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Recently there is a report of the experimental signatures of a fractional quantum spin hall (FQSH) state at hole filling n=3 in a twisted MoTe_{2} bilayer. Previous theories of FQSH phases simply considered a decoupled pair of a fractional quantum Hall phase and its time reversal partner. Here, we show the first construction of an FQSH phase beyond the decoupling picture. We consider a pair of half-filled C=±1 Chern bands in the two valleys, similar to the well-studied quantum Hall bilayer, but now with opposite chiralities. Because of the strong intervalley repulsion, we expect a charge gap to open with low-energy physics dominated by the neutral intervalley excitons. However, the presence of an effective "flux" frustrates exciton condensation by proliferating vortices. Here, we construct a vortex liquid of excitons dubbed a vortex spin liquid, formed from exciton pairing of the composite fermions in the decoupled composite Fermi liquid 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 intervalley-coherent order. Unlike a conventional Mott insulator, the vortex spin liquid phase also exhibits a quantized FQSH effect with gapless helical charge modes along the edge. Our work demonstrates the possibility of nontrivial FQSH phases and provides predictions to detect them in future experiments.

Recently, a significant amount of attention has been attracted toward a third classification of magnetism, altermagnetism, due to the unique physical properties of altermagnetic materials, which are compensated collinear antiferromagnets that host time-reversal symmetry-breaking phenomena like a ferromagnet. In an altermagnetic material, through the nonrelativistic altermagnetic spin-splitting effect (ASSE), a transverse spin current is generated upon charge current injection. However, it is very challenging to experimentally establish the ASSE since it is inevitably mixed with the spin Hall effect due to the relativistic spin-orbit coupling of the material. Additionally, the dependence on the hard-to-probe and hard-to-control Néel vectors makes it even more difficult to observe and establish the ASSE. In this Letter, we utilize the thermal spin injection from the ferrimagnetic insulator yttrium iron garnet and detect an inverse altermagnetic spin-splitting effect (IASSE) in the high-quality epitaxial altermagnetic RuO_{2} thin films. We observe an opposite sign for the spin-to-charge conversion through the IASSE compared to the inverse spin Hall effect (ISHE). The efficiency of the IASSE is approximately 70% of the ISHE in RuO_{2}. Moreover, we demonstrate that the ASSE or IASSE effect is observable only when the Néel vectors are well aligned. By modifying the Néel vector domains via RuO_{2} crystallinity, we study the ASSE or IASSE unequivocally and quantitatively. Our Letter provides significant insight into the spin-splitting effect in altermagnetic materials.

Utilizing spin pumping, we present a comparative study of the spin-charge conversion in RuO_{2}(101) and RuO_{2}(110) films. RuO_{2}(101) shows a robust in-plane crystal-axis dependence, whereas RuO_{2}(110) exhibits an isotropic but stronger one. Symmetry-based analysis and first-principles calculations reveal that the spin-charge conversion in RuO_{2}(110) originates from the inverse spin Hall effect (ISHE) due to nodal lines splitting. In RuO_{2}(101), the ISHE also dominates although the inverse spin splitting effect (ISSE) may coexist. These findings, in sharp contrast to previously attributed ISSE, are further corroborated by the reciprocal relation between the spin pumping and the spin-torque ferromagnetic resonance measurements.

The recently discovered Van der Waals antiferromagnets have suffered from the lack of a comprehensive method to study their magnetic properties. Here, we propose an ac intrinsic magnon spin Hall current driven by surface acoustic waves as a novel probe for such antiferromagnets. Our results pave the way towards mechanical detection and manipulation of the magnetic order in two-dimensional antiferromagnets. Furthermore, they will overcome the difficulties with weak magnetic responses inherent in the use of antiferromagnets and hence provide a building block for future antiferromagnetic spintronics.

When a spin-splitting field is introduced to a thin film superconductor, the spin currents polarized along the field couples to energy currents that can only decay via inelastic scattering. We study spin and energy injection into such a superconductor where spin-orbit impurity scattering yields inverse spin-Hall and spin-swapping currents. We show that the combined presence of a spin-splitting field, superconductivity, and inelastic scattering gives rise to a strong enhancement of the ordinary inverse spin-Hall effect, as well as unique inverse spin-Hall and spin-swapping signals orders of magnitude stronger than the ordinary inverse spin-Hall signal. These can be completely controlled by the orientation of the spin-splitting field, resulting in a long-range charge and spin accumulations detectable much further from the injector than in the normal state. While the enhanced inverse spin-Hall signals offer a major improvement in spin detection sensitivity, the unique spin-swap signals can be utilized for designing devices where both the spin and current directions are controlled and altered throughout the geometry.

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

We report the observation of the isotropic spin Hall effect in a ferromagnet. We show that the spin Hall effect in an epitaxially grown Fe_{3}Si generates a sizable spin current with a spin direction that is noncollinear with the magnetization. Furthermore, we find that the spin Hall current is independent of the relative orientation between its spin direction and the magnetization; the spin Hall effect is isotropic. This observation demonstrates that the intrinsically generated transverse spin component is protected from dephasing, providing fundamental insights into the generation and transport of spin currents in ferromagnets.

Optical bound states in the continuum (BICs) are exotic topological defects in photonic crystal slabs, carrying polarization topological vortices in momentum space. The topological vortex configurations not only topologically protect the infinite radiation lifetime of BICs, but also intrinsically contain many unexploited degrees of freedom for light manipulation originating from BICs. Here, we theoretically propose and experimentally demonstrate the spin Hall effect of light in photonic crystal slabs via momentum-space topological vortices around BICs. The strong spin-orbit interactions of light are induced by using the topological vortices around BICs, introducing both wave-vector-dependent Pancharatnam-Berry phase gradients and cross-polarized resonant phase gradients to the spinning light beam, which lead to spin-dependent in-plane-oblique lateral light beam shifts. Our work reveals intriguing spin-related topological effects around BICs, opening an avenue toward applications of BICs in integrated spin-optical devices and information processing.

Previously, it has been shown that rapid cooling of yttrium-iron-garnet-platinum nanostructures, preheated by an electric current sent through the Pt layer, leads to overpopulation of a magnon gas and to subsequent formation of a Bose-Einstein condensate (BEC) of magnons. The spin Hall effect (SHE), which creates a spin-polarized current in the Pt layer, can inject or annihilate magnons depending on the electric current and applied field orientations. Here we demonstrate that the injection or annihilation of magnons via the SHE can prevent or promote the formation of a rapid cooling-induced magnon BEC. Depending on the current polarity, a change in the BEC threshold of -8% and +6% was detected. These findings demonstrate a new method to control macroscopic quantum states, paving the way for their application in spintronic devices.

We propose a light-induced spin Hall effect for interlayer exciton gas in monolayer MoSe2-WSe2 van der Waals heterostructure. By applying two infrared, spatially varying laser beams coupled to the exciton internal states, a spin-dependent gauge potential on the exciton center-of-mass motion is induced. This gauge potential deflects excitons in different spin states towards opposite directions, leading to a finite spin current but vanishing mass current. In the Hall bar geometry, the spin-dependent deflection gives rise to spin-dependent chiral edge states with spin-velocity locking. The spin current and chiral edge states of the excitons can be detected by spatially resolved photoluminescence spectroscopy. [ABSTRACT FROM AUTHOR]

Dissipationless flows in single-component superfluids have a significant degree of universality. In ^{4}He, the dissipationless mass flow occurs with a superfluid velocity determined by the gradient of the superfluid phase. However, in interacting superfluid mixtures, principally new effects appear. In this Letter, we demonstrate a new kind of dissipationless phenomenon arising in mixtures of interacting bosons in optical lattices. We point out that for a particular class of optical lattices, bosons condense in a state where one of the components' superflow results in dissipationless mass flow of the other component, in a direction different from either of the components' superfluid velocities. The free-energy density of these systems contains a vector productlike interaction of superfluid velocities, producing the dissipationless noncollinear entrainment. The effect represents a superfluid counterpart of the Spin Hall effect.

We study the spin Hall effect (SHE) in disordered π-conjugated organic solids, where individual molecules are oriented randomly and electrical conduction is via carrier hopping. The SHE, which arises from interference between direct (i→j) and indirect (i→k→j) hoppings in a triad consisting of three molecules i, j, and k, is found to be proportional to λ(ni×nj+nj×nk+nk×ni), where λ is the spin admixture of π electrons due to the spin-orbit coupling and ni is the orientation vector of molecule i. Electrical conductivity σqq (q=x,y,z) and spin Hall conductivity σsh are computed by numerically solving the master equations of a system containing 32×32×32 molecules and summing over contributions from all triads in the system. The obtained value of the spin Hall angle Θsh is consistent with experimental data in PEDOT:PSS, with a predicted temperature dependence of logΘsh~T-1/4. [ABSTRACT FROM AUTHOR]

We use a phase-sensitive, quantitative technique to separate inductive and ac inverse spin Hall effect (ISHE) voltages observed in Ni81Fe19/normal metal multilayers under the condition of ferromagnetic resonance. For Ni81Fe19/Pt thin film bilayers and at microwave frequencies from 7 to 20 GHz, we observe an ac ISHE magnitude that is much larger than that expected from the dc spin Hall angle ΘPtSH= 0.1. Furthermore, at these frequencies, we find an unexpected, ≈110° phase of the ac ISHE signal relative to the in-plane component of the resonant magnetization precession. We attribute our findings to a dominant intrinsic ac ISHE in Pt. [ABSTRACT FROM AUTHOR]

The spin Hall effect of light (SHEL) is the photonic analogue of the spin Hall effect occurring for charge carriers in solid-state systems. This intriguing phenomenon manifests itself when a light beam refracts at an air-glass interface (conventional SHEL) or when it is projected onto an oblique plane, the latter effect being known as the geometric SHEL. It amounts to a polarization-dependent displacement perpendicular to the plane of incidence. In this work, we experimentally investigate the geometric SHEL for a light beam transmitted across an oblique polarizer. We find that the spatial intensity distribution of the transmitted beam depends on the incident state of polarization and its centroid undergoes a positional displacement exceeding one wavelength. This novel phenomenon is virtually independent from the material properties of the polarizer and, thus, reveals universal features of spin-orbit coupling. [ABSTRACT FROM AUTHOR]

Through combined ferromagnetic resonance, spin pumping, and inverse spin Hall effect experiments in Co∣Pt bilayers and Co∣Cu∣Pt trilayers, we demonstrate consistent values of ℓsfPt = 3.4 ± 0.4 nm and θSHEPt= 0.056 ± 0.010 for the respective spin diffusion length and spin Hall angle for Pt. Our data and model emphasize the partial depolarization of the spin current at each interface due to spin-memory loss. Our model reconciles the previously published spin Hall angle values and explains the different scaling lengths for the ferromagnetic damping and the spin Hall effect induced voltage. [ABSTRACT FROM AUTHOR]

We propose a scheme which realizes spin-orbit coupling and the quantum spin Hall effect for neutral atoms in optical lattices without relying on near resonant laser light to couple different spin states. The spin-orbit coupling is created by modifying the motion of atoms in a spin-dependent way by laser recoil. The spin selectivity is provided by Zeeman shifts created with a magnetic field gradient. Alternatively, a quantum spin Hall Hamiltonian can be created by all-optical means using a period-tripling, spin-dependent superlattice. [ABSTRACT FROM AUTHOR]

Recently, a positive spin Hall angle (SHA) of 0.021 was observed experimentally in nonmagnetic Culr alloys [Niimi et al, Phys. Rev. Lett. 106,126601 (2011)] and attributed predominantly to an extrinsic skew scattering mechanism, while a negative SHA was obtained from ab initio calculations [Fedorov etal, Phys. Rev. B 88, 085116 (2013)], using consistent definitions of the SHA. We reconsider the SHA in Culr alloys, with the effects of the local electron correlation U in 5d orbitals of Ir impurities, included by the quantum Monte Carlo method. We found that the SHA is negative if we ignore such local electron correlation, but becomes positive once U approaches a realistic value. This may open up a way to control the sign of the SHA by manipulating the occupation number of impurities. [ABSTRACT FROM AUTHOR]

The geometric Pancharatnam-Berry (PB) phase not only is of physical interest but also has wide applications ranging from condensed-matter physics to photonics. Space-varying PB phases based on inhomogeneously anisotropic media have previously been used effectively for spin photon manipulation. Here we demonstrate a novel wave-vector-varying PB phase that arises naturally in the transmission and reflection processes in homogeneous media for paraxial beams with small incident angles. The eigenpolarization states of the transmission and reflection processes are determined by the local wave vectors of the incident beam. The small incident angle breaks the rotational symmetry and induces a PB phase that varies linearly with the transverse wave vector, resulting in the photonic spin Hall effect (PSHE). This new PSHE can address the contradiction between spin separation and energy efficiency in the conventional PSHE associated with the Rytov-Vladimirskii-Berry phase, allowing spin photons to be separated completely with a spin separation up to 2.2 times beam waist and a highest energy efficiency of 86%. The spin separation dynamics is visualized by wave coupling equations in a uniaxial crystal, where the centroid positions of the spin photons can be doubled due to the conservation of the angular momentum. Our findings can greatly deepen the understanding in the geometric phase and spin-orbit coupling, paving the way for practical applications of the PSHE.

We show that an electric field parallel to the wave fronts of an electron-hole grating in a GaAs quantum well generates, via the electronic spin Hall effect, a spin grating of the same wave vector and with an amplitude that can exceed 1% of the amplitude of the initial density grating. We refer to this phenomenon as the "collective spin Hall effect." A detailed study of the coupled spin-charge dynamics for quantum wells grown in different directions reveals rich features in the time evolution of the induced spin density, including the possibility of generating a helical spin grating. [ABSTRACT FROM AUTHOR]

Large spin Hall angles have been observed in 3d ferromagnets, but their origin, and especially their link with the ferromagnetic order, remain unclear. Here, we investigate the evolution of the inverse spin Hall effect of Ni_{60}Cu_{40} and Ni_{50}Cu_{50} across their Curie temperatures using spin-pumping experiments. We show that the inverse spin Hall effect in these samples is comparable to that of platinum, and that it is insensitive to the magnetic order. These results point toward a Heisenberg localized model of the transition and suggest that the large spin Hall effects in 3d ferromagnets can be independent of the magnetic phase.

We report an unconventional quantum spin Hall phase in the monolayer WTe_{2}, which exhibits hitherto unknown features in other topological materials. The low symmetry of the structure induces a canted spin texture in the yz plane, which dictates the spin polarization of topologically protected boundary states. Additionally, the spin Hall conductivity gets quantized (2e^{2}/h) with a spin quantization axis parallel to the canting direction. These findings are based on large-scale quantum simulations of the spin Hall conductivity tensor and nonlocal resistances in multiprobe geometries using a realistic tight-binding model elaborated from first-principle methods. The observation of this canted quantum spin Hall effect, related to the formation of topological edge states with nontrivial spin polarization, demands for specific experimental design and suggests interesting alternatives for manipulating spin information in topological materials.

The inverse spin Hall effect (ISHE) has been observed only in nonmagnetic metals, such as Pt and Au, with a strong spin-orbit coupling. We report the observation of ISHE in a ferromagnetic permalloy (Py) on ferromagnetic insulator yttrium iron garnet (YIG). Through controlling the spin current injection by altering the Py-YIG interface, we have isolated the spin current contribution and demonstrated the ISHE in a ferromagnetic metal, the reciprocal phenomenon of the anomalous Hall effect. A large spin Hall angle in Py, determined from Py thin films of different thicknesses, indicates many other ferromagnetic metals may be exploited as superior pure spin current detectors and for applications in spin current. [ABSTRACT FROM AUTHOR]

We study the phase diagram of the inverted InAs/GaSb bilayer quantum wells. For a small tunneling amplitude between the layers, we find that the system is prone to the formation of an 5-wave exciton condensate phase, where the spin structure of the order parameter is uniquely determined by the small spinorbit coupling arising from the bulk inversion asymmetry. The phase is topologically trivial and does not support edge transport. On the contrary, for a large tunneling amplitude, we obtain a topologically nontrivial quantum spin Hall insulator phase with a p-wave exciton order parameter, which enhances the hybridization gap. These topologically distinct insulators are separated by an insulating phase with spontaneously broken time-reversal symmetry. Close to the phase transition between the quantum spin Hall and time-reversal broken phases, the edge transport shows quantized conductance in small samples, whereas in long samples the mean free path associated with the backscattering at the edge is temperature independent, in agreement with recent experiments. [ABSTRACT FROM AUTHOR]

Noncollinear antiferromagnets can have additional spin Hall effects due to the net chirality of their magnetic spin structure, which provides for more complex spin-transport phenomena compared to ordinary nonmagnetic materials. Here we investigated how ferromagnetic resonance of permalloy (Ni_{80}Fe_{20}) is modulated by spin Hall effects in adjacent epitaxial IrMn_{3} films. We observe a large dc modulation of the ferromagnetic resonance linewidth for currents applied along the [001] IrMn_{3} direction. This very strong angular dependence of spin-orbit torques from dc currents through the bilayers can be explained by the magnetic spin Hall effect where IrMn_{3} provides novel pathways for modulating magnetization dynamics electrically.

In the absence of external magnetic field and Dzyaloshinskii-Moriya interaction, the magnon excitations in a uniaxial antiferromagnet insulator are usually described by two degenerate magnon modes with the same dispersion but opposite polarizations. In this Letter, we show that these two modes are actually coupled intrinsically through an effective spin-orbit coupling due to the dipolar interaction. The magnon spin dynamics and transport thus display various electronlike spin-orbit phenomena, such as the D'yakonov-Perel'-type spin relaxation and an intrinsic (inverse) spin Hall effect. Our work may potentially broaden the applications of antiferromagnetic insulators in spintronic devices.

We report an experiment showing the submillimeter Imbert-Fedorov shift from the ultrastrong spin-orbital angular momentum coupling, which is a photonic version of the spin Hall effect, by measuring the reflection of light from the surface of a birefringent symmetrical metal cladding planar waveguide. The light incidents at a near-normal incident angle and excites resonant ultrahigh-order modes inside the waveguide. A 0.16-mm displacement of separated reflected light spots corresponding to two polarization states is distinguishable by human eyes. In our experiment, we demonstrate the control of polarizations of light and the direct observation of the spin Hall effect of light, which opens an important avenue towards potential applications for optical sensing and quantum information processing, where the spin nature of photons exhibits key features.

Over the past decades, topology has provided unique insight into numerous physical phenomena. Here, we report on a topological mechanism for spin-dependent photonic transport. We observe photonic topological defects of bound vortex pairs and unbound vortices generated from a two-dimensional array of nanoantennas, i.e., a metasurface, which is achieved by randomly inserting local deformations in the metasurfaces, inducing the Pancharatnam-Berry phase. The observed spin-dependent bound vortex pairs are established as the origin of the photonic topological spin Hall effect-a subdiffraction-limited spin-split mode in momentum space, while the spin-dependent unbound vortices induce random spin-split modes throughout the entire momentum space as a random Rashba effect. The topological phenomena-creation of bound vortex pairs and unbound vortices-indicate the universality of the topological effect for particles of different natures.

We propose mechanisms for the spin Hall effect in metallic systems arising from the coupling between conduction electrons and local magnetic moments that are dynamically fluctuating. Both a side-jump-type mechanism and a skew-scattering-type mechanism are considered. In either case, dynamical spin fluctuation gives rise to a nontrivial temperature dependence in the spin Hall conductivity. This leads to the enhancement in the spin Hall conductivity at nonzero temperatures near the ferromagnetic instability. The proposed mechanisms could be observed in 4d or 5d metallic compounds.

The quantum spin Hall (QSH) effect is known to be unstable to perturbations violating time-reversal symmetry. We show that creating a narrow ferromagnetic region near the edge of a QSH sample can push one of the counterpropagating edge states to the inner boundary of the ferromagnetic region and leave the other at the outer boundary, without changing their spin polarizations and propagation directions. Since the two edge states are spatially separated into different "lanes," the QSH effect becomes robust against symmetry-breaking perturbations. [ABSTRACT FROM AUTHOR]

In the normal-metal-ferromagnetic-insulator bilayer (such as Pt/Y3Fe5O12) and the normal-metalferromagnetic- metal-oxide trilayer (such as Pt/Co/A1Ox) where spin injection and ejection are achieved by the spin Hall effect in the normal metal, we propose a minimal model based on quantum tunneling of spins to explain the spin-transfer torque and spin pumping caused by the spin Hall effect. The ratio of their dampinglike to fieldlike component depends on the tunneling wave function that is strongly influenced by generic material properties such as interface s-d coupling, insulating gap, and layer thickness, yet the spin relaxation plays a minor role. The quantified result renders our minimal model an inexpensive tool for searching for appropriate materials. [ABSTRACT FROM AUTHOR]

The geometric Pancharatnam-Berry (PB) phase not only is of physical interest but also has wide applications ranging from condensed-matter physics to photonics. Space-varying PB phases based on inhomogeneously anisotropic media have previously been used effectively for spin photon manipulation. Here we demonstrate a novel wave-vector-varying PB phase that arises naturally in the transmission and reflection processes in homogeneous media for paraxial beams with small incident angles. The eigenpolarization states of the transmission and reflection processes are determined by the local wave vectors of the incident beam. The small incident angle breaks the rotational symmetry and induces a PB phase that varies linearly with the transverse wave vector, resulting in the photonic spin Hall effect (PSHE). This new PSHE can address the contradiction between spin separation and energy efficiency in the conventional PSHE associated with the Rytov-Vladimirskii-Berry phase, allowing spin photons to be separated completely with a spin separation up to 2.2 times beam waist and a highest energy efficiency of 86%. The spin separation dynamics is visualized by wave coupling equations in a uniaxial crystal, where the centroid positions of the spin photons can be doubled due to the conservation of the angular momentum. Our findings can greatly deepen the understanding in the geometric phase and spin-orbit coupling, paving the way for practical applications of the PSHE. [ABSTRACT FROM AUTHOR]

We show that optical beams propagating in transversally disordered materials exhibit a spin Hall effect and a spin-to-orbital conversion of angular momentum as they deviate from paraxiality. We theoretically describe these phenomena on the basis of the microscopic statistical approach to light propagation in random media, and show that they can be detected via polarimetric measurements under realistic experimental conditions.

We study the spin-orbit coupling induced by the splitting between TE and TM optical modes in a photonic honeycomb lattice. Using a tight-binding approach, we calculate analytically the band structure. Close to the Dirac point, we derive an effective Hamiltonian. We find that the local reduced symmetry (D3h) transforms the TE-TM effective magnetic field into an emergent field with a Dresselhaus symmetry. As a result, particles become massive, but no gap opens. The emergent field symmetry is revealed by the optical spin Hall effect. [ABSTRACT FROM AUTHOR]

We report an unconventional quantum spin Hall phase in the monolayer WTe2, which exhibits hitherto unknown features in other topological materials. The low symmetry of the structure induces a canted spin texture in the yz plane, which dictates the spin polarization of topologically protected boundary states. Additionally, the spin Hall conductivity gets quantized (2e²/h) with a spin quantization axis parallel to the canting direction. These findings are based on large-scale quantum simulations of the spin Hall conductivity tensor and nonlocal resistances in multiprobe geometries using a realistic tight-binding model elaborated from first-principle methods. The observation of this canted quantum spin Hall effect, related to the formation of topological edge states with nontrivial spin polarization, demands for specific experimental design and suggests interesting alternatives for manipulating spin information in topological materials. [ABSTRACT FROM AUTHOR]