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The physics of the anomalous and spin Hall effects is one of the most intriguing aspects of condensed matter physics. An important finding from a large collection of experimental and theoretical results is the universal scaling of the anomalous or spin Hall conductivity with the electric conductivity. This scaling has been successfully described by the intrinsic Berry curvature and extrinsic scattering mechanisms for metallic systems, revealing the topological nature of these effects. In contrast, the underlying physics in the opposite limit, the disordered insulating regime, is still unclear. In particular, it remains a major challenge, both experimentally and theoretically, to explore the spin Hall effect in the insulating regime. Here, we report the observation of the crossover between the metallic and insulating regimes of the spin Hall effect. The result demonstrates a direct correspondence between the spin and anomalous Hall effects, which will advance the fundamental understanding of spin transport.

We investigated Pt/Ir/Pt and Pt/Ir multilayers as candidates of nonmagnetic spacer layers in synthetic antiferromagnetic (AF) layers, which are available for the systematic study on AF spintronics. In these systems, we observed (i) AF interlayer exchange coupling in Pt/Ir/Pt and Pt/Ir nonmagnetic spacer layers sandwiched by Co layers and (ii) large spin Hall conductivity in Pt/Ir multilayer heavy-metal systems which is essential to achieve low power consumption spin-orbit torque switching. We found that total nonmagnetic spacer layer thickness $[{t}_{\mathrm{total}}={t}_{\mathrm{Pt}}(\mathrm{Pt}\phantom{\rule{0.16em}{0ex}}\mathrm{thickness})+{t}_{\mathrm{Ir}}(\mathrm{Ir}\phantom{\rule{0.16em}{0ex}}\mathrm{thickness})]$ range in which AF interlayer exchange coupling is observed is wide in Co/nonmagnetic spacer layer/Co with Pt/Ir/Pt and Pt/Ir nonmagnetic spacer layers. Moreover, the large spin Hall angle of ${\ensuremath{\theta}}_{\mathrm{SH}}=10.3%$ and low resistivity of ${\ensuremath{\rho}}_{xx}=35\phantom{\rule{0.16em}{0ex}}\ensuremath{\mu}\mathrm{\ensuremath{\Omega}}\phantom{\rule{0.16em}{0ex}}\mathrm{cm}$ in Pt/Ir multilayer heavy metal are observed. These results indicate that Pt/Ir/Pt and Pt/Ir are nonmagnetic spacer layers allowing us to achieve the AF interlayer exchange coupling and generation of large spin-orbit torque via spin Hall effect in synthetic AF coupling layer system.

We investigated spin-Hall effect (SHE) and degree of MgO (100) orientation in artificially synthesized (W/Hf)-multilayer/CoFeB/MgO systems with various W thicknesses. We found that the artificially synthesized multilayer systems can enhance the spin-Hall effect and control the value of spin diffusion length. We observed a maximum magnitude in both spin-Hall angle and spin-Hall conductivity as a function of W thickness in W/Hf-multilayer systems, and found that the values of spin-Hall conductivity are larger than that for β-phase W. In addition, a more highly oriented MgO (100) texture on CoFeB is obtained for (W/Hf)-multilayer systems prepared under low-Ar-pressure condition, which would be suitable for preparation of magnetic tunnel junctions with high tunnel magnetoresistance properties on (W/Hf)-multilayer heavy metal electrode. These results suggest that the artificially synthesized multilayer system is one of the avenues for realizing spin devices using spin-orbit torque.

Manganites have shown potential in spintronics because they exhibit high spin polarization. Here, by ferromagnetic resonance we have studied the damping properties of La0.67Sr0.33MnO3/Pt bilayers which are prepared by oxide molecular beam epitaxy. The damping coefficient (α) of a La0.67Sr0.33MnO3 (LSMO) single layer is found to be 0.0104. However the LSMO/Pt bilayers exhibit a decrease in α with an increase in Pt thickness. This decrease in the value of α is probably due to high anti-damping like torque. Furthermore, we have investigated the angle dependent inverse spin Hall effect (ISHE) to quantify the spin pumping voltage from other spin rectification effects such as the anomalous Hall effect and anisotropic magnetoresistance. We have observed a high spin pumping voltage (∼20 μV). The results indicate that both anti-damping and spin pumping phenomena occur simultaneously.

We report on the spin Hall effect in epitaxial Pt films with well-defined crystalline (200), (220), and (111) orientations and smooth surfaces. The magnitude of the spin Hall effect has been determined by spin–torque ferromagnetic resonance measurements on epitaxial Pt/Py heterostructures. We observed a 54% enhancement of the charge-to-spin conversion efficiency of the epitaxial Pt when currents are applied along the in-plane <002> direction. Temperature-dependent harmonic measurements on epitaxial Pt/Co/Ni heterostructures compared to a polycrystalline Pt/Co/Ni suggest the extrinsic mechanism underlying spin Hall effect in epitaxial Pt. Our work contributes to the development of energy-efficient spintronic devices by engineering the crystalline anisotropy of non-magnetic metals.

The inverse spin Hall effect (ISHE) has been recently demonstrated through the photoinduced inverse spin Hall effect (PISHE), where a focused laser normal to the device plane generates photocurrent that depends on the helicity of the photoexcitation. Here, we have employed a finite element method to rigorously simulate the helicity-dependent photocurrent (HDPC) under local helical photoexcitation, taking into account the complications of minority carriers, metal contact junctions, and spin relaxation. We found that the ISHE-induced electromotive force is inversely proportional to the doping level of the material, caused by the diffusion and drift current balance. Furthermore, the HDPC near the metal contact can either increase or decrease, because of the competing mechanisms of fast carrier recombination and spin relaxation at the contact. These simulation results provide insightful visualization of charge, spin, electric field, and current density distributions and deeper understanding of photoinduced ISHE.

We report the coherent-incoherent crossover of the spin Hall effect in Pd. By measuring spin-orbit torques generated by oxygen-incorporated Pd films, we find two distinct regimes of the spin Hall effect; one in which the spin Hall conductivity is insensitive to the electric conductivity, and the other in which the spin Hall conductivity decreases with decreasing electric conductivity. The crossover between the two regimes is consistent with the prediction of the coherent-incoherent crossover of the spin Hall effect, which is analogous to that of the anomalous Hall effect. Unlike the anomalous Hall effect, for which the crossover has been observed for a wide class of ferromagnets, the crossover of the spin Hall effect has been confirmed only for Pt and Pt-based alloys. The observation of the crossover of the spin Hall effect for Pd supports the generality of this phenomenon, illustrating an important correspondence between the spin Hall effect and the anomalous Hall effect.

All-optical switching connectors (AOSC) are made of topological insulators (three-dimensional magnetic materials) which reverse the magnetization field using short laser pulses. They gained extensive attention in the past decade due to its high potential for fast and energy-efficient data writing in the spintronic memory applications. Regrettably, using of AOSC in the ferromagnetic multilayers needs multiple pulses for the magnetization reversal that losing its speed and energy efficiency. Here we use the single-pulse mid-infrared and microwave photoexcitation to enable ultrafast manipulation of surface private intraband terahertz and gigahertz transitions in result of spin Hall effect driven motion of magnetic domains in Bi2Se3 synthetic ferromagnetic material of AOSC. This optical excitation is achieved in the magnetic tunnel cell by the optical Hall effect (OHE) of magnetic tunnel junction cells. Therefore, by measuring the (z) axis of optical field of spin Hall effect on the ferromagnetic topological material, the data stored by the optical excitation can be calculated and the write efficiency on the ferromagnetic material is verified. Our experiments show that the use of Bi2Se3 type topological material in both single-pulse AOSC optical excitations is powerful to amplify the OHE field amplitude, which may eventually pave the way for integrated photonic current based memory circuits.

It is now well established that the peculiar linear-in-momentum dependence of the Rashba (and of the Dresselhaus) spin-orbit coupling leads to the vanishing of the spin Hall conductivity in the bulk of a two-dimensional electron gas (2DEG). In this paper we discuss how generic magnetic couplings change this behaviour providing then a potential handle on the spin Hall effect. In particular we examine the influence of magnetic impurities and an in-plane magnetic field. We find that in both cases there is a finite spin Hall effect and we provide explicit expressions for the spin Hall conductivity. The results can be obtained by means of the quasiclassical Green function approach, that we have recently extended to spin-orbit coupled electron systems.

THz spintronics emitters represent today novel sources for broadband emission using nanometer-scaled materials. We experimentally investigate and model THz spintronic emission based on the spin Hall effect in 3d/5d transition metals and on the inverse Rashba-Edelstein effect in the optimized topological insulator Bi1-xSbx.

The link between magnetization and Spin Hall Effect (SHE) has remained mostly unclear for now. In a first part of this contribution, we study oh the presence of the magnetization affect the SHE, by performing in the weak ferromagnet NiCu Spin Pumping-FMR measurements across the ferromagnetic / paramagnetic critical temperature. We show that the high spin Hall effects which can be obtained in 3d ferromagnets seems to be independent of the magnetic phase. In a second part, we show that the spin absorption process in a ferromagnetic material depends on the spin orientation relative to the magnetization. Using a ferromagnet to absorb the pure spin current created within a lateral spin valve, we evidence and quantify a sizable orientation dependence of the spin absorption in Co, CoFe, and NiFe. These experiments allow us to determine the spin-mixing conductance, an elusive but fundamental parameter of the spin-dependent transport.

We report the robustness of the intrinsic spin Hall effect in Pt against a change in the lattice constant. We measure spin-torque ferromagnetic resonance for $\mathrm{Pt}/{\mathrm{Ni}}_{81}{\mathrm{Fe}}_{19}$ bilayers, where the lattice constant and carrier scattering time of the Pt layer are varied by incorporating the nitrogen atoms as interstitial impurities. We find that the spin Hall angle is enhanced by a factor of 3 as the resistivity of the Pt layer is increased by the nitrogen incorporation. The variation of the spin Hall conductivity is consistent with the prediction of the crossover of the intrinsic spin Hall effect from the moderately dirty regime to the dirty-metal regime. This result demonstrates the variation of the intrinsic spin Hall conductivity in Pt is dominated by the change in the scattering time, rather than the change in the band structure, under a few percent change in the lattice constant.

Sizable Rashba spin-orbit coupling (SOC) is of critical importance in potential applications of two-dimensional materials in spintronics devices. However, due to the presence of vertical mirror symmetry, Rashba SOC is absent in 2H transition-metal dichalcogenide monolayers and the spin Hall conductivities are attributed only to Zeeman splitting. We study theoretically the electronic structures and intrinsic spin Hall conductivity of two-dimensional monolayer Janus MoSSe by performing first-principles calculations as well as by using the Kubo formula with Wannier interpolations. We find out that monolayer Janus MoSSe possesses considerable spin Hall conductivities both in conduction and valence bands. In valence bands, the spin Hall conductivity of Janus MoSSe is comparable to that in ${\mathrm{MoS}}_{2}$ and ${\mathrm{MoSe}}_{2}$. Moreover, in the conduction bands, the spin Hall conductivities are enhanced up to two orders of magnitude because of strong Rashba SOC. The spin Hall conductivity can be tuned significantly by adjusting the Fermi level or external strains. Our results show that monolayer Janus MoSSe could be a potential candidate to realize two-dimensional flexible spintronics devices.

Under the terms of the Creative Commons Attribution License 3.0 (CC-BY)., We report an intriguing transition from the quantum spin Hall phase to the spin Hall effect upon segregation of thallium adatoms adsorbed onto a graphene surface. Landauer-Büttiker and Kubo-Greenwood simulations are used to access both edge and bulk transport physics in disordered thallium-functionalized graphene systems of realistic sizes. Our findings not only quantify the detrimental effects of adatom clustering in the formation of the topological state, but also provide evidence for the emergence of spin accumulation at opposite sample edges driven by spin-dependent scattering induced by thallium islands, which eventually results in a minimum bulk conductivity ~4e2/h, insensitive to localization effects., S. R. acknowledges the Spanish Ministry of Economy and Competitiveness for funding (MAT2012-33911), the Severo Ochoa Program (MINECO SEV-2013-0295), and the Secretaria de Universidades e Investigación del Departamento de Economía y Conocimiento de la Generalidad de Cataluña. The research leading to these results has received funding from the European Union Seventh Framework Programme under Grant Agreement No. 604391 Graphene Flagship.

Dissipationless flows in single-component superfluids have a significant degree of universality. In He4, 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 product-like interaction of superfluid velocities, producing the dissipationless noncollinear entrainment. The effect represents a superfluid counterpart of the Spin Hall effect., 4 pages, 3 figures and supplemental material; version accepted for publication in Phys. Rev. Lett

Using samples of ${\mathrm{Co}}_{100\ensuremath{-}x}{\mathrm{Tb}}_{x}/\mathrm{Cu}/{\mathrm{Y}}_{3}{\mathrm{Fe}}_{5}{\mathrm{O}}_{12}$, we investigate the heat-to-charge current conversion phenomena in amorphous ${\mathrm{Co}}_{100\ensuremath{-}x}{\mathrm{Tb}}_{x}$ alloys. We find an enhancement of the inverse spin Hall voltage owing to the $\mathrm{Tb}$ impurity by means of the spin Seebeck effect. The spin Hall angle of ${\mathrm{Co}}_{68}{\mathrm{Tb}}_{32}$ is 3.5 times larger than that of $\mathrm{Co}$, and mainly originates from the extrinsic spin Hall effect. Meanwhile, we detect an anomalous Nernst voltage owing to the magnetic properties of ${\mathrm{Co}}_{100\ensuremath{-}x}{\mathrm{Tb}}_{x}$ alloy. The sign of the inverse spin Hall voltage is observed to be the same for all ${\mathrm{Co}}_{100\ensuremath{-}x}{\mathrm{Tb}}_{x}$ samples, whereas the anomalous Nernst voltage changes its sign around the magnetization compensation composition. Our finding proves ${\mathrm{Co}}_{100\ensuremath{-}x}{\mathrm{Tb}}_{x}$ is an efficient spin-to-charge current convertor, and it has advantages for manipulating not only the inverse spin Hall effect but also the anomalous Nernst effect by means of adjusting the $\mathrm{Tb}$ concentration.

The spin Hall effect in heavy-metal thin films is routinely employed to convert charge currents into transverse spin currents and can be used to exert torque on adjacent ferromagnets. Conversely, the inverse spin Hall effect is frequently used to detect spin currents by charge currents in spintronic devices up to the terahertz frequency range. Numerous techniques to measure the spin Hall effect or its inverse were introduced, most of which require extensive sample preparation by multi-step lithography. To enable rapid screening of materials in terms of charge-to-spin conversion, suitable high-throughput methods for measuring the spin Hall angle are required. Here, we compare two lithography-free techniques, terahertz emission spectroscopy and broadband ferromagnetic resonance, to standard harmonic Hall measurements and theoretical predictions using the binary-alloy series Au$_x$Pt$_{1-x}$ as benchmark system. Despite being highly complementary, we find that all three techniques yield a spin Hall angle with approximately the same $x$~dependence, which is also consistent with first-principles calculations. Quantitative discrepancies are discussed in terms of magnetization orientation and interfacial spin-memory loss., Comment: 9 pages, 3 figures

Determining the detailed spin texture of topological surface states is important when one wants to apply topological insulators in spintronic devices. In principle, the in-plane spin component of the surface states can be measured by a method analogous to the so-called Meservey-Tedrow technique. In the present work we suggest that the out-of-plane spin component can be determined by spin Hall effect tunneling spectroscopy. We derive an analytical formula that allows to extract the out-of-plane spin component from spin Hall effect tunneling spectra. We test our formula using realistic tight-binding models of Bi$_2$Se$_3$ and Sb$_2$Te$_3$. We demonstrate that the extracted out-of-plane spin polarization is in very good agreement with the actual out-of-plane spin polarization.

THz spintronics emitters represent today novel sources for broadband emission using nanometer-scaled materials. We present and model the THz spintronic emission based on the spin Hall effect in 3d metals and on the inverse Rashba-Edelstein effect in the optimized topological insulator Bi1 -x Sbx.

Funding Information: We thank D. I. Pikulin for useful discussions and comments. The paper is supported by the Foundation for Polish Science through the IRA Programme cofinanced by EU within SG OP and the Academy of Finland Project No. 331094. We acknowledge the computational resources provided by the Aalto Science-IT project and the access to the computing facilities of the Interdisciplinary Center of Modeling at the University of Warsaw, Grants No. GB82-13, No. G78-13, and No. G75-10. Publisher Copyright: © 2022 American Physical Society. The band-inverted electron-hole bilayers, such as InAs/GaSb, are an interesting playground for the interplay of quantum spin Hall effect and correlation effects because of the small density of electrons and holes and the relatively small hybridization between the electron and hole bands. It has been proposed that Coulomb interactions lead to a time-reversal symmetry broken phase when the electron and hole densities are tuned from the trivial to the quantum spin Hall insulator regime. We show that the transport properties of the system in the time-reversal symmetry broken phase are consistent with recent experimental observations in InAs/GaSb. Moreover, we carry out a quantum transport study on a Corbino disk where the bulk and edge contributions to the conductance can be separated. We show that the edge becomes smoothly conducting and the bulk is always insulating when one tunes the system from the trivial to the quantum spin Hall insulator phase, providing unambiguous transport signatures of the time-reversal symmetry broken phase.

We have found the acoustic spin Hall effect that facilitates lattice motion-induced spin current in strong spin-orbit metals., We report on the observation of the acoustic spin Hall effect that facilitates lattice motion–induced spin current via spin-orbit interaction (SOI). Under excitation of surface acoustic wave (SAW), we find that a spin current flows orthogonal to the SAW propagation in nonmagnetic metals (NMs). The acoustic spin Hall effect manifests itself in a field-dependent acoustic voltage in NM/ferromagnetic metal bilayers. The acoustic voltage takes a maximum when the NM layer thickness is close to its spin diffusion length, vanishes for NM layers with weak SOI, and increases linearly with the SAW frequency. To account for these results, we find that the spin current must scale with the SOI and the time derivative of the lattice displacement. These results, which imply the strong coupling of electron spins with rotating lattices via the SOI, show the potential of lattice dynamics to supply spin current in strong spin-orbit metals.

Non-magnetic materials exhibiting large spin-Hall effect (SHE) are eagerly desired for high-performance spintronic devices. Here, we report that non-equilibrium Cu-Ir binary alloys with compositions beyond the solubility limit are candidates as spin-Hall materials, even though Cu and Ir do not exhibit remarkable SHE themselves. Thanks to non-equilibrium thin film fabrication, the Cu-Ir binary alloys are obtained over a wide composition range even though they are thermodynamically unstable in bulk form. We investigate the SHE of Cu-Ir by exploiting a combinatorial technique based on spin Peltier imaging, and find that the optimum Ir concentration for enhancing SHE is around 25 at.%. We achieve a large spin-Hall angle of 6.29 ± 0.19% for Cu76Ir24. In contrast to Cu-Ir, non-equilibrium Cu-Bi binary alloys do not show remarkable SHE. Our discovery opens a new direction for the exploration of spin-Hall materials. Materials with a large spin-Hall effect are highly desirable for spintronic devices. Here, non-equilibrium thin film synthesis is used to fabricate copper-iridium binary alloys beyond their solubility limit, achieving a large spin-Hall angle of approximately 6% in Cu76Ir24.

An efficient conversion of a charge current into a spin current is a crucial point for application of the spin Hall effect in practical spintronic devices. Recently, we revealed that this goal can be achieved by using ultrathin fcc (111) and (001) noble metal films doped with Bi impurities, which possess spin Hall angles up to 80%. Here, we show that the effect can be further amplified in monolayer films with a strong crystalline anisotropy. This is demonstrated by considering noble metal films with fcc (110) geometry. Our theoretical study predicts related spin Hall angles exceeding 100% especially when the crystalline anisotropy is increased, which tunes the Fermi surface topology.

The discovery of the spin Hall effect1 enabled the efficient generation and manipulation of the spin current. More recently, the magnetic spin Hall effect2,3 was observed in non-collinear antiferromagnets, where the spin conservation is broken due to the non-collinear spin configuration. This provides a unique opportunity to control the spin current and relevant device performance with controllable magnetization. Here, we report a magnetic spin Hall effect in a collinear antiferromagnet, Mn2Au. The spin currents are generated at two spin sublattices with broken spatial symmetry, and the antiparallel antiferromagnetic moments play an important role. Therefore, we term this effect the ‘antiferromagnetic spin Hall effect’. The out-of-plane spins from the antiferromagnetic spin Hall effect are favourable for the efficient switching of perpendicular magnetized devices, which is required for high-density applications. The antiferromagnetic spin Hall effect adds another twist to the atomic-level control of spin currents via the antiferromagnetic spin structure. A magnetic spin Hall effect is reported in the collinear antiferromagnet Mn2Au.

Spin-orbit coupling in graphene can be enhanced by chemical functionalization, adatom decoration or proximity with a van der Waals material. As it is expected that such enhancement gives rise to a sizeable spin Hall effect, a spin-to-charge current conversion phenomenon of technological relevance, it has sparked wide research interest. However, it has only been measured in graphene/transition metal dichalcogenide van der Waals heterostructures with limited scalability. Here, we experimentally demonstrate spin Hall effect up to room temperature in bilayer graphene combined with a nonmagnetic insulator, an evaporated bismuth oxide layer. The measured spin Hall effect raises most likely from an extrinsic mechanism. With a large spin-to-charge conversion efficiency, scalability, and ease of integration to electronic devices, we show a promising material heterostructure suitable for spin-based device applications., Comment: 12 pages, 4 figures, supporting information

The quantum spin Hall effect lays the foundation for the topologically protected manipulation of waves, but is restricted to one-dimensional-lower boundaries of systems and hence limits the diversity and integration of topological photonic devices. Recently, the conventional bulk-boundary correspondence of band topology has been extended to higher-order cases that enable explorations of topological states with codimensions larger than one such as hinge and corner states. Here, we demonstrate a higher-order quantum spin Hall effect in a two-dimensional photonic crystal. Owing to the non-trivial higher-order topology and the pseudospin-pseudospin coupling, we observe a directional localization of photons at corners with opposite pseudospin polarizations through pseudospin-momentum-locked edge waves, resembling the quantum spin Hall effect in a higher-order manner. Our work inspires an unprecedented route to transport and trap spinful waves, supporting potential applications in topological photonic devices such as spinful topological lasers and chiral quantum emitters., The quantum spin Hall effect is limited to one-dimensional lower boundary states which limits the possibilities for its exploitation in photonic devices. Here, the authors demonstrate a higher-order quantum spin Hall effect in a photonic crystal and observe opposite pseudospin corner states.

The photo-excited electrons and holes move in the same direction in the diffusion and in the opposite direction in the drift under an electric field. Therefore, the contribution to the inverse spin Hall current of photo-excited electrons and holes in the diffusion regime is different to that in the drift regime under electric field. By comparing the classical Hall effect with the inverse spin Hall effect in both diffusion and drift regime, we develop an optical method to distinguish the contributions of electrons and holes in the inverse spin Hall effect. It is found that the contribution of the inverse spin Hall effect of electrons and holes in an InGaAs/AlGaAs un-doped multiple quantum well is approximately equal at room temperature.

Silicon's weak intrinsic spin-orbit coupling and centrosymmetric crystal structure are a critical bottleneck to the development of Si spintronics, because they lead to an insignificant spin Hall effect (spin current generation) and inverse spin Hall effect (spin current detection). Here, we undertake current, magnetic field, crystallography dependent magnetoresistance, and magnetothermal transport measurements to study the spin transport behavior in freestanding Si thin films. We observe a large spin Hall magnetoresistance in both $p\text{\ensuremath{-}}\mathrm{Si}$ and $n\text{\ensuremath{-}}\mathrm{Si}$ at room temperature and it is an order of magnitude larger than that of Pt. One explanation of the unexpectedly large and efficient spin Hall effect is spin-phonon coupling instead of spin-orbit coupling. The macroscopic origin of the spin-phonon coupling can be large strain gradients that can exist in the freestanding Si films. This discovery in a light, earth abundant and centrosymmetric material opens a new path of strain engineering to achieve spin dependent properties in technologically highly developed materials.

The authors provide experimental results that show the onset of the Nernst effect, thermovoltages and an inverse spin-Hall effect in the polymer PEDOT:PSS. Specifically, the observed inverse spin-Hall effect appears to be smaller than other measurements, but in better agreement with theoretical calculations.

We theoretically investigate the vortex spin Hall effect, i.e., a novel spin Hall effect driven by the motion of superconducting vortices, by focusing on the role of superconducting fluctuations. Within the BCS-Gor'kov microscopic approach combined with the Kubo formula, we find a strong similarity between the vortex spin Hall effect and the vortex Nernst/Ettingshausen effect. Calculated temperature dependence of the voltage signal due to the inverse vortex spin Hall effect exhibits a strong enhancement by vortex fluctuations. This result not only provides a possible explanation for a prominent peak found in the spin Seebeck effect in a NbN/Y$_3$Fe$_5$O$_{12}$ system, but also leads to a proposal of new experiments using other superconductors with strong fluctuations, such as cuprate or iron-based superconductors., Comment: 13 pages, 8 figures

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 inverse spin Hall effect of Ni60Cu40 and Ni50Cu50 across their Curie temperature using spin pumping experiments. We evidence 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 points towards 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., 3 figures

In bilayers of ferromagnets and heavy metals, which form the so-called spintronic emitters, the phenomena of ultrafast demagnetization and the inverse spin Hall effect (ISHE) conspire to yield remarkably efficient emission of electric pulses in the THz band. Light-induced demagnetization of the ferromagnet launches a pulse of spin current into the heavy metal, wherein it bifurcates into a radiative charge transient due to the ISHE. The influence of temperature on this combined effect should depend on both the magnetic phase diagram and the microscopic origin of spin Hall conductivity, but its exact dependence remains to be clarified. Here, we experimentally study the temperature dependence of an archetypal spintronic emitter, the Co/Pt bilayer, using electro-optic sampling of the emitted THz pulses in the time domain. The emission amplitude is attenuated with decreasing temperature, consistent with an inverse spin Hall effect in platinum of predominantly intrinsic origin.

We propose and analyze a mechanism for inducing spin Hall currents in ordinary (1H phase) monolayer transition metal dichalcogenides (TMDs) due to the nonlinear process of optical rectification. The photo-induced spin current is proportional to the light intensity, and originates from the intrinsic spin-orbit coupling in TMDs. The spin current spectrum is strongly influenced by electron-hole interactions, i.e. excitonic effects, analogous to the optical absorption. Remarkably, excitons change the temperature dependence of the induced spin current, to the point that the current direction can even be reversed by varying the temperature. This peculiar excitonic behavior is shown to emerge from the relative strength of two distinct mechanisms contributing to the optical response, i.e. a purely interband part and a mixed inter/intraband contribution. Furthermore, we investigate the valley dichrosim of second-harmonic charge and spin currents, and demonstrate different valley polarization of $s$ and $p$ excitons that stem from their distinct angular momenta. Our findings pave the path to the generation of dc spin currents in ordinary TMDs without external static electric or magnetic fields.

Recent experiments demonstrate that antiferromagnets exhibit the spin Hall effect. We study a tight-binding model of an antiferromagnet on a square lattice with Rashba spin-orbit coupling and disorder. By exact diagonalization of a finite system connected to reservoirs within the Landauer-B$\ddot{\text{u}}$ttiker formalism, we compute the transverse spin Hall current in response to a longitudinal voltage difference. Surprisingly, the spin Hall conductance can be considerably larger in antiferromagnets than in normal metals. We compare our results to the Berry-phase-induced spin Hall effect governed by the intrinsic contribution in the Kubo formula. The Berry-phase-induced intrinsic spin Hall conductivity in bulk systems shows the opposite behavior: large exchange couplings in AFs drastically reduce the spin Hall current., 12 Figures

The spin Hall effect, a key enabler in the field of spintronics, underlies the capability to control spin currents over macroscopic distances. The effect was initially predicted by D'Yakonov and Perel1 and has been recently brought to the foreground by its realization in paramagnetic metals by Hirsch2 and in semiconductors3 by Sih et al. Whereas the rapid dephasing of electrons poses severe limitations to the manipulation of macroscopic spin currents, the concept of replacing fermionic charges with neutral bosons such as photons in stratified media has brought some tangible advances in terms of comparatively lossless propagation and ease of detection4–7. These advances have led to several manifestations of the spin Hall effect with light, ranging from semiconductor microcavities8,9 to metasurfaces10. To date the observations have been limited to built-in effective magnetic fields that underpin the formation of spatial spin currents. Here we demonstrate external control of spin currents by modulating the splitting between transverse electric and magnetic fields in liquid crystals integrated in microcavities.

The results of a nanoscale experimental study of the spin Hall effect in platinum and highly resistive tungsten films are reported. These results are obtained by using scanning tunneling microscopy based measurements with tungsten and iron-coated tungsten tips. These measurements reveal an appreciable asymmetry of tunneling currents observed by changing the polarity of tunneling voltages or the direction of electric currents through the films. This asymmetry is a manifestation of accumulations of spin-polarized electrons on conducting film boundaries occurring as a result of the spin Hall effect.

We show that the quantum geometry of the Fermi surface can be numerically described by a three-dimensional discrete quantum manifold. This approach not only avoids singularities in the Fermi sea, but it also enables the precise computation of the intrinsic Hall conductivity resolved in spin, as well as any other local properties of the Fermi surface. The method assures numerical accuracy when the Fermi level is arbitrarily close to singularities, and it remains robust when Kramers degeneracy is protected by symmetry. The approach is demonstrated by calculating the anomalous Hall and spin Hall conductivities of a two-band lattice model of a Weyl semimetal and a full-band ab initio model of zinc-blende GaAs.

An inverse spin Hall effect (ISHE) in $n$-type silicon was observed experimentally when conduction electrons were scattered on the spin-orbit potential of bismuth. The spin current in the silicon layer was generated by excitation of the magnetization precession during ferromagnetic resonance in a thin Permalloy (Py) layer deposited on a Si layer doped by phosphor and bismuth. From the angular dependences of the dc voltage for different $\mathrm{Py}/n$-Si:Bi structures aligned along the [011] or [100] crystal axes, we were able to distinguish the planar Hall effect (PHE) and ISHE contributions. The ISHE dc voltage signal was proportional to the $sin\ensuremath{\theta}sin2\ensuremath{\theta}$ product for the structure aligned to the [011] crystal axis and to $sin\ensuremath{\theta}cos2\ensuremath{\theta}$ for the [100] direction. In addition, the PHE dc voltage was observed for the angles corresponding to the $sin\phantom{\rule{0.16em}{0ex}}2\ensuremath{\theta}$ dependence. This means that for silicon as a many-valley semiconductor, the scattering of spins due to the spin-orbit potential induced by shallow donor in $n$-type material is dependent on the orientation of the valley axes relative to the direction of the magnetic field.

The spintronic properties of a palladium thin film have been investigated in the presence of hydrogen gas in cobalt/palladium bilayers. Measurements of the inverse spin Hall Effect (ISHE) using cavity ferromagnetic resonance allow estimations of the spin Hall conductivity and spin diffusion length in both nitrogen and hydrogen gas atmospheres. Unwanted spin rectification effects are removed using a simple method of inverting the spin current direction with respect to the measurement setup. Absorption of hydrogen gas in the Pd layer at just 3% concentration results in a reduced ISHE voltage amplitude and bilayer resistance. Fitting the ISHE voltage against the Pd layer thickness demonstrates that the spin diffusion length decreases by 23% in the presence of a hydrogen gas. On the other hand, the results indicate that there is no significant change in the spin Hall conductivity of Pd due to hydrogen absorption., Comment: 6 pages, 3 figures

We measure magnetic field dependence of the Hall angle in a metallic ferromagnetic nanomagnet with stable local magnetic moments where the adopted mechanisms of Hall effect predict linear plus a constant dependence on the external field originating from the ordinary and anomalous Hall effects, respectively. We suggest that the experimentally observed deviations from this dependence is caused by the inverse spin Hall effect (ISHE) and develop a phenomenological theory, which predicts a unique nonlinear dependence of the ISHE contribution on the external magnetic field. Perfect agreement between theory and experiment supports the considerable role of the ISHE in the Hall transport in ferromagnetic metals., Comment: 5 pages, 5 figures

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., M. V. acknowledges support from “La Caixa” Foundation and the Centre for Advanced 2D Materials at the National University of Singapore for its hospitality. X. W. acknowledges the ANR Flagera GRANSPORT funding. ICN2 authors were supported by the European Union Horizon 2020 research and innovation programme under Grant Agreement No. 881603 (Graphene Flagship) and No. 824140 (TOCHA, H2020-FETPROACT-01-2018). ICN2 is funded by the CERCA Programme/Generalitat de Catalunya, and is supported by the Severo Ochoa program from Spanish MINECO (Grant No. SEV2017-0706). V. M. P. acknowledges the support of the National Research Foundation (Singapore) under its Medium-Sized Centre Programme (R-723-000-001-281).

The influence of hydrogen gas absorption on the inverse spin Hall effect (iSHE) is measured in palladium/cobalt bilayer films. The iSHE is driven by ferromagnetic resonance in the Co layer and manifests as a dc voltage across the Pd layer. In the presence of hydrogen gas, the iSHE peak shifts downward in applied field together with the ferromagnetic resonance absorption peak for the material. In parallel, an increase in the iSHE peak height and width is measured.

We have studied the intrinsic spin Hall conductivity of 3d transition metal ferromagnets using first-principles calculations. We find the spin Hall conductivity of bcc Fe and fcc Ni, prototypes of ferromagnetic systems, depends on the direction of magnetization. The spin Hall conductivity of electrons with their spin orientation orthogonal to the magnetization are found to be larger than that when the two are parallel. For example, the former can be more than four times larger than the latter in bcc Fe. Such a difference arises due to the anisotropy of the spin current operator in the spinor space: Its expectation value with the Bloch states depends on the relative angle between the conduction electron spin and the magnetization. A simple analytical form is developed to describe the relation between the spinor states, with respect to the magnetization direction, and the Berry and spin Berry curvatures. The model can account for the characteristics found in the calculations. These results show that ferromagnets can be used to generate spin current and its magnitude can be controlled by the magnetization direction., Comment: 5 pages, 3 figures

Controllable antiferromagnetic alignment of magnetizations is vital for the systematic study of antiferromagnetic spintronics. Along this path, antiferromagnetically coupled metallic superlattices are promising systems, exploiting the interlayer exchange coupling. Here, the authors report that, as a spacer-layer material sandwiched between ferromagnetic cobalt layers, nonmagnetic Ir-doped Cu exhibits simultaneously a definite interlayer exchange coupling and an appreciable spin-orbit torque. This experimental demonstration and findings offer an avenue to antiferromagnetic spintronics, based on antiferromagnetically coupled metallic superlattices.

Magnetic tunnel junctions (MTJs) switched by spin-orbit torque (SOT) have attracted substantial interest owing to their advantages of ultrahigh speed and prolonged endurance.Both field-free magnetization switching and high tunneling magnetoresistance (TMR) are critical for the practical application of SOT magnetic random access memory (MRAM).In this work, we propose an MTJ structure based on an iridium (Ir) bottom layer. Ir metal is a desirable candidate for field-free SOT switching owing to its strong intrinsic spin Hall conductivity (SHC), which can be enhanced via doping. Herein, we study TMR in Ir-based MTJs with symmetric and asymmetric structures.Ir-based MTJs exhibit large TMR, which can be further enhanced by heavy metal symmetry owing to the resonant tunneling effect. Our comprehensive investigations illustrate that Ir-based MTJs are promising candidates for realizing SOT switching and high TMR.

We study spin-dependent direct and Hall conductivities in the threshold region of Fermi energy, ɛ F = 2 J , where J is the exchange integral between the conduction electron spins and the skyrmion spin texture. For ɛ F at the threshold value and above the spin-down electrons are allowed to exist. We find the two in the direct and four narrow peaks in the Hall conductivities for Fermi energies slightly below the threshold value. The found effects are dramatic because the electric current changes by approximately eight times in the narrow range of gate voltages ( ∼ 4 meV). The values of the peaks strongly depend on skyrmion size. For small and very large skyrmion sizes the peak amplitudes are small compared to the conductivity absolute values. At the skyrmion radius a = 6 nm and very light conduction electrons, m ∗ ∼ 1 0 − 2 m e , the extrema are the most pronounced. The temperature evolution reveals the strong smearing effect where the peak-wise behavior completely disappears at room temperatures. Spin transistor could be considered for possible applications where in the narrow region of gate voltage the sharp conductivity change occurs.

The spin Hall effect of light originates from spin-orbit interaction of light, which manifests two types of geometric phases. In this paper, we report the observation of a geometric spin Hall effect by generating a light beam with inhomogeneous polarization distribution. Unlike the previously reported geometric spin Hall effect observed in a tilted beam-detector system, which is believed to result from an effective spin-redirection Berry geometric phase, the geometric spin Hall effect demonstrated here is attributed to an effective, spatially varying Pancharatnam-Berry geometric phase generated by the inhomogeneous polarization geometry. Our further experiments show that the geometric spin Hall effect can be tuned by tailoring the polarization geometry of light, demonstrating the spin states of photons can be steered with a great flexibility.

Non-equilibrium Cu–Ir binary alloys are interesting materials because these alloys show a large spin Hall effect (SHE) despite the non-remarkable spin Hall angles of pure Cu and pure Ir. In this study, the temperature dependence of the SHE on a non-equilibrium Cu–Ir binary alloy was investigated in order to understand the mechanism of its large SHE. We measured the spin Hall magnetoresistance for the Cu76Ir24/CoFeB bilayer at various measurement temperatures. The spin Hall conductivity remains practically constant against temperature and electrical conductivity, indicating that the side jump or the intrinsic process based on the band structure is dominant for the SHE in the present Cu76Ir24.

Here, we investigate the photonic spin Hall effect in twisted bilayer graphene. The optical conductivities for several rotation angles of twisted bilayer graphene are calculated by first principles, based on which a theoretical framework is established to describe the light–matter interaction. To enhance the photonic spin Hall effect, twisted bilayer graphene is placed on a BK7 glass substrate and a Gaussian beam is launched near the Brewster angle. The spin splitting as well as Goos–Hänchen shifts are investigated, which are associated, respectively, with the imaginary and real parts of the surface conductivities of the twisted bilayer graphene. These findings provide a deeper understanding of the photonic spin Hall effect in two-dimensional materials and have potential application in characterizing bilayer graphene.

Due to the weak spin-orbit interaction, the photonic spin Hall effect (SHE) is generally very weak, which is disadvantageous for potential applications of nanophotonic devices. Surface plasmon resonance (SPR) has been proposed to enhance the photonic SHE. In this paper, by covering the heterostructure material composed of graphene and molybdenum sulfide (MoS2) on the SPR structure, it is demonstrated that the two-dimensional (2-D) material heterostructure can effectively enhance the photonic SHE. The transverse shift of light beam in the heterostructure is larger than those in SPR structure due to the larger refractive index gradient in the heterostructure. The maximum transverse shift can be up to 27.5 μm under the optimized parameters, which is much larger than the previously reported values. This interesting phenomenon is attributed to the larger light absorption and hence the refractive index variation gradient of graphene/MoS2 heterostructure. These findings provide us with a new way to modulate the photonic SHE, and also establish foundation for developing nanophotonic devices based on 2-D nanomaterials heterostructure.