 nm thick permalloy (Py) films used in this study are deposited at an oblique angle with respect to the substrate plane which induces an in-plane easy axis in the magnetization of the initial nucleating layers of the films which is distinct from the overall bulk magnetic properties of the film. This unusual magnetic texture provides a platform for the direct detection of inverse spin Hall effect in Hall bar shaped macroscopic devices at room temperatures which we denote as Anomalous Inverse Spin Hall Effect (AISHE). Control samples fabricated by normal deposition of permalloy with slow rotation of substrate shows significant reduction of the harmonic Hall signal that further substantiates the model. The analysis of the second harmonic Hall signal corroborates the presence of spin-orbit torque arising from the unconventional spin-currents in the single-layer ferromagnets.

The phenomenon of Spin Hall Effect (SHE) generates a pure spin current transverse to an applied current in materials with strong spin-orbit coupling, although not detectable through conventional electrical measurement. An intuitive Hall effect like measurement configuration is implemented to directly measure pure spin chemical potential of the accumulated spins at the edges of heavy metal (HM) channels that generates large SHE. A pair of transverse linearly aligned voltage probes in placed in ohmic contact with the top surface of HM , one being a ferromagnetic metal (FM) with non-zero spin polarization and other is the reference metal (RM) with zero polarization of carriers. This combination of FM/RM electrodes is shown to induce an additional voltage proportional to a spin accumulation potential, which is anti symmetric with respect to opposite orientations of FM controlled by a 2D vector magnet. Proof of concept of the measurement scheme is verified by comparing the signs of voltages for HM channels of Tungsten (W) and Platinum (Pt) which are known to generate opposite spin accumulation under similar conditions of applied current. The same devices are also able to detect the reciprocal effect, inverse spin Hall effect (ISHE) by swapping the current and voltage leads and the results are consistent with reciprocity principle. Further, exploiting a characteristic feature of W thin film deposition, a series of devices were fabricated with W resistivity varying over a wide range of 10 - 750 $\mu \Omega$-cm and the calculated spin Hall resistivity exhibits a pronounced power law dependence on resistivity. Our measurement scheme combined with almost two decades of HM resistivity variation provides the ideal platform required to test the underlying microscopic mechanism responsible for SHE/ISHE.

In the photonic spin Hall effect (SHE), also known as transverse shift, incident light photons with opposite spins are spatially separated in the transverse direction due to the spin-orbit interaction of light. Here, we propose a gain-assisted model to control the SHE in the reflected probe light. In this model, a probe light is incident on a cavity containing a three-level dilute gaseous atomic medium, where the interaction between the atom and the control field follows two-photon Raman transitions. We show that the direction of photonic spin accumulations can be switched between positive and negative values across the Brewster angle in both the anomalous and normal dispersion regimes. For the same magnitude of control fields, the peak value of the photonic SHE is higher in the anomalous dispersion region compared to the normal dispersion regime. Additionally, the angular range around the Brewster angle is wider in the normal dispersion regime than in the anomalous dispersion region. Furthermore, the peak value of the photonic SHE and the angular range is controllable by changing the Rabi frequencies of the control fields and the probe field detuning. The measurement of photonic SHE based on gain assistance may enable spin-related applications such as optical sensing.

The intrinsic spin Hall effect (ISHE) proposed in [\href{https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.92.126603} {Sinova \textit{et al.} Phys. Rev. Lett. \textbf{92}, 126603 (2004)}] is driven by the spin Berry curvature. Herein, we establish the concept of \textit{spin quantum metric}, which is the counterpart of the spin Berry curvature in the \textit{spin quantum geometric tensor} defined in a similar way to the quantum geometric tensor. Dual to the $\mathcal{T}$-even ($\mathcal{T}$, time reversal) spin Berry curvature, the spin quantum metric features a $\mathcal{T}$-odd characteristic. Notably, we show that the $\mathcal{T}$-odd spin quantum metric can also drive an ISHE ($\mathcal{T}$-odd ISHE) under a high-frequency electric field. Guided by symmetry, we evaluate this $\mathcal{T}$-odd ISHE in the magnetically tilted surface Dirac cone and in ferromagnetic monolayer MnBi$_2$Te$_4$. We find that this $\mathcal{T}$-odd ISHE dominates when the Fermi level is close to the band (anti)crossing point, where its magnitude can be as large as the $\mathcal{T}$-even ISHE when an infrared driving field is applied. Our work not only uncovers an indispensable ingredient in the emergent community of quantum geometric physics but also offers a novel mechanism for ultrafast spintronics., Comment: Three figures

Symmetry-protected edge states serve as direct evidence of nontrivial electronic topology in atomically thin materials. Finding these states in experimentally realizable single-phase materials presents a substantial challenge for their use for both fundamental studies and developing functional nanoscale devices. Here, we show the presence of robust edge states in phosphorene and group-Va monolayers with puckered lattice structures. By carefully analyzing the symmetry of the atomic sites and edge modes properties, we demonstrate that these atomically thin two-dimensional (2D) materials realize recently introduced obstructed atomic insulator states with partially occupied edge modes. The obstructed edge modes attain a Rashba-type spin splitting with Rashba parameter ($\alpha$) of 1.52 eV \r{A} for arsenene. Under strain or doping effects, these obstructed insulators transition to a phase with substantial spin-Berry curvature, yielding a double quantum spin Hall state with a spin Hall conductivity of 4$\frac{e^2}{h}$. The experimental availability of phosphorene and other group-Va materials featuring puckered lattice structures could enable verification of obstructed atomic states and enhanced spin-Berry curvature effects discussed in this study, offering the potential for applications in topological electronic and spintronic devices.

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.

We develop a time-dependent Ginzburg-Landau theory of the vortex spin Hall effect, i.e., a spin Hall effect that is driven by the motion of superconducting vortices. For the direct vortex spin Hall effect in which an input charge current drives the transverse spin current accompanying the vortex motion, we start from the well-known Schmid-Caroli-Maki solution for the time-dependent Ginzburg-Landau equation under the applied electric field, and find out the expression of the induced spin current. For the inverse vortex spin Hall effect in which an input spin current drives the longitudinal vortex motion and produces the transverse charge current, we microscopically construct the time-dependent Ginzburg-Landau equation under the applied spin accumulation gradient, and calculate the induced transverse charge current as well as the open circuit voltage. The time-dependent Ginzburg-Landau equation and its analytical solution developed here can be a basis for more quantitative numerical simulations of the vortex spin Hall effect., Comment: 12 pages, 5 figures

Atomically-thin materials based on transition metal dichalcogenides and graphene offer a promising avenue for unlocking the mechanisms underlying the spin Hall effect (SHE) in heterointerfaces. Here, we develop a microscopic theory of the SHE for twisted van der Waals heterostructures that fully incorporates twisting and disorder effects, and illustrate the critical role of symmetry breaking in the generation of spin-Hall currents. We find that an accurate treatment of vertex corrections leads to a qualitatively and quantitatively different SHE than that obtained from popular approaches like the ``$i\,\eta$'' and ladder approximations. A pronounced oscillatory behavior of skew-scattering processes with twist angle, $\theta$, is predicted, reflecting a non-trivial interplay of Rashba and valley-Zeeman effects and yields a vanishing SHE for $\theta = 30^\circ$ and, for graphene-WSe$_2$, an optimal SHE for $\theta \approx 17^\circ$. Our findings reveal disorder and broken symmetries as important knobs to optimize interfacial SHEs., Comment: 8 pages, 3 figures (includes supplemental material); accepted version in Phys. Rev. B

Integer and fractional quantum anomalous Hall (QAH) effects have been widely seen in moir\'e systems. Recently there is even observation of a time reversal invariant fractional quantum spin hall (FQSH) state at filling $n=3$ in twisted MoTe$_2$ bilayer. We consider a pair of half-filled $C=\pm 1$ Chern band in the two valleys, similar to the well-studied quantum Hall bilayer, but now with opposite chiralities. Due to the strong inter-valley repulsion, we expect a charge gap opening with low energy physics dominated by the neutral inter-valley excitons. However, the presence of an effective `flux' frustrates exciton condensation by proliferating vortices. Here we construct a vortex liquid of excitons dubbed as vortex spin liquid (VSL), from exciton pairing of the composite fermions in the decoupled composite Fermi liquids (CFL) phase. This insulator is a quantum spin liquid with gapless spin excitations carried by the flux of an emergent U(1) gauge field. Additionally, there exist neutral and spinless Fermi surfaces formed by fermionic vortices of a nearby inter-valley-coherent (IVC) order. Unlike a conventional Mott insulator, the VSL phase also exhibits FQSH effect with gapless helical charge modes along the edge. Our work suggests a new platform to search for quantum spin liquid enriched by fractional quantum spin Hall effect. We also point out the possibility of quantum oscillations and thermal Hall effect under Zeeman field in this exotic insulator., Comment: 5+5 pages; This is a new version of an unpublished preprint in 2018, arXiv:1810.03600 . v2: add more discussions of the edge theory

Topological polaritons, combining the robustness of the topological protected edge states to defects and disorder with the strong nonlinear properties of polariton bosons, represent an excellent platform to investigate novel photonic topological phases. In this work, we demonstrated the optical spin Hall effect (OSHE) and its symmetry switching in the exciton-polariton regime of pure DPAVBi crystals. Benefiting from the photonic Rashba-Dresselhaus spin-orbit coupling in organic crystals, we observed the separation of left- and right-circularly-polarized polariton emission in two-dimensional momentum space and real space, a signature of the OSHE. Above the lasing threshold, the OSHE pattern changes due to transverse quantization in the microbelt. This device without superlattice structure has great potential applications in topological polaritonics, such as information transmission, photonic integrated chips and quantum information.

We describe how the spin Hall effect (SHE) can be studied from ab-initio by combining density functional theory with the non-equilibrium Green's functions technique for quantum transport into the so-called DFT+NEGF method. After laying down our theoretical approach in particular discussing how to compute charge and spin bond currents, DFT+NEGF calculations are carried out for ideal clean systems. In these the transport is ballistic and the linear response limit is met. The SHE emerges in a central region attached to two leads when we apply a bias voltage so that electrons are accelerated by a uniform electric field. As a result, we obtain a finite spin-Hall current and, by performing a scaling analysis with respect to the system size, we estimate the ballistic spin Hall conductivity (SHC). We consider 5d metals with fcc and bcc crystal structures, finding that the SHC exhibits a rough qualitative dependence on the d-band filling, and comment on these results in relation to existing literature. Finally, within the same DFT+NEGF approach, we also predict the appearance of a current-induced spin dipole moment inside the materials' unit cell and estimate its magnitude., Comment: 16 pages, 8 figures

An experiment in moir\'e MoTe$_2$ bilayers reported the first observation of a topologically ordered state with zero Hall conductivity and half of the edge conductance of a standard time-reversal invariant quantum spin Hall insulator. This state is believed to emerge at total filling one of a pair of bands with Chern numbers $C=\pm1$ related by time reversal symmetry. By viewing these bands as a pair of Landau levels with opposite magnetic fields, and starting from a parent magnet with one filled band, we demonstrate that a class of Halperin states constructed by adding particles to the empty Chern band and holes to the occupied Chern band have all the properties observed in MoTe$_2$. Remarkably, these states break time-reversal symmetry but have exactly zero Hall conductivity and helical edge conductance of $e^2/2h$. These states also feature a spinless composite fermion with the same charge as the electron but split equally between both valleys. In a standard Halperin 331 state, this particle would be a neutral Bogoliubov composite fermion. However, in our context this composite fermion is charged but remains itinerant because it is split into the two valleys that effectively experience opposite magnetic fields. The existence of such charged itinerant particles is a key difference between Landau levels with opposite magnetic fields and standard multi-components Landau levels, where all the itinerant particles are charge neutral, such as the magneto-roton of the Laughlin state or the Bogoliubov composite fermion of the Moore-Read state. When the electron density changes away from the ideal filling and these itinerant charged particles are added to the parent state, the disorder potential is less efficient at localizing them as compared to standard Lanadau levels. This can explain why the state in MoTe$_2$ did not display a robust Hall plateau upon changing the electron density., Comment: 12 pages, 2 figures

The recent experimental observation of a potential fractional quantum spin Hall (FQSH) state in the twisted MoTe$_2$ system has sparked theoretical explorations at total filling $\nu_T=1$ of a pair of $C=\pm 1$ Chern bands from the two spins (locked to valley). One intriguing candidate is a vortex spin liquid (VSL), which can be viewed as an exciton version of composite fermi liquid (CFL). The VSL insulator is incompressible in the charge channel, while compressible in the spin channel. Here we investigate fully gapped descendants of the VSL phase at the total filling $\nu_T=\nu_{\uparrow}+\nu_{\downarrow}=1$. At zero magnetization, a non-Abelian state with both FQSH and thermal Hall effect emerges from weak $p+ip$ pairing of the neutral Fermi surface, hosting 12 anyons (up to addition of physical electron) including two independent Ising anyons separately carrying charge and spin. Strong pairing leads to a Z$_4$ topological order with only FQSH effect. At non-zero magnetization $m=2S_z$, there is a Jain sequence of magnetic plateaus with $m=\frac{1}{p}, p \in Z$, exhibiting both half FQSH effect and spin fractional quantum Hall effect (SFQH). Our work highlights the VSL's potential as a parent state to organize numerous FQSH insulators with non-trivial inter-valley correlations at $\nu_T=1$. The quantized FQSH behavior remains robust even in the presence of ferromagnetism, thanks to the spin-charge separation nature inherent in the parent VSL phase. Future experimental investigations are crucial to validate or rule out spontaneous magnetization and time reversal symmetry breaking., Comment: 5 pages, 1 figure

Quantum spin Hall (QSH) effect, where electrons with opposite spin channels are deflected to opposite sides of a two-dimensional system with a quantized conductance, was believed to be characterized by a nontrivial topological index $Z_{2}$. However, spin mixing effects in realistic materials often lead to deviation of the spin Hall conductance from exact quantization. In this Letter, we present a universal symmetry indicator for diagnosing QSH effect in realistic materials, termed spin $U$(1) quasi-symmetry. Such a symmetry eliminates the first-order spin-mixing perturbation and thus protects the near-quantization of SHC, applicable to time-reversal-preserved cases with either $Z_{2}=1$ or $Z_{2}=0$, as well as time-reversal-broken scenarios. We propose that spin $U$(1) quasi-symmetry is hidden in the subspace spanned by the doublets with unquenched orbital momentum and emerges when SOC is present, which can be realized in 19 crystallographic point groups. Particularly, we identify a previous overlooked even spin Chern phase with a trivial $Z_{2}$ index as an ideal platform for achieving a near-double-quantized SHC, as exemplified by twisted bilayer transition metal dichalcogenides and monolayer RuBr$_{3}$. Our work offers a new perspective for understanding QSH effect and significantly expands the material pool for the screening of exemplary material candidates., Comment: 6 pages, 4 figures

Quantum spin Hall (QSH) insulators are two-dimensional electronic materials that have a bulk band gap like an ordinary insulator but have topologically protected pairs of edge modes of opposite chiralities. To date, experimental studies have found only integer QSH insulators with counter-propagating up-spins and down-spins at each edge leading to a quantized conductance G0=e^2/h. Here we report transport evidence of a fractional QSH insulator in 2.1-degree-twisted bilayer MoTe2, which supports spin-Sz conservation and flat spin-contrasting Chern bands. At filling factor v = 3 of the moir\'e valence bands, each edge contributes a conductance 3/2 G0 with zero anomalous Hall conductivity. The state is likely a time-reversal pair of the even-denominator 3/2-fractional Chern insulators. Further, at v = 2, 4 and 6, we observe a single, double and triple QSH insulator with each edge contributing a conductance G0, 2G0 and 3G0, respectively. Our results open up the possibility of realizing time reversal symmetric non-abelian anyons and other unexpected topological phases in highly tunable moir\'e materials.

The photonic spin Hall effect of light beams reflected from the surfaces of various two-dimensional hexagonal crystalline structures, considering their associated time-reversal $\mathcal{T}$ and inversion $\mathcal{I}$ symmetries, is investigated. Employing the Haldane model with tunable parameters as a generic model, we examine the longitudinal and transverse spin-separations of the reflected beam in both topological non-trivial and trivial systems. The study reveals that the sign switching of the PSHE in these materials is attributed to the non-trivial and trivial topology. By manipulating the interplay between spin-orbit coupling and external electric fields, we demonstrate topological phase transitions in buckled Xene monolayer materials through the photonic spin Hall effect. Different behaviors of the photonic spin Hall effect are observed in various topological phases within these materials. Additionally, we explore the reflected spin and valley-polarized spatial shifts in monolayer transition metal dichalcogenides. The photonic spin Hall effect in buckled Xene monolayer materials and transition metal dichalcogenides is highly influenced by the spin and valley degrees of freedom of charge carriers, offering a promising avenue to explore spintronics and valleytronics in these hexagonal materials. We propose that the photonic spin Hall effect in Haldane materials can serve as a metrological tool for optical parameter characterization and as a promising method for determining Chern numbers and topological phase transitions through direct optical weak measurement techniques.

Crystallographic anisotropy of the spin-dependent conductivity tensor can be exploited to generate transverse spin-polarized current in a ferromagnetic film. This ferromagnetic spin Hall effect is analogous to the spin-splitting effect in altermagnets and does not require spin-orbit coupling. First-principles screening of 41 non-cubic ferromagnets revealed that many of them, when grown as a single crystal with tilted crystallographic axes, can exhibit large spin Hall angles comparable with the best available spin-orbit-driven spin Hall sources. Macroscopic spin Hall effect is possible for uniformly magnetized ferromagnetic films grown on some low-symmetry substrates with epitaxial relations that prevent cancellation of contributions from different orientation domains. Macroscopic response is also possible for any substrate if magnetocrystalline anisotropy is strong enough to lock the magnetization to the crystallographic axes in different orientation domains., Comment: 10 pages, 2 tables

The efficient generation of spin currents and spin torques via spin-orbit coupling is an important goal of spintronics research. One crucial metric for spin current generation is the spin Hall angle, which is the ratio of the spin Hall current to the transversely flowing charge current. A typical approach to measure the spin Hall angle in nonmagnetic materials is to generate spin currents via spin pumping in an adjacent ferromagnetic layer and measure the transverse voltage from the inverse spin Hall effect in the nonmagnetic layer. However, given that the spin Hall effect also occurs in ferromagnets, single ferromagnetic layers could generate a self-induced transverse voltage during spin pumping as well. Here we show that manganite based La$_{0.67}$Sr$_{0.33}$MnO$_{3}$ (LSMO) films deposited by pulsed laser deposition exhibit a significant self-induced inverse spin Hall voltage while undergoing spin pumping. We observe efficient spin to charge conversion in the LSMO films via the inverse spin Hall effect. A spin pumping voltage of 1.86 $\mu$V is observed in the LSMO (12 nm) film. Using density functional theory and the Kubo formalism, we calculate the intrinsic spin current conductivities of these films and show that they are in reasonable agreement with the experimental measurements.

In this work, the spin pumping technique was employed to investigate the anomalous inverse spin Hall effect in BIG/NiO/Fe samples where BIG[(Bi,Tm)3(Fe,Ga)5O12] exhibits perpendicular magnetic anisotropy. Our results reveal an intriguing phenomenon: when the magnetizations of both ferromagnetic layers align perpendicularly, a distinct spin-to-charge current conversion mechanism occurs. This conversion is intricately linked to the magnetization of the converting layer, spin polarization, and the spin current orientation., Comment: 11 pages, 4 figures

Physical properties such as the conductivity are usually classified according to the symmetry of the underlying system using Neumann's principle, which gives an upper bound for the number of independent components of the corresponding property tensor. However, for a given Hamiltonian, this global approach usually can not give a definite answer on whether a physical effect such as spin Hall effect (SHE) exists or not. It is found that the parity and types of spin-orbit interactions (SOIs) are good indicators that can further reduce the number of independent components of the spin Hall conductivity for a specific system. In terms of the parity as well as various Rashba-like and Dresselhaus-like SOIs, we propose a local approach to classify SHE in two-dimensional (2D) two-band models, where sufficient conditions for identifying the existence or absence of SHE in all 2D magnetic point groups are presented.

Generating a pure spin current using electrons, which have degrees of freedom beyond spin, such as electric charge and valley index, presents challenges. In response, we propose a novel mechanism based on intervalley exciton dynamics in {\em arc-shaped} strained transition metal dichalcogenides (TMDs) to achieve the {\em exciton spin Hall effect} in an electrically insulating regime, without the need for an external electric field. The interplay between strain gradients and strain-induced pseudomagnetic fields results in a net Lorentz force on long-lived intervalley excitons in WSe$_2$, carrying non-zero spin angular momentum. This process generates an exciton-mediated pure spin Hall current, resulting in opposite-sign spin accumulations and local magnetization on the two sides of the single-layer arc-shaped TMD. We demonstrate that the magnetic field induced by spin accumulation, at approximately $\sim {\rm mT}$, can be detected using techniques such as superconducting quantum interference magnetometry or spatially-resolved magneto-optical Faraday and Kerr rotations.

We present a spin-induced none-geodesic effect of Dirac wave packets in a static uniform gravitational field. Our approach is based on the Foldy-Wouthuysen transformation of Dirac equation in a curved spacetime, which predicts the gravitational spin-orbit coupling. Due to this coupling, we find that the dynamics of the free-fall Dirac wave packets with opposite spin polarization will yield the transverse splitting in the direction perpendicular to spin orientation and gravity, which is known as the gravitational spin Hall effect. Even in a static uniform gravitational field, such effect suggests that the weak equivalence principle is violated for quantum particles., Comment: 6 pages, 1 PDF figure

We present a prediction of chiral topological metals with several classes of unconventional quasiparticle fermions in a family of SrGePt-type materials in terms of first-principles calculations. In these materials, fourfold spin-3/2 Rarita-Schwinger-Weyl (RSW) fermion, sixfold excitation, and Weyl fermions coexist around the Fermi level as spin-orbit coupling is considered, and the Chern number for the first two kinds of fermions is the maximal value four. We found that large Fermi arcs from spin-3/2 RSW fermion emerge on the (010)-surface, spanning the whole surface Brillouin zone. Moreover, there exist Fermi arcs originating from Weyl points, which further overlap with trivial bulk bands. In addition, we revealed that the large spin Hall conductivity can be obtained, which attributed to the remarkable spin Berry curvature around the degenerate nodes and band-splitting induced by spin-orbit coupling. Our findings indicate that the SrGePt family of compounds provide an excellent platform for studying on topological electronic states and the intrinsic spin Hall effect., Comment: 10 pages and 7 figures in the main text