Strong electron spin-Hall effect by a coherent optical potential

Spin-orbit coupling plays an important role in the spin Hall effect and topological insulators. Bose-Einstein condensates with spin-orbit coupling show remarkable quantum phase transition. In this work we control an exciton polariton condensate – a macroscopically coherent state of hybrid light and matter excitations – by virtue of the Rashba-Dresselhaus (RD) spin-orbit coupling. This is achieved in a liquid-crystal filled microcavity where CsPbBr3 perovskite microplates act as the gain material at room temperature. Specifically, we realize an artificial gauge field acting on the CsPbBr3 exciton polariton condensate, splitting the condensate fractions with opposite spins in both momentum and real space. Besides the ground states, higher-order discrete polariton modes can also be split by the RD effect. Our work paves the way to manipulate exciton polariton condensates with a synthetic gauge field based on the RD spin-orbit coupling at room temperature.

A normal metallic film sandwiched between two insulators may have strong spin-orbit coupling near the metal-insulator interfaces, even if spin-orbit coupling is negligible in the bulk of the film. In this paper, we study two technologically important and deeply interconnected effects that arise from interfacial spin-orbit coupling in metallic films. The first is the spin Hall effect, whereby a charge current in the plane of the film is partially converted into an orthogonal spin current in the same plane. The second is the Edelstein effect, in which a charge current produces an in-plane, transverse spin polarization. At variance with strictly two-dimensional Rashba systems, we find that the spin Hall conductivity has a finite value even if spin-orbit interaction with impurities is neglected and ``vertex corrections'' are properly taken into account. Even more remarkably, such a finite value becomes ``universal'' in a certain configuration. This is a direct consequence of the spatial dependence of spin-orbit coupling on the third dimension, perpendicular to the plane of the film. The nonvanishing spin Hall conductivity has a profound influence on the Edelstein effect, which we show to consist of two terms, the first with the standard form valid in a strictly two-dimensional Rashba system, and a second arising from the presence of the third dimension. Whereas the standard term is proportional to the momentum relaxation time, the new one scales with the spin relaxation time. Our results, although derived in a specific model, should be valid rather generally, whenever a spatially dependent Rashba spin-orbit coupling is present and the electron motion is not strictly two dimensional.

Spin-orbit interactions in two-dimensional electron liquids are responsible for many interesting transport phenomena in which particle currents are converted to spin polarizations and spin currents and vice versa. Prime examples are the spin Hall effect, the Edelstein effect, and their inverses. By similar mechanisms, it is also possible to partially convert an optically induced electron-hole density wave to a spin density wave and vice versa. In this paper, we present a unified theoretical treatment of these effects based on quantum kinetic equations that include not only the intrinsic spin-orbit coupling from the band structure of the host material, but also the spin-orbit coupling due to an external electric field and a random impurity potential. The drift-diffusion equations we derive in the diffusive regime are applicable to a broad variety of experimental situations, both homogeneous and nonhomogeneous, and include on equal footing ``skew scattering'' and ``side jump'' from electron-impurity collisions. As a demonstration of the strength and usefulness of the theory we apply it to the study of several effects of current experimental interest: the inverse Edelstein effect, the spin-current swapping effect, and the partial conversion of an electron-hole density wave to a spin density wave in a two-dimensional electron gas with Rashba and Dresselhaus spin-orbit couplings, subject to an electric field.

The generation, manipulation and detection of spin-polarized electrons in nanostructures define the main challenges of spin-based electronics. Among the different approaches for spin generation and manipulation, spin-orbit coupling--which couples the spin of an electron to its momentum--is attracting considerable interest. In a spin-orbit-coupled system, a non-zero spin current is predicted in a direction perpendicular to the applied electric field, giving rise to a spin Hall effect. Consistent with this effect, electrically induced spin polarization was recently detected by optical techniques at the edges of a semiconductor channel and in two-dimensional electron gases in semiconductor heterostructures. Here we report electrical measurements of the spin Hall effect in a diffusive metallic conductor, using a ferromagnetic electrode in combination with a tunnel barrier to inject a spin-polarized current. In our devices, we observe an induced voltage that results exclusively from the conversion of the injected spin current into charge imbalance through the spin Hall effect. Such a voltage is proportional to the component of the injected spins that is perpendicular to the plane defined by the spin current direction and the voltage probes. These experiments reveal opportunities for efficient spin detection without the need for magnetic materials, which could lead to useful spintronics devices that integrate information processing and data storage.

The spin Hall effect (SHE) is closely related to the spin-orbit coupling. Therefore, heavy metals are usually considered as materials of choice to obtain large spin Hall angles. Among these materials, some 5d transition metals such as Pt, Ta or W offer the largest spin-charge interconversion efficiency for spin current detections through the inverse spin Hall effect or to obtain efficient current induced magnetization switching in SOT-MRAM devices [1].Despite a weaker spin orbit coupling, spin Hall angles comparable to that of the best 5d materials has also been obtained in 3d ferromagnetic metals such as Co [2] or Ni [3]. More recently nonmagnetic alloys containing Nickel atoms such as NiCu [4] and CoNiB [5] attracted great interest for their large spin Hall angles and their potential for spintronic applications. Using the spin pumping by ferromagnetic resonance technique we could compare the spin to charge current conversion in Ni60Cu40 to the one of Pt. As can be seen in figure 1 a) the normalized spin pumping signal obtained in CFB/NiCu is comparable to that of CFB/Pt. We performed a thickness dependence shown in figure 1 b) to extract the spin Hall angle (θSHE) and spin diffusion length (λs) and obtained results comparable to the one of 5d metals using similar method with λs = 2.4 ± 0.3 nm and θSHE = 4.1 ± 0.5 % [6].Keller and coworkers [4] noticed similarities in the bandstructure of paramagnetic Nickel and Platinum possibly explaining the origin of the effect. The calculated band structure of ferromagnetic Nickel does not resemble that of Platinum and the origin of the large spin Hall effect observed in ferromagnetic Ni [3] could thus be different. The interplay between the spin-orbit coupling and magnetism is known to be at the origin of specific transport properties such as the anomalous magnetoresistance and the anomalous Hall effect. However, the link between the SHE and the magnetic order is complex and still unexplored [7].In order to study the effect of the phase transition we performed spin pumping as a function of temperature in Ni60Cu40 and Ni50Cu50 alloys above and below the Curie temperature. To avoid direct contact between the ferromagnetic spin injector CFB and the magnetic NiCu alloy that would modify CFB resonance properties due to the direct coupling [8] we used a 5 nm thick Cu interlayer. The spin pumping measurements performed in CFB\Cu\ Ni60Cu40 and CFB\Cu\ Ni50Cu50 shown in figure 2 indicate that in NiCu the SHE is insensitive to the magnetic order [6].A large variety of alloys composed of Ni, Co or Fe in the ferromagnetic or paramagnetic phase could be explored as spin current generators and detectors, extending the number of possible light metal systems with a large SHE. In particular, the large spin Hall effect in NiCu shows that it is a promising alternative to obtain large spin orbit torque without heavy metals. **

Photonic spin Hall effect (SHE) refers to the transverse separation of spin photons in refraction and reflection phenomena. The photonic SHE has been investigated in various optical systems including air–glass interfaces, interfaces containing 2D materials, random media, etc. Here, the spin–orbit coupling (SOC) in nonlinear uniaxial crystals is investigated, and the SHE of second‐harmonic photons is demonstrated theoretically and experimentally. The generation and evolution processes of nonlinear spin photons within the crystal are visualized by the derived four wave coupling equations and wavevector‐varying Berry phases. For a focused fundamental beam, two cascaded SOCs occurring in the fundamental and second‐harmonic fields are connected by the nonlinear wave mixing near the focal position. Thus the SHE of nonlinear photons depends on the focal position, different strongly from linear photons whose SHE is independent of the focal position. Similar to the focal‐position‐dependent SHE, the focal‐position‐dependent optical vortex generations are also demonstrated for the nonlinear fields. Finally, a high‐speed modulation scheme for the SHE is proposed based on an electro‐optical polarization controller, which routes nonlinear spin photons into different destinations. These findings deepen the understanding of spin–orbit coupling in nonlinear systems and facilitate the development of spin multiplexed electrooptic devices.

The spin Hall effect and its inverse effect, caused by the spin orbit interaction, provide the interconversion between spin current and charge current. Since the effects make it possible to generate and manipulate spin current electrically, how to realize the large effects is an important issue in both physics and applications. To do so, materials with heavy elements, which have strong spin orbit interaction, have been examined so far. Here, we propose a new mechanism to enhance the spin Hall effect without heavy elements, \ie surface roughness in metallic thin films. We examine Cu and Al thin films with surface roughness and find that they give the spin Hall effect comparable to that in bulk Au. We demonstrate that the spin Hall effect induced by surface roughness has the side jump contribution but not skew scattering.

In contrast to the ordinary spin Hall effect (SHE), which is a single-body phenomenon caused by the spin-orbit interaction (SOI), we propose amany-body SHE induced by the dipole-dipole interaction (DDI) between particles and demonstrate it in a system of ultracold magnetic atoms. While the SOI usually requires the breaking of space-inversion symmetry, the DDI preserves it. The many-body SHE can, in principle, be observed in a wide range of systems with large dipole moments and offers a powerful tool to generate spin currents, an essential ingredient in spintronics and atomtronics.

We point out the existence of finite charge and spin Hall conductivities of graphene in the presence of a spin orbit interaction (SOI) and localized magnetic impurities. The SOI in graphene results in different transverse forces on the two spin channels yielding the spin Hall current. The magnetic scatterers act as spin-dependent barriers, and in combination with the SOI effect lead to a charge imbalance at the boundaries. As indicated here, the charge and spin Hall effects should be observable in graphene by changing the chemical potential close to the gap.

The absorption of linearly polarized light in low-dimensional semiconductor structures is investigated. It is shown that the absorption under consideration can give rise to spin orientation of free carriers. A theory of this optical orientation by linearly polarized light is developed for resonant intersubband optical transitions in n-type quantum wells. It is demonstrated that, in the vicinity of the resonance, the optical orientation undergoes spectral inversion, namely, the electron spin orientation reverses sign with increasing frequency. This behavior can be accounted for by the spin-orbit subband splitting, which is linear in the wave vector, and by the energy and quasi-momentum conservation laws.

The spin Hall effect on the Josephson tunneling through a two-dimensional normal contact with a spin-orbit split conduction band has been studied in the diffusive regime and at the zero electric bias. Linearized Usadel equations for triplet components of the pairing function in the presence of intrinsic spin-orbit interaction have been derived. These equations have been employed for analysis of the spin Hall effect induced by the supercurrent. We predict that a nondissipative out-of-plane spin Hall polarization accumulates at lateral edges and an in-plane polarization is induced throughout the entire normal region. At the same time, in contrast to the spin Hall effect in normal systems, the spin current is absent in the considered case of the stationary Josephson effect.

The spin Hall effect (SHE) of light originates from the spin-orbit interaction, which can be explained in terms of two geometric phases: the Rytov-Vladimirskii-Berry phase and the Pancharatnam-Berry phase. Here we present a unified theoretical description of the SHE based on the two types of geometric phase gradients, and observe experimentally the SHE in structured dielectric metasurfaces induced by the PB phase. Unlike the weak real-space spin-Hall shift induced by the SRB phase occurring at interfacial reflection/refraction, the observed SHE occurs in momentum space is large enough to be measured directly.

A microscopic theory of the spin Hall effect in a diffusive two-dimensional electron gas in the presence of both extrinsic spin-orbit coupling (due to spin-orbit dependent impurity scatterings) and $k$-linear intrinsic spin-orbit coupling (due to spin-orbit splitting of the conduction band) is developed. We show that the spin Hall effect in the presence of both extrinsic and $k$-linear intrinsic spin-orbit coupling has basically an extrinsic origin from the theoretical points of view, but due to the interplay of extrinsic and intrinsic spin-orbit coupling, it may exhibit some interesting new features that were not found in the usual extrinsic or the usual intrinsic spin Hall effect.

The spin of a single electron in an electrically defined quantum dot in a two-dimensional electron gas can be manipulated by moving the quantum dot adiabatically in a closed loop in the two-dimensional plane under the influence of applied gate potentials. In this paper we present analytical expressions and numerical simulations for the spin-flip probabilities during the adiabatic evolution in the presence of the Rashba and Dresselhaus linear spin-orbit interactions. We use the Feynman disentanglement technique to determine the non-Abelian Berry phase and we find exact analytical expressions for three special cases: (i) the pure Rashba spin-orbit coupling, (ii) the pure Dresselhause linear spin-orbit coupling, and (iii) the mixture of the Rashba and Dresselhaus spin-orbit couplings with equal strength. For a mixture of the Rashba and Dresselhaus spin-orbit couplings with unequal strengths, we obtain simulation results by solving numerically the Riccati equation originating from the disentangling procedure. We find that the spin-flip probability in the presence of the mixed spin-orbit couplings is generally larger than those for the pure Rashba case and for the pure Dresselhaus case, and that the complete spin-flip takes place only when the Rashba and Dresselhaus spin-orbit couplings are mixed symmetrically.

As one type of important topological quantum states, the quantum spin Hall (QSH) effect realized in two-dimensional (2D) materials still maintains sufficient attractiveness due to its promising spintronic applications. By using the first-principles calculations, we theoretically investigate the structural, electronic and topological properties of a newly 2D honeycomb-Kagome WI3 monolayer (ML). The WI3 ML possesses the excellent dynamical, thermal and mechanical stabilities, as has been confirmed by phonon spectra, molecular dynamics simulations and elastic constants calculations, respectively. It is found that the WI3 ML behaves a type-II quadratic non-Dirac band dispersion around the Fermi level in the absence of spin–orbit coupling (SOC), while that may be adjusted to the type-I and/or type-III case based on the half-unilateral hydrogenation method. In the presence of SOC, the system may transform from the quadratic non-Dirac semimetal state into an intrinsic QSH state with nonzero topological invariant and Dirac-like edge states. The nontrivial topology of the system should originate from the strong SOC interaction of the degenerate W dx 2–y2/dxy states at Γ point, and a nearly 0.10 eV nontrivial global band gap has been obtained under the 4% compressive strain. The half/fully-substitutional Mo doping, hydrogenation modulation as well as substrate effect on the electronic structures and topological states of the WI3 ML have been explored. Intriguingly, the unilateral hydrogenated WI3 ML present a topological semimetal phase with robust nontrivial edge stets against SOC and in-plane biaxial strain, while the fully hydrogenated one exhibits a Dirac-type QSH state around the high-symmetry K/K′ points. Therefore, the honeycomb-Kagome WI3 ML should be the potential candidate platform for future low-power nanoelectronic and spintronic applications.